Haldane's "The Cost of Natural Selection"
Robert Williams
In his 1957 paper "The Cost of Natural Selection" (Journal of Genetics
55:511-524), J.B.S. Haldane makes the claim that natural selection is
limited to something like one gene substitution per 300 generations.
This claim is based upon a scenario in which a change in an organism's
environment leads to a common allele becoming disfavorable. Haldane
calculated the "cost" of natural selection as the summation of
individual deaths over many generations leading to the fixation of a
rare, formerly disfavorable allele over the common, formerly favored
allele. He determined that natural selection under these conditions (a
deterioration in the environment leading to the replacement of a common
allele by a rare allele) would require the deaths of about 30 times the
population of a single generation for relatively small selection
coefficients.
My question to anyone who is familiar with this topic is why did Haldane
only consider the case where a deteriorating environment causes a common
allele to become disadvantageous? Why didn't he consider the case of a
new allele arising that is favored over the common allele? In this case,
natural selection could proceed without the huge cost in substitution
deaths that Haldane envisioned. (I will be happy to provide the
mathematics if anyone is interested - unless I am mistaken, the pattern
of deaths is completely different in these two cases.) Haldane makes no
mention of the possibility of a favorable allele arising in this paper,
so I have to assume that either the thought didn't occur to him, or he
knew that his audience would be well aware that this issue did not need
to be considered. If this was once the case (all selection was thought
to be due to deteriorating environments), it is certainly no longer
accepted as I have seen many discussions in population genetics texts of
rare favorable alleles.
Robert Williams
Hamish G. Spencer
>In his 1957 paper "The Cost of Natural Selection" (Journal of Genetics
>55:511-524), J.B.S. Haldane makes the claim that natural selection is
>limited to something like one gene substitution per 300 generations.
The issue of substitutional load generated an exchange of papers among Ewens,
Kimura and Nei in the early 1970s. My memory of these papers is a little
vague, but I seem to recall that Ewens (for one) argued that Haldane's
calculations hid an assumption that he (Ewens) believed was not easily
supported. Anyway, the references are:
Kimura, M., and T. Maruyama. 1969. The substitutional load in a finite
population. Heredity 24: 101-114.
Ewens, W.J. 1970. Remarks on the substitutional load. TPB 1: 129-139.
Ewens, W.J. 1972. The substitutional load in a finite population. Am. Nat.
106: 273-282.
Ewens, W.J. 1972. Concepts of substitutional load in finite populations.
TPB 3: 153-161.
Nei, M. 1973. Ewens on the substitutional load. Am. Nat. 107: 459-462.
Ewens, W.J. 1973. Comments on Nei's letter on substitutional loads. Am.
Nat. 107: 462-463.
Ewens, W.J. 1973. Comments on Dr. Kimura's paper. Genetics 73 (Suppl.):
36-38.
See also Ewens's (1979) book, Mathemetical Population Genetics
(Springer-Verlag, Berlin), pages 66-69 and 252-255.
Hamish G. Spencer
Joe Felsenstein
In article <64smg7$feu$1...@nntp6.u.washington.edu>,
Hamish G. Spencer <h.sp...@otago.ac.nz> wrote:
[in response to a posting by Robert Williams]
>The issue of substitutional load generated an exchange of papers among Ewens,
>Kimura and Nei in the early 1970s.
Let's add two more papers:
Felsenstein, J. 1971. On the biological significance of the cost of gene
substitution. American Naturalist 105: 1-11.
and
Felsenstein, J. 1972. The substitutional load in a finite population.
Heredity 28: 57-69.
The latter is basically a redo of Kimura and Maruyama's results, and may be
relevant to the dispute between Ewens and Kimura. But the former makes the
Cost of Natural Selection very interpretable, and I recommend it to anyone
trying to understand that concept. It points out that the cost is imposed
by the change of environment, not by the selection that responds to it.
In the case where there is no deterioration of the environment, but rather a
favorable mutation arising, there is no cost, and indeed there is an increase
in the population's ability to bear such costs.
--
Joe Felsenstein j...@genetics.washington.edu
Dept. of Genetics, Univ. of Washington, Box 357360, Seattle, WA 98195-7360 USA
Guy A. Hoelzer
> Felsenstein, J. 1971. On the biological significance of the cost of gene
> substitution. American Naturalist 105: 1-11.
> [This paper] makes the
> Cost of Natural Selection very interpretable, and I recommend it to anyone
> trying to understand that concept. It points out that the cost is imposed
> by the change of environment, not by the selection that responds to it.
> In the case where there is no deterioration of the environment, but rather a
> favorable mutation arising, there is no cost, and indeed there is an increase
> in the population's ability to bear such costs.
Thanks to Joe for emphasizing the distinction between the "loads" produced
by favorable vs. unfavorable mutations. IMHO, this is the most generally
underappreciated aspect of the theory of genetic loads.
--
Guy Hoelzer e-mail: hoe...@med.unr.edu
Department of Biology phone: 702-784-4860
University of Nevada Reno fax: 702-784-1302
Reno, NV 89557
Robert Williams
Donal Hickey wrote:
>
> Robert Williams wrote:
> >
> >
> > My question to anyone who is familiar with this topic is why did Haldane
> > only consider the case where a deteriorating environment causes a common
> > allele to become disadvantageous? Why didn't he consider the case of a
> > new allele arising that is favored over the common allele? In this case,
> > natural selection could proceed without the huge cost in substitution
> > deaths that Haldane envisioned. (I will be happy to provide the
> > mathematics if anyone is interested - unless I am mistaken, the pattern
> > of deaths is completely different in these two cases.)
>
>
> I believe the result is not affected by the question of whether the
> environment deteriorates (thus lowering the fitness of the existing
> allele) or whether a new, "better" allele arises. For the new allele to
> replace the old one, all individuals bearing the old allele must become
> genetically dead. Of course, this is only true in a finite population
> where the population size remains fairly constant - a reasonable
> assumption for most real populations. In your calculation, if you allow
> the population size to become very large (or you treat the case of
> infinite popualtion size), then you can avoid the "cost". This is
> because you add individuals of the new genotype without decreasing the
> absolute numbers with the old genotype - although their relative
> frequency will decrease. The problem with this scenario is that it
> requires a constantly increasing populations size.
>
> I hope this helps.
>
> Donal.
First of all, I would like to thank Hamish G. Spencer and Joe
Felsenstein for the references they have provided here. Those papers
provide a wealth of information regarding substitution load - I had no
idea any of them existed. I have already obtained every one of them and
even some of their references.
Donald, thank you for your input as well. I currently disagree with you
about a beneficial mutation leading to a decrease in the population of a
species, but the reason I have raised this issue here is to test my
assumptions and conclusions - perhaps I am the one who is mistaken.
Unfortunately, I do not have time right now to go into the details of my
justification for this belief. I should be able to post the details when
I get home from work tonight.
Thank you all again for your input.
Robert Williams
Guy A. Hoelzer
In article <651unn$1gj8$1...@nntp6.u.washington.edu>, Donal Hickey
<dhi...@uottawa.ca> wrote:
> Robert Williams wrote:
> >
> >
> > My question to anyone who is familiar with this topic is why did Haldane
> > only consider the case where a deteriorating environment causes a common
> > allele to become disadvantageous? Why didn't he consider the case of a
> > new allele arising that is favored over the common allele?
> The problem with this scenario is that it
> requires a constantly increasing populations size.
Not necessarily. It only requires an increasing population size if
advantageous alleles are the only ones you consider in your model. If you
allow both advantageous and deleterious alleles to occur, then the effects
of the advantageous alleles will offset the effects of the deleterious
alleles to some extent, depending on the relative frequencies of both
types of mutations.
Jonah Thomas
I was never certain I was clear on this concept. I'd like to try to
explain it and see whether someone will tell me where I went wrong.
OK, first, you can do the math for natural selection without any
reference to "cost". Calculate the selective coefficients, apply them,
and you're done. The concept works independent of cost. What happens to
population size during selection is then simply left out of the model.
So you could have pathological cases. For example, a pathological gene
might on average result in 1.5 offspring where 2 would be required for
long-term survival. But if it results in very effectively poisoning the
individuals that don't carry the gene, it can be selected even while the
population size drops to nothing.
It looks to me like "cost" involves tracking the effect of selection on
population size. Why care about population size? If N drops then
selection can happen marginally faster, if what you care about is only
maximising the rate of evolution of the population, that isn't
necessarily a bad thing. But for external reasons we do care. If we're
interested in long-term evolution, a large population can generate
favorable mutations faster than a small population can. And in a large
population there's less opportunity for random drift, as there are more
selected mutations spreading at any given time. Large populations are
better buffered against extinction. So it makes a kind of sense to look
at how fast a selection we can have without reducing population size.
As a first approximation, that depends on the fecundity. Suppose there's
a particular carrying capacity, C. If the C existing individuals produce
2C offspring, then half of them must die. If 100C offspring are produced
then 99% of them must die. Selection that preferentially culls part of
the surplus has no cost. Selection that culls more than that will reduce
the population.
A given mutant might have a larger carrying capacity than the wild-type.
Then as it increases the population can grow. Its increased numbers
might cause the competing alleles to die out quicker because they might
not survive well in an environment that has so many individuals present.
They barely replaced themselves at C, at C' they may survive worse. But
that isn't necessarily the case, the mutant might be good for the others
too. Like, if a particular vitamin was limiting for a bacterial
population, a mutant that produces that vitamin can grow to larger
numbers. It might produce excess vitamin that the others can use, and
then they can grow to larger numbers too. Will it ever drive out the
others? It depends. None of this has to go any particular way.
What happens when two favorable mutants are being selected at once? If
they aren't linked, and if they have precisely the right interaction, so
the individuals who have both are selected the right amount relative to
those who have one or neither, then they can increase together almost as
fast as they would apart. Similarly when it's a dozen being selected at
once or a hundred. As they start to get common, the individuals who get
_none_ of them are weeded out quickly. Put all the bad eggs in one
basket and then drop the basket. Selection proceeds as fast for all of
them as it would for one alone -- except that they increase the
variability of results some, for each other. Since each is competing in
a population that varies greatly in survival value, stochastic effects
will be larger than for a uniform population. But that's a subtle effect.
Mostly, unlinked multiplicative mutations will be selected independently,
and they won't "cost" more than single ones.
But so much depends on the particular selection, it's hard to generalize.
When the wild-type population can't replace itself but the mutants have a
surplus, there's a cost to being wild-type that's independent of the
mutants. Very hard selection indeed. When the mutants can ensure that
no mutant will be surplus provided there's a wild-type to take that spot,
there's no cost to the population. There are so many ways selection can
go, and they don't matter to the simple model but they do matter to the
cost.
So, have I missed the point? Is there some other reason to think about
cost? Is there a better way to look at it?
Donal Hickey
Robert Williams wrote:
> Donald, thank you for your input as well. I currently disagree with you
> about a beneficial mutation leading to a decrease in the population of a
> species, but the reason I have raised this issue here is to test my
> assumptions and conclusions - perhaps I am the one who is mistaken.
> Unfortunately, I do not have time right now to go into the details of my
> justification for this belief. I should be able to post the details when
> I get home from work tonight.
>
> Thank you all again for your input.
>
> Robert Williams
Robert,
I didn't say that natural selection leads inevitably to a decrease in
the population of a species, and I don't think that Haldane said so
either. His point was that reproductive rate placed an upper limit on
the rate of allelic sustitution, if one wished to maintain population
size. In his introduction, he points out that "especially in slow
breeding animals such as cattle, one cannot cull even half the females,
even though only one in a hundred of them combines the various qualities
desired". He goes on to say that "the situation with respect to natural
selection is comparable". To expand on his example, one could imagine a
British dairy farmer in 1957 with a herd of one hundred cows, ninety
nine of which were the more traditional British Shorthorn breed and one
of which was the then-trendy Holstein-Friesen breed. If Haldane's farmer
wished to favor the Friesen breed by articficial selection within his
herd, there was a perceived limit on how quickly that could be achieved
without decimating the herd, given the fact that cows usually produce
only a single calf per year. You could do a rough calculation of how
many years this process would take by assuming that a cow produces a
heifer calf every two years (on average) and that these heifers would,
in turn, begin producing calves of their own at the age of two years.
One could complicate the issue by discussing selection for twinning rate
in Friesen cows, but the basic argument seems pretty obvious to me.
I think the reason that many people disagree with Haldane (myself
included) is that when he goes on to quantify this limitation on
substitution rate, he phrases it as an attempt "to estimate the effect
of natural selection in depressing the fitness of a species". One can
easily take issue with this latter statement, and in many different
ways depending on how one interprets it. Nevertheless, I still think
there is a necessary relationship between the maximum rate of allelic
substitution and the reproductive rate "especially in slow breeding
animals such as cattle". Of course, we could argue that altough "the
situation with respect to natural selection is comparable", it is much
more complex than the simplistic scenarios proposed by Haldane. For
instance, even dairy farmers are not as naive as he imagined. They did,
in fact, transform their herds of Shorthorns into herds of Freisens in
very few years - simply by inseminating all their cows with semen from
Friesen bulls. Perhaps nature has some comparable tricks!
Donal.
wjre...@mmm.com
In his recent post about Haldane's Dilemma, Joe Felsenstein wrote:
<snip>
> ... the cost [of substitution] is imposed
> by the change of environment, not by the
> selection that responds to it. In the case
> where there is no deterioration of the
> environment, but rather a favorable mutation
> arising, there is no cost, and indeed there
> is an increase in the population's ability
> to bear such costs.
Felsenstein is referring to an idea he (and some others) have promoted
for decades: that a beneficial mutation is good for the population, and
therefore does not incur a cost, because it actually helps the
population.
Felsenstein's mistake results from a mis-interpretation of the word
"cost". He re-interprets it in the casual sense as a 'negative', or a
'bad thing' -- and since a beneficial mutation is not a 'negative' or a
'bad thing' there can be no cost associated with it, or so argues
Felsenstein.
But the cost of substitution (as used for example in Haldane's Dilemma)
is not defined that way, it has a more precise definition, and
Felsenstein's misuse of the term does not get around it. In fact,
fundamental misunderstandings of the term "cost of substitution" are
very common, and are a main reason why Haldane's Dilemma was never
actually solved, it was merely obscured and brushed aside. Leading
experts today do not even agree on a solution.
The central concept embodied in the cost of substitution is this:
Nothing can go from 'few' to 'many' without a reproductive cost being
paid. It doesn't matter whether the trait is beneficial, or neutral,
(or even harmful). To go from 'few' to 'many', a reproductive excess is
required -- absolutely, positively, no exceptions. The formulas for
cost of substitution calculate just how much reproductive excess is
required for a given scenario. If the species is incapable of supplying
the necessary level of reproductive excess, then the given scenario is
not plausible. The cost of substitution is a criterion of plausibility,
(not a theory of extinction, as occasionally mistaken by some in yet
another avenue of confusion).
Many confusion factors obscured the issue for decades already. For that
reason an appendix of my book derives the standard formula for the
minimum cost of substitution without any reference to the confusion
factors. That is, the derivation does not refer to:
the individuals with the old trait
(that die out)
how the individuals die out
the fitness values
(of the old or new traits)
whether the new trait is beneficial,
neutral, or harmful
the environment
natural selection
ploidy
dominance
sexual reproduction
recombination
or genetic models
The derivation shows that a cost of substitution is simple, mechanical,
and unavoidable. The problem even shows up in computer simulations of
evolution. It cannot be gotten around by linguistic maneuvering (such
as Felsenstein's).
Yet Felsenstein's error is a simple one. It is remarkable it was
allowed to thrive for so long.
-- Walter ReMine
For more see:
http://www1.minn.net/~science/contents.htm#dilemma
The Biotic Message
Jonah Thomas
In article <65f1sd$qlo$1...@nntp6.u.washington.edu>,
wjre...@mmm.com wrote:
>But the cost of substitution (as used for example in Haldane's Dilemma)
>is not defined that way, it has a more precise definition, and
>Felsenstein's misuse of the term does not get around it. In fact,
>fundamental misunderstandings of the term "cost of substitution" are
>very common, and are a main reason why Haldane's Dilemma was never
>actually solved, it was merely obscured and brushed aside. Leading
>experts today do not even agree on a solution.
>The central concept embodied in the cost of substitution is this:
>Nothing can go from 'few' to 'many' without a reproductive cost being
>paid. It doesn't matter whether the trait is beneficial, or neutral,
>(or even harmful). To go from 'few' to 'many', a reproductive excess is
>required -- absolutely, positively, no exceptions.
Yes. You need a reproductive excess. If two parents can never produce
more than two offspring, then the population will dwindle away and
selection can at best result in some alleles dwindling slower than others.
>The formulas for
>cost of substitution calculate just how much reproductive excess is
>required for a given scenario. If the species is incapable of supplying
>the necessary level of reproductive excess, then the given scenario is
>not plausible. The cost of substitution is a criterion of plausibility,
>(not a theory of extinction, as occasionally mistaken by some in yet
>another avenue of confusion).
Why isn't it a theory of extinction? If what you call an implausible
selection is imposed, then the population size will drop. Unless that gets
turned around, it will lead to extinction. On the other hand, if a given
"scenario" is implausible, that doesn't mean the same alleles can't be
selected without reducing the population size, only slower. And the
difference depends on the form of selection imposed from the environment.
Sometimes that will be imposed ruthlessly, and the population size will
drop. Sometimes it will be a soft selection and the change will happen at
whatever pace the reproductive surplus allows -- and if the changes result
in increased reproductive surplus then the change can speed up as it
progresses.
So anyway, it looks like it's fundamentally misleading to call it a cost.
After all, what happens if you don't pay? What if there's nothing to
select, what do you get to buy instead with the cost you don't pay to
selection? No extra individuals survive, merely a random set of them
dies. So where's the cost? What you have here is a constraint, a maximum
rate of substitution at an allele with population size held constant.
Wesley R. Elsberry
[...]
WJR>The derivation shows that a cost of substitution is simple, mechanical,
WJR>and unavoidable. The problem even shows up in computer simulations of
WJR>evolution. It cannot be gotten around by linguistic maneuvering (such
WJR>as Felsenstein's).
[...]
I've written several simulations myself, and I'm intrigued. How
do I write up a subroutine to detect whether my simulation has
"shown" Haldane's dilemma or not? I'm asking for the objective
quantification here such that it can be reduced to software.
--
Wesley R. Elsberry, 6070 Sea Isle, Galveston TX 77554.
Student in Wildlife & Fisheries Sciences. http://www.rtis.com/nat/user/elsberry
"I'm the eyeman of TV\With my ocular TB" - BOC
WirtAtmar
Walter ReMine writes:
>The derivation shows that a cost of substitution is simple, mechanical,
>and unavoidable. The problem even shows up in computer simulations of
>evolution. It cannot be gotten around by linguistic maneuvering (such
>as Felsenstein's).
>
>Yet Felsenstein's error is a simple one. It is remarkable it was
>allowed to thrive for so long.
The difference between science and propaganda is that one examines every aspect
of the data with an intensely critical eye for signs of misinterpretation and
mismeasurement while in the promotion of propaganda, one bends the facts to
fit one's preconceived notions.
It's important to know that Walter lies squarely in the second category. In
this specific instance, Walter wants to use "Haldane's Dilemma" as a mechanism
to demonstrate that evolution proceeds far too slowly to have occurred by any
other means than that of a omnipotent, omniscient creator. He writes elsewhere:
===============================================
"Just as the cost of substitution has been confused by evolutionists, so has
the supposed solution posed by the neutral theory. They claimed neutral
substitutions incurred no cost. This chapter untangles the confusions. The rule
is: All substitutions incur a cost, even neutral substitutions. This chapter
shows the novel way the cost is paid by neutral mutations, and why this does
not ease Haldane's Dilemma. It also shows how the evolutionists' focus on
genetic load obscured the problems, rather than revealed them.
Using straightforward data and theory supplied by Motoo Kimura himself (the
author of the neutral theory), this chapter shows that in ten million years a
human-like population could, at best, substitute 25,000 expressed neutral
mutations. That amounts to 0.0007 percent of the genome, and is not remotely
enough to solve Haldane's Dilemma or explain human evolution.
-- http://www1.minn.net/~science/contents.htm#neutral
==============================================
In that regard, Walter is recapitulationg the old creationist argument that the
improbabilities of life are such that it could never have formed in a billion
billion universes if left just to chance alone, but this time in different
clothing.
If there were any part of evolutionary biology that I wish we could roll the
clock back on and start over, it would mathematical genetics. For the most
part, it misconstrues and misrepresents the evolutionary process -- although at
least it does it honestly. It doesn't constrain itself to a predefined
philosophical conclusion. That, unfortunately, is not true of Walter's work --
and thus no amount of intellectual disguise will ever make what he has written
to date "scientific."
Wirt Atmar
wjre...@mmm.com
Jonah Thomas wrote:
<snip>
> Why isn't it a theory of extinction? If what you call an implausible
> selection is imposed, then the population size will drop. Unless that gets
> turned around, it will lead to extinction.
Haldane's Dilemma is not about (what Jonah calls) "implausible
selection". In fact, the problem is visible even for exceedingly slight
levels of selection, (such as when selective advantage is one percent or
less). This is not "implausible selection".
Also, Haldane's Dilemma is not about just any kind of change, or any
kind of selection. It is specifically about the substitution of
beneficial mutations into a population.
Most importantly, Haldane's Dilemma does not predict extinction.
Instead, it is a criterion of plausibility, like this: A given
substitution rate requires a specific level of reproductive excess, and
if the species cannot supply that, then the given substitution rate is
not plausible. Haldane's Dilemma puts a *limit* on the maximum
plausible substitution rate -- and in the case of extinction, no further
limit is possible, or necessary. If you focus on extinction not only
will you be in error, but you will miss the thrust of Haldane's Dilemma.
>....
> So anyway, it looks like it's fundamentally misleading to call it a cost.
> After all, what happens if you don't pay?
If you don't pay the cost, then you don't get the substitution. That is
not an option evolutionary theory can be comfortable with.
> What if there's nothing to
> select, what do you get to buy
> instead with the cost you don't pay to
> selection?
There are many reproductive costs involved in an evolutionary scenario.
For example there are the following costs:
(1) substitution
(2) harmful mutation
(3) heterozygote advantage
(4) random death
(5) recombination
Even taken individually, costs 2, 3, & 4 can potentially be large,
perhaps even overwhelming. Thus, even without substitutions, there are
other costs to be paid if an evolutionary scenario is to be plausible.
My book discusses this in detail.
-- Walter ReMine
The Biotic Message
http://www1.minn.net/~science
Standard disclaimer: These thoughts are mine.
wjre...@mmm.com
Wesley R. Elsberry wrote:
> I've written several simulations myself, and I'm intrigued. How
> do I write up a subroutine to detect whether my simulation has
> "shown" Haldane's dilemma or not? I'm asking for the objective
> quantification here such that it can be reduced to software.
For those interested in computer simulations of evolution, my book
dismantles the most widely known example, the "METHINKS IT IS LIKE A
WEASEL" simulation from Dawkins' book, _The Blind Watchmaker_. It
identifies many unrealistic assumptions in the simulation that favored
evolution. Some of the key ones Dawkins did not tell his readers
about. For example, his simulation used a reproduction rate that would
require females to produce 200 offspring each, (a rate which is not
plausible for most higher organisms). The book shows how the simulation
actually demonstrates the phenomenon and problem of Haldane's Dilemma.
For those serious about this issue, I can recommend no better place to
start than there.
Robert Williams
Donal Hickey wrote:
>
> Robert Williams wrote:
> >
> >
> > My question to anyone who is familiar with this topic is why did Haldane
> > only consider the case where a deteriorating environment causes a common
> > allele to become disadvantageous? Why didn't he consider the case of a
> > natural selection could proceed without the huge cost in substitution
> > deaths that Haldane envisioned. (I will be happy to provide the
> > mathematics if anyone is interested - unless I am mistaken, the pattern
> > of deaths is completely different in these two cases.)
>
> Rob,
>
> I believe the result is not affected by the question of whether the
> environment deteriorates (thus lowering the fitness of the existing
> allele) or whether a new, "better" allele arises. For the new allele to
> replace the old one, all individuals bearing the old allele must become
> genetically dead. Of course, this is only true in a finite population
> where the population size remains fairly constant - a reasonable
> assumption for most real populations. In your calculation, if you allow
> the population size to become very large (or you treat the case of
> infinite popualtion size), then you can avoid the "cost". This is
> because you add individuals of the new genotype without decreasing the
> absolute numbers with the old genotype - although their relative
> requires a constantly increasing populations size.
>
>
> Donal.
I agree that the cost can be avoided by allowing a growing population
size, but I also believe that the cost is non-existant in the case of a
new, beneficial allele in a constant population size. Note that the
density dependant selection that I will be talking about here is not an
effort to side-step the cost of natural selection - it is simply a
device to maintain a constant (not increasing) population. Let's look at
what happens for the haploid case.
s = selection coefficient, s > 0 for a beneficial allele.
p = frequency of favored allele (near zero at first)
q = frequency of common allele (near 1 at first)
N = population number
F = fecundity, the average number of offspring in a generation
A - refers to the new, beneficial allele
a - refers to the old allele
I'm assuming discrete generations and that allele A will replace allele
a by competition of individuals containing these alleles.
Before selection (pretending that all selection is post-zygotic), F*N
individuals will be produced:
F*N*p + F*N*q = F*N
The favored allele (A) will be replacing the old allele (a) by
competition. The constant selection coefficient (s) refers to head to
head competition, but because the A individuals are initially rare, we
will need functions of s, p, and q to describe the fitness of A and a.
I will denote the fitness of an A individual as X, and the fitness of an
a individual as Y. I assume that X and Y can be related by X = (1 + s)
* Y, as would be expected from the definition of the fitness constant.
Applying selection to the previous reproduction equation will ideally
return the population to N :
X * F*N*p + Y * F*N*q = N.
We are now in a position to solve for the selection equations.
Since X = (1 + s) * Y,
Y * (1 + s) * F*N*p + Y * F*N*q = N.
Dividing through by the common factor (F*N) of the left side of the
equation gives us:
Y * (1 + s) * p + Y * q = 1/F
Collecting our Y terms yields:
Y * [ (1 + s) * p + q] = 1 / F.
Multiplying out the 1 + s term yields:
Y * (p + p*s + q) = 1/F.
Since p + q = 1,
Y * (1 + s*p) = 1/F.
Dividing by 1 + s*p:
Y = 1 / [ F * ( 1 + s*p)].
Remembering that X = (1 + s) * Y,
X = (1 + s) / [ F * ( 1 + s*p)].
We can gain further insight into the behavior of our selection
coefficients by separating them out using the method of partial
fractions:
Y = 1 / [ F * ( 1 + s*p)] = 1/F + A/( 1 + s*p).
Putting the terms on the right over the common denominator of F * (1 +
s*p) gives us:
1/[F * (1 + s*p)] = [1 + s*p + A*F] / [F * (1 + s*p)].
Paying attention to just the numerator:
1 = 1 + s*p + A*F.
Solving for A:
A = -s*p / F.
Therefor,
Y = 1 / F - s*p / [F * (1 + s*p)].
Putting X through the same process:
X = (1 + s) / [F * ( 1 + s*p)] = 1 / F + B / (1 + s*p)
1 + s = 1 + s*p + B*F
B = (s - s*p) / F
B = s*(1 - p) / F
B = s*q / F.
Therefor,
X = 1/F + s*q / [ F * (1 + s*p)].
Finally, we can plug all of this back into our selection equation and
see what happens:
(1/F + s*q / [ F * (1 + s*p)]) * p + (1 / F - s*p / [F * (1 + s*p)])
* q = 1 / F.
This can be multiplied out by the gene frequencies to yield:
(1/F) * p + s*q*p / [ F * (1 + s*p)] + (1/F) * p - s*q*p / [ F *
(1 + s*p)] = 1/F.
(By the way, does anybody notice the pleasing similarity of this
equation to Maynard-Smith's equation for selection using game theory?)
There are three things clearly apparent from this equation:
First, notice that the population replacement numbers decompose into two
components - 1/F (the expected fitness of each individual if no
substitution were occurring), and a deviation from 1/F that is dependant
upon the selection coefficient and the relative frequency of the two
genotypes. Secondly, notice that the deviations from 1/F are equal, but
of opposite sign and thus cancel. Therefor, the average fitness of the
population remains 1/F, whether substitution is occurring or not. This
is of course due to the imposition of the requirement that the
population number remains constant in our assumptions. If we were to
relax that requirement, the population numbers would trend upward in the
case of a beneficial mutation. Thirdly, notice what happens to this
equation at the extreme values of p and q. If p is very close to zero
and q is nearly 1, the fitness of an "A" individual approaches (1 + s) /
F and the fitness of an "a" individual is 1/F. This indicates that the
fitness of the "a" individuals is maximized because the world is rich in
inferior "A" individuals, and fitness is also at a maximum for the "a"
individuals because there are currently so few "A" individuals beating
them out of required resources. As p approaches 1 (and q 0), notice that
the fitness of the "A" individuals tends toward 1/F and the fitness of
the "a" individuals approaches 1 / [ F *(1 +s)] as the "a" gene goes
extinct.
The big thing apparent from all of this is that Haldane's idea that
selection requires the deaths of on average 30 times the current
population is falsified for the case of a beneficial mutation. The most
that can be said is that the cost of substitution is 1 - that is that
the entire population must be replaced to replace the "a" individuals
with "A" individuals. On the other hand, since the entire population is
replaced every generation anyway, I'm not sure that a cost of 1 has any
real significance.
At any rate, what I am really interested in is what is the maximal
substitution rate under these conditions? The maximal (theoretical)
value of s is F - 1 ( as I believe Dr. Felsenstein pointed out (in
1971!) in one of the papers mentioned earlier in this thread). This is
because the fitness of an organism cannot be greater than its fecundity,
and we have imposed the condition of constant population size, so we
cannot increase F to increase the substitution rate. Unfortunately, I
have not come up with a simple solution for the equation I have derived
above, but I have written a program that determines the number of
generations to raise the frequency of an allele from 1 individual to 99%
of the population having the allele. Here are the results for various
values of s and N.
s N # of Generations
Until p = 0.99
------- ---------------- --------------------
0.01 10,000 1388
0.01 100,000 1619
0.01 1,000,000 1851
0.01 1,000,000 2545
0.1 10,000 145
0.1 100,000 170
0.1 1,000,000 194
0.1 1,000,000,000 266
1 10,000 20
1 100,000 24
1 1,000,000 27
1 1,000,000,000 37
2 10,000 13
2 100,000 15
2 1,000,000 17
2 1,000,000 24
3 10,000 10
3 100,000 12
3 1,000,000 14
3 1,000,000,000 19
4 10,000 9
4 100,000 11
4 1,000,000 12
4 1,000,000,000 16
The following QBASIC program was used to generate the results shown
above by manually changing the values for s and N. (OK, not the world's
greatest programming environment, but at least it's available on
virtually all PCs, it's easy to use for quick programs, and many of us
have been exposed to BASIC somewhere along the way.)
10 mod1 = 1
20 N = 100000
30 p = 1 / N
40 q = 1 - p
50 s = .01
60 gen = 0
70 gen = gen + 1
80 p = (1 + s * q / (1 + s * p)) * p
90 q = 1 - p
100 IF gen MOD mod1 = 0 THEN PRINT "N - "; gen, "p is : "; p, "q is: ";
q
110 IF p < .99 THEN 70
120 PRINT "p is : "; p, "n is: "; gen
Notice that for the very high selection coefficients, the genes can
substitute in very few generations. For example, in an organism that has
a fecundity of 4 were to mutate a gene that was so fit that all carriers
were guaranteed to survive, it would require only 12 generations for the
gene to go from 1 individual to 100,000 copies. Of course, I am not
implying that a single gene of such fitness ever existed, but if fitness
coefficients of genes are additive and many genes are simultaneously in
the process of being fixed on the same chromosome, then the fitness of
individuals could more plausibly approach these high values. Note that
if this were to happen, not just 1 gene would be replaced in 12
generations, but rather many genes would be replaced in 12 generations,
resulting in possibly more than 1 gene being replaced per generation! I
am currently working on "simulations" about as sophisticated as the
program sample above (please note my sarcasm) to consider the additive
effects of multiple gene substitutions upon fitness. A lot of this will
have to do with the average expected rate of crossing over for different
loci (having reasonably small fitness coefficients) on the same
chromosome. I have no idea of the "average" crossing over rate, so if
anyone has any ideas on this, please let me know! At any rate, since
humans have 23 independent pairs of chromosomes, it appears that we
could easily have 23 beneficial mutations becoming fixed at the same
time even without crossing over.
Phew, I'm glad to get that off my chest. What do you think, Donal, how
does all of the above fit in with your ideas of a cost for substitution
of a beneficial allele? I hope I haven't made any horrible blunders in
my reasoning, but the only way I know of to find out is to present my
thoughts to those who are qualified to evaluate them.
To see similar derivations for the diploid case, and to learn why I am
so interested in this, see my web page on Haldane's Dilemma at
http://www.gate.net/~rwms/haldane1.html .
Robert Williams
wjre...@mmm.com
It is unfortunate that Wirt Atmar chose to lash out with innuendo,
rather than serious argument. It appears from his post he is not
familiar with my book, but has instead merely picked up very incomplete
descriptions from the Internet, and then misrepresented even those for
your benefit. For example:
> ... Walter wants to use "Haldane's Dilemma"
> as a mechanism to demonstrate that evolution
> proceeds far too slowly to have occurred by any
> other means than that of a omnipotent,
> omniscient creator.
Wirt is mistaken. He misrepresents my stance on Haldane's Dilemma, so
here it is again. I say the standard model of genetic evolution (the
one model prominent in all evolution books) cannot solve the problems
arrayed before it, of which Haldane's Dilemma is an historic example.
The standard model has failed, the key data needed to see this were
available decades ago -- and it is time for evolutionary geneticists to
address the matter. I believe they will (per force) replace that model
with 'something' different. In the mean time, I point out that
evolutionists and their textbooks continue to sell as true a model many
of them know to be false. In this context I need only site Wirt himself
(with his curiously backwards reference to "honesty").
> If there were any part of evolutionary biology
> that I wish we could roll the clock back on and
> start over, it would mathematical genetics. For
> the most part, it misconstrues and misrepresents
> the evolutionary process -- although at
> least it does it honestly.
Joe Felsenstein
(Some insulting objections to my comments.)
ReMine seems to think that in my recent
comments and my 1971 paper I made elementary mistakes.
Here are some of the kind comments he made:
>Felsenstein's mistake results from a mis-interpretation of the word
>"cost".
....
>The derivation shows that a cost of substitution is simple, mechanical,
>and unavoidable. The problem even shows up in computer simulations of
>evolution. It cannot be gotten around by linguistic maneuvering (such
>as Felsenstein's).
....
>Yet Felsenstein's error is a simple one. It is remarkable it was
>allowed to thrive for so long.
....
>Felsenstein's misuse of the term does not get around it.
Gee thanks, Walter, for your kind comments.
On closer reading of ReMine's posts, I see that the central argument, which he
applies to neutral as well as selective substitutions, is that
>The central concept embodied in the cost of substitution is this:
>Nothing can go from 'few' to 'many' without a reproductive cost being
>paid. It doesn't matter whether the trait is beneficial, or neutral,
>(or even harmful). To go from 'few' to 'many', a reproductive excess is
>required -- absolutely, positively, no exceptions. The formulas for
>cost of substitution calculate just how much reproductive excess is
>required for a given scenario. If the species is incapable of supplying
>the necessary level of reproductive excess, then the given scenario is
>not plausible.
This is unequivocally wrong. Suppose we have a population with *no*
reproductive excess. Each pair produces exactly two offspring. There is
Mendelian segregation, so that it is quite possible that a gene with
present-day frequency p could change to frequency p' in the next
generation. Neutral mutants could fix (as genetic drift occurs owing to
Mendelian segregation even when there is no variation in offspring number).
Furthermore neutral mutations can occur at many loci, and fix independently.
This is, of course, a thought-experiment, but is enough to show the
failure of ReMine's argument.
wjre...@mmm.com
Jonah Thomas wrote:
> >Haldane's Dilemma is not about (what Jonah calls) "implausible
> >selection". In fact, the problem is visible even for exceedingly slight
> >levels of selection, (such as when selective advantage is one percent or
> >less). This is not "implausible selection".
>
> It is if it exceeds the reproductive excess.
Jonah is here using terms imprecisely, and, because of that, is likely
to add confusion rather than reduce it. Haldane's Dilemma does not
identify "implausible selection", rather it identifies implausible
substitution rates -- substitution rates that require more reproductive
excess than the species can provide.
The focus of the implausibility is the substitution rates, not the
selection itself. This is a clearer way to state the case.
> I don't want to _focus_ on extinction, I want to point out that Haldane's
> Dilemma gives conditions of extinction as a side benefit. If for any
> reason you exceed the maximum plausible substitution rate for one allele,
> the population size will decrease. If that continues you get extinction.
Jonah offers a self-contradictory scenario. He proposes as 'realistic'
a situation that "exceeds the maximum plausible" -- that is
self-contradictory. He then compounds it by proposing this implausible
situation "continues" at length. It is doubly implausible.
But there are additional deeper reasons why Jonah is mistaken. To see
these let us momentarily agree to one of Jonah's key assumptions, that
the population size decreases if it lacks sufficient reproductive excess
to pay for ongoing substitutions. What happens then? The population
(as a whole) receives fewer beneficial substitutions, precisely because
there are fewer individuals. This would slow the substitution rate, and
the ongoing cost of substitution would therefore be reduced. The
situation would come into balance, where the cost of substitution is
matched by plausible reproductive payments.
Let me put it this way. If the population cannot provide the required
level of reproductive excess, then the given evolutionary scenario is
not plausible. The scenario must then be amended to a lower
substitution rate. Nothing about this predicts extinction.
Above I described what happens when the population shrinks -- the
substitution rate starves and slows due to fewer beneficial mutations.
Now let me take that one step further. Suppose we *artificially* inject
beneficial mutations into a population at a high rate. Will the
population go extinct as Jonah expects? No, there is no inherent reason
to expect that. Jonah is completely mistaken. The cost of substitution
does not predict extinction. Instead it is a criterion of
plausibility.
> >> So anyway, it looks like it's fundamentally misleading to call it a cost.
> >> After all, what happens if you don't pay?
>
> >If you don't pay the cost, then you don't get the substitution. That is
> >not an option evolutionary theory can be comfortable with.
>
> I can. If you select slower then you don't pay more than you can afford.
> No problem.
In other words, Jonah agrees with me here -- the cost of substitution
says you only get what you pay for.
> >There are many reproductive costs involved in an evolutionary scenario.
> >For example there are the following costs:
>
> > (1) substitution
> > (2) harmful mutation
> > (3) heterozygote advantage
> > (4) random death
> > (5) recombination
>
> >Even taken individually, costs 2, 3, & 4 can potentially be large,
> >perhaps even overwhelming. Thus, even without substitutions, there are
> >other costs to be paid if an evolutionary scenario is to be plausible.
>
> Of course if the level of harmful mutations is too high, selection gets
> swamped by them. Then the occasional favorable mutation will probably
> carry a load of linked harmful mutations with it. Its selective value is
> reduced by them. Selah.
Jonah missed my point. The various costs 2 thru 5 (listed above) each
take a bite out of the limited reproductive excess of the species,
thereby reducing the amount available to pay for substitutions. The
higher those costs, the lower the maximum plausible substitution rate.
> Species where an
> individual can produce a million eggs have a much greater reproductive
> excess than those like humans where an individual woman produces only 15 or
> so children, and can potentially evolve much faster. OK, I have no problem
> with that.
In other words, Jonah agrees with me on a key point that began this
thread. The cost of substitution is real -- Joe Felsenstein is
mistaken.
wjre...@mmm.com
Robert Williams wrote:
<snip>
> I agree that the cost can be avoided by allowing
>a growing population size, ...
The cost is not avoided by allowing a growing population size. The cost
of substitution can never be avoided. There are some specialized
mechanisms (especially as in the case of neutral substitutions) that can
increase the reproductive payments, but the cost can never be completely
avoided.
In fact, larger populations have a *higher* cost of substitution, not
lower. Allowing the population to grow does not reduce the cost even
slightly.
Robert next sets out to show "that the cost is non-existant in the case
of a new, beneficial allele in a constant population size." He sets up
a situation involving density-dependant selection, and derives its
selection equations. All of that is irrelevant -- he never calculates
the cost of substitution. He merely makes assertions about it that are
entirely disconnected from his formulas and derivations.
Indeed he continues with the traditional misunderstandings, as follows:
> The big thing apparent from all of this is that Haldane's idea that
> selection requires the deaths of on average 30 times the current
> population is falsified for the case of a beneficial mutation. The most
> that can be said is that the cost of substitution is 1 - that is that
> the entire population must be replaced to replace the "a" individuals
> with "A" individuals. On the other hand, since the entire population is
> replaced every generation anyway, I'm not sure that a cost of 1 has any
> real significance.
Robert has shown no such thing. He is here making the traditional error
of over-emphasizing "deaths", focusing on deaths as though death were
the issue. It isn't. Substitution is the issue. Growth of the new
trait is the issue. The deaths are just a way to tally the *births*
required. I will explain that next.
For ease of discussion (and solely for ease of discussion) let us
suppose the population size remains constant. Suppose that in a given
generation 100 individuals with the old trait meet their genetic deaths
-- the end of a line of inheritance -- finito. Over that generation
there are now 100 fewer individuals with the old trait. If the
population is to remain the same size, then these must be replaced. By
what? By individuals with the new trait, and this requires genetic
births -- excess births by individuals with the new trait.
Devastatingly simple, yes?
Next suppose the generation began with only 2 individuals with the new
trait. This scenario would require them to have a reproductive excess
of 50 (=100/2). This is the cost of substitution incurred for that
generation. If the species cannot supply that level of reproductive
excess, then the scenario is not plausible. Indeed, the scenario is not
plausible for higher mammals.
This is the central issue that has been garbled for forty years. Do not
focus on the deaths or on individuals with the old trait -- they're
goners. Forget 'em! Do not focus on them or you'll get confused. Do
not focus on the fitness values, or the population size, or the many
other traditional confusion factors.
Just get this: If a trait is alleged to increase by, say, five percent
in a generation, then the species must be capable of applying five
percent excess reproduction to this task. If it can't, then the
scenario is not plausible. The central issue is the growth of the new
trait, and how it is limited by the finite reproduction of the species.
That is precisely what is going on in Haldane's formulas. By tallying
up the genetic deaths per survivor the formulas calculate the excess
reproduction (in genetic births per survivor) required by a given
scenario.
******
At any rate, Robert's formulas where not about the cost of
substitution. He merely used them as an (irrelevant) backdrop for his
mistaken comments about cost.
He then discusses results from his computer simulation:
> Notice that for the very high selection coefficients, the genes can
> substitute in very few generations. For example, in an organism that has
> a fecundity of 4 were to mutate a gene that was so fit that all carriers
> were guaranteed to survive, it would require only 12 generations for the
> gene to go from 1 individual to 100,000 copies.
Robert finds that a substitution can occur in merely 12 generations.
That is faster than Haldane's conclusion that the average rate in higher
mammals could be no faster than 300 generations. How did Robert get a
faster rate?
Haldane understood (correctly) that a species' entire fecundity could
not all be used to pay the cost of substitution. Only a portion of it
could. He estimated that higher mammals have a reproductive excess of
ten percent (0.1) that can be applied to substitutions. Robert used a
figure fully 30 times higher, thereby achieving a substitution rate
nearly 30 times faster. That's all Robert did. He did not reduce the
cost of substitution one whit. He merely artificially increased the
reproductive payments.
******
The above mistakes are visible throughout Robert's web page. He gives
his reader's the unmistakable impression that he deals with, and
refutes, the material in my book. As best I can tell, he has not read
my book, he misrepresents it that badly. He continues to express the
traditional confusions about Haldane's Dilemma, without even mentioning
the many explicit arguments my book makes against them.
wjre...@mmm.com
As I stated previously, I claim:
The central concept embodied in the cost of substitution is this:
Nothing can go from 'few' to 'many' without a reproductive cost being
paid. It doesn't matter whether the trait is beneficial, or neutral,
(or even harmful). To go from 'few' to 'many', a reproductive excess is
required -- absolutely, positively, no exceptions. The formulas for
cost of substitution calculate just how much reproductive excess is
required for a given scenario. If the species is incapable of supplying
the necessary level of reproductive excess, then the given scenario is
not plausible.
Joe Felsenstein responds:
> This is unequivocally wrong. Suppose we have a population with *no*
> reproductive excess. Each pair produces exactly two offspring. There is
> Mendelian segregation, so that it is quite possible that a gene with
> present-day frequency p could change to frequency p' in the next
> generation. Neutral mutants could fix (as genetic drift occurs owing to
> Mendelian segregation even when there is no variation in offspring number).
>
> Furthermore neutral mutations can occur at many loci, and fix independently.
>
> This is, of course, a thought-experiment, but is enough to show the
> failure of ReMine's argument.
Felsenstein poses a situation where each pair (a male and female)
produces exactly two offspring, thus there is "*no* reproductive
excess", he says -- yet neutral mutations are still able to increase to
fixation. How is this possible, as it seems to break the rule I stated
above?
It doesn't break the rule, rather Felsenstein misunderstood his
example. In truth there *is* reproductive excess in his example, and it
pays for the neutral substitutions. What is the source of this
reproductive excess?
Over the full life-cycle the genome is alternately halved, then doubled
-- for example, halved as it goes to sperm or egg, then doubled when
sperm unites with egg. Graham Bell calls this the alternation of
generations (say, haploid sperm, diploid adults, back and forth). The
process overall keeps the genome nominally the same size as before. But
specifically it is this DOUBLING that is the secret source of
reproductive excess. From the gene's eye-view, this is a source of
growth! Sometimes it aids the gene to fixation, sometimes it hurts it
-- randomly, with zero average effect (averaged over infinity). This is
what I call "stochastic reproductive excess", it is random, and can
*randomly* move a gene toward or away-from fixation via short-term
fluctuations to-and-fro.
That is why Felsenstein's example does not counter my claim, but
fulfills it: Nothing can go from 'few' to 'many' without a reproductive
cost being paid. As a thought experiment, one can amend Felsenstein's
example to eliminate all sources of reproductive excess including the
random stochastic form I described above. You will then see that even a
new neutral mutation cannot increase in numbers to fixation, just as I
predicted. Without reproductive excess evolutionary substitutions
cease.
My book discusses all this and goes further. Traditionally, neutral
substitutions were mistakenly viewed as having "zero cost", (largely
because traditional commentators confused the concepts of load and
cost). It turns out that neutral substitutions are exceedingly costly.
They increase, then decrease, then increase again -- back and forth --
incurring cost all along the way as they traverse, and re-traverse,
ground already covered previously. All that must be driven, and paid
for, by reproductive excess (of various types).
So if neutral substitutions are so costly, how do they achieve an
overall faster substitution rate than beneficial mutations? The book
answers that question in detail, by identifying several payment
mechanisms (such as stochastic reproductive excess and others) that aid
neutral substitutions, but which are, on average, unhelpful or
unavailable to beneficial substitutions. The book shows precisely why
the neutral substitution rate is limited by mutation rate, not by an
inability to pay the costs of substitution. (That last sentence reaches
the same conclusion as Motoo Kimura and his neutral theory, but
disagrees as to the explanation why. ALL substitutions require that a
reproductive cost be paid, even neutral substitutions.)
In other words, the book offers a coherent and consistent cost/payment
theory that is unavailable (downright confused and mistaken) in other
sources today.
******
One last matter. Joe Felsenstein has taken offense at my comments, but
there was no personal insult in them. I said his idea is mistaken and
should not have lasted as long as it did. That comment was not aimed at
Joe, for any given scientist makes mistakes from time to time. Rather,
it was intended to peak your interest. One cannot find in the
literature any evolutionists directly challenging Felsenstein's solution
to Haldane's Dilemma. They posed a number of *other* so-called
solutions, (some of them very complicated too), and demonstrated they at
least correctly understood the cost of substitution. But they allowed
Felsenstein's mistaken notion to thrive for decades unchallenged -- and
it is such a straightforward mistake, a simple linguistic
misinterpretation of the cost of substitution. In other words, my
comment is not about Felsenstein -- it is about many others who should
have, or must have, (or did?) see his error, but said nothing.
In all those years no one publicly challenged Felsenstein's solution.
Now we see in this thread that not one person (other than Felsenstein)
comes to its defense. This situation is curious and ought to strike
even casual bystanders. I offer it to demonstrate the sense of
confusion and mayhem surrounding this classic unsolved problem.
Lastly, I respect people who honestly engage, dig, and grapple toward
the truth -- and Joe Felsenstein has done that.
Per Erik Jorde
wjre...@mmm.com writes:
>
> Over the full life-cycle the genome is alternately halved, then doubled
> -- for example, halved as it goes to sperm or egg, then doubled when
> sperm unites with egg. Graham Bell calls this the alternation of
> generations (say, haploid sperm, diploid adults, back and forth). The
> process overall keeps the genome nominally the same size as before. But
> specifically it is this DOUBLING that is the secret source of
> reproductive excess. From the gene's eye-view, this is a source of
> growth! Sometimes it aids the gene to fixation, sometimes it hurts it
> -- randomly, with zero average effect (averaged over infinity). This is
> what I call "stochastic reproductive excess", it is random, and can
> *randomly* move a gene toward or away-from fixation via short-term
> fluctuations to-and-fro.
>
There is no "doubling" involved in this scenario: at the haploid stage
there are 2N gametes (sperm/egg) with one gene each; at the diploid
stage there are N zygotes with 2 genes each. The number of genes, 2N,
is the same at all stages.
> That is why Felsenstein's example does not counter my claim, but
> fulfills it: Nothing can go from 'few' to 'many' without a reproductive
> cost being paid. As a thought experiment, one can amend Felsenstein's
> example to eliminate all sources of reproductive excess including the
> random stochastic form I described above. You will then see that even a
> new neutral mutation cannot increase in numbers to fixation, just as I
> predicted. Without reproductive excess evolutionary substitutions
> cease.
An heterozygote individual, Aa, may produce the following sets of two
gametes: {A,A} {A,a} {a,A} and {a,a}; all with equal probability.
There are no "reproductive excess" involved here, yet two of the
outcomes do result in change in the allele frequencies, even if
the alleles are selectively neutral. Hence, all species can bear
this "cost", because there is no cost.
--
Per Erik Jorde p.e....@bio.uio.no
"The whole was a structure of misunderstood facts, carelessly accepted
rumors, and half-digested theoretical concepts, cemented by
superstition." -Willy Ley
Joe Felsenstein
In article <6647jn$1ghe$1...@nntp6.u.washington.edu>, <wjre...@mmm.com> wrote:
>The central concept embodied in the cost of substitution is this:
>Nothing can go from 'few' to 'many' without a reproductive cost being
>paid.
>The formulas for
>cost of substitution calculate just how much reproductive excess is
>required for a given scenario. If the species is incapable of supplying
>the necessary level of reproductive excess, then the given scenario is
>not plausible.
I had raised the issue that a neutral substitution can fix even in a population
that has exactly two offspring per pair of parents, owing to random change of
gene frequencies due to Mendelian segregation. ReMine proclaims:
>It doesn't break the rule, rather Felsenstein misunderstood his
>example. In truth there *is* reproductive excess in his example, and it
>pays for the neutral substitutions. What is the source of this
>reproductive excess?
>
>Over the full life-cycle the genome is alternately halved, then doubled
>-- for example, halved as it goes to sperm or egg, then doubled when
>sperm unites with egg.
...
>specifically it is this DOUBLING that is the secret source of
>reproductive excess.
So apparently ReMine wants to redefine reproductive excess (proclaiming all the
while that he and he alone has understood the concept) so that there will
be one in this case (a factor of two, owing to the reduction division of
meiosis and then the subsequent doubling of DNA content at fertilization).
The rest of us simply are asking whether there are extra offspring needed
beyond the two per parent that is needed to maintain population size. We
want to know whether in neutral, advantageous, or deleterious allele
substitution this reproductive excess sets a limit to the number of
substitutions.
In fact, ReMine concedes that the reproductive excess does not set any limit
on the rate of neutral substitution:
>... It turns out that neutral substitutions are exceedingly costly.
...
>... The book shows precisely why
>the neutral substitution rate is limited by mutation rate, not by an
>inability to pay the costs of substitution. (That last sentence reaches
>the same conclusion as Motoo Kimura and his neutral theory, but
>disagrees as to the explanation why. ALL substitutions require that a
>reproductive cost be paid, even neutral substitutions.)
So the cost does not place any limit on the rate of neutral substitution.
OK, is there any limit set in the case of advantageous mutation? I would
have said no, as each advantageous mutation increases the fitness of
the population, in effect creating extra reproductive excess. If ReMine
cannot show that there is a limit on the rate of substitutions that are
due to advantageous mutation (aside from the limit set by the rate of
the mutations themselves), then his conclusions are no different than the
previous literature, except for his wanting to make it sound like they
identify a problem for evolution.
Oh yes, the matter of his tone:
>One last matter. Joe Felsenstein has taken offense at my comments, but
>there was no personal insult in them. I said his idea is mistaken and
>should not have lasted as long as it did.
...
>In other words, the book offers a coherent and consistent cost/payment
>theory that is unavailable (downright confused and mistaken) in other
>sources today.
...
>One cannot find in the
>literature any evolutionists directly challenging Felsenstein's solution
>to Haldane's Dilemma.
...
>... But they allowed
>Felsenstein's mistaken notion to thrive for decades unchallenged -- and
>it is such a straightforward mistake, a simple linguistic
>misinterpretation of the cost of substitution.
...
>In all those years no one publicly challenged Felsenstein's solution.
>Now we see in this thread that not one person (other than Felsenstein)
>comes to its defense.
...
> This situation is curious and ought to strike
>even casual bystanders. I offer it to demonstrate the sense of
>confusion and mayhem surrounding this classic unsolved problem.
Interesting. ReMine thinks there has been a large literature on this
that has been confused and has allowed what he thinks is a mistake on
my part to go unchallenged. Clearly a situation needing ReMine to sell
us a book.
This picture is of a pompous and confused scientific community that
needs straightening out by ReMine.
I would have said that my 1971 paper has been relatively little-noticed
since then, and the whole discussion of cost of natural selection subsided
soon after, and has attracted little attention since. (Haven't
noticed any mayhem.) However my 1971 paper is one I am pleased with, as
it was clear and correct and I think it helps identify the cases in which
the reproductive excess limits the rate of evolution, and those in which
it does not. And while there are mistakes here and there in many of my
papers, ReMine is wrong about there being a crucial mistake in that
paper.
Donal Hickey
I thought we all agreed on this, ever since Darwin first proposed it
(reproductive excess) as a prerequisite for natural selection. This
discussion seems to risk degenerating into a discussion about the
definition of various words, largely due to the use of culturally-loaded
(groaner!) terminology to describe a biological process. My impression
is that your implied conclusion is that the semantic confusion of
biologists can be taken as evidence against evolution in this case. Is
that true?
Jonah Thomas
In article <661is5$1eos$1...@nntp6.u.washington.edu>,
>> >Haldane's Dilemma is not about (what Jonah calls) "implausible
>> >selection". In fact, the problem is visible even for exceedingly slight
>> >levels of selection, (such as when selective advantage is one percent or
>> >less). This is not "implausible selection".
>> It is if it exceeds the reproductive excess.
>Jonah is here using terms imprecisely, and, because of that, is likely
>to add confusion rather than reduce it. Haldane's Dilemma does not
>identify "implausible selection", rather it identifies implausible
>substitution rates -- substitution rates that require more reproductive
>excess than the species can provide.
>The focus of the implausibility is the substitution rates, not the
>selection itself. This is a clearer way to state the case.
You have utterly missed my point. I'll try again: It's quite possible to
impose a substitution rate that would be "implausible" by Haldane's
estimate. In that case the population will decline.
>> I don't want to _focus_ on extinction, I want to point out that Haldane's
>> Dilemma gives conditions of extinction as a side benefit. If for any
>> reason you exceed the maximum plausible substitution rate for one allele,
>> the population size will decrease. If that continues you get extinction.
>Jonah offers a self-contradictory scenario. He proposes as 'realistic'
>a situation that "exceeds the maximum plausible" -- that is
>self-contradictory.
The problem here is not my scenario, it's your incorrect assumptions.
>He then compounds it by proposing this implausible
>situation "continues" at length. It is doubly implausible.
Again you assume this from your theory, which is unfortunately incorrect.
>But there are additional deeper reasons why Jonah is mistaken. To see
>these let us momentarily agree to one of Jonah's key assumptions, that
>the population size decreases if it lacks sufficient reproductive excess
>to pay for ongoing substitutions. What happens then? The population
>(as a whole) receives fewer beneficial substitutions, precisely because
>there are fewer individuals. This would slow the substitution rate, and
>the ongoing cost of substitution would therefore be reduced. The
>situation would come into balance, where the cost of substitution is
>matched by plausible reproductive payments.
You consistently reason backward from your conclusions. Try the following
scenario: A population size one trillion is growing in a toxic environment
in which they on average produce .98 offspring per individual. A variant
subpopulation which on average produces .99 offspring per individual is
present, their population size is one billion.
There is no reproductive excess, in fact there is a reproductive deficit.
The variant type will be selected and its frequency in the total population
will rise, even while its total numbers decline. If some beneficial
mutation occurs that results in a reproductive excess, the population may
not go completely extinct. Otherwise extinction is unavoidable barring a
beneficial environmental change. There is no necessary balance that will
create "plausible" substitution rates. That's something you made up from
theory.
>Let me put it this way. If the population cannot provide the required
>level of reproductive excess, then the given evolutionary scenario is
>not plausible. The scenario must then be amended to a lower
>substitution rate. Nothing about this predicts extinction.
If the scenario happens to be amended to a lower substitution rate, then
extinction is not predicted. But the environment which does the selection
isn't necessarily bound by your theory.
>Above I described what happens when the population shrinks -- the
>substitution rate starves and slows due to fewer beneficial mutations.
>Now let me take that one step further. Suppose we *artificially* inject
>beneficial mutations into a population at a high rate. Will the
>population go extinct as Jonah expects? No, there is no inherent reason
>to expect that. Jonah is completely mistaken. The cost of substitution
>does not predict extinction. Instead it is a criterion of
>plausibility.
There are published cases of segregation distorter mutations artificially
injected into a population at even a moderate rate, which tended to drive
populations toward extinction. I don't have references handy, perhaps
someone else reading this does. I didn't say that addition of beneficial
mutations necessarily results in reduced population size. I do say that
your "criterion of plausibility" is not a criterion to predict what
selection rates won't happen, it's more complicated than that. Those
selection rates can happen and there are consequences when they do.
>> >> So anyway, it looks like it's fundamentally misleading to call it a
>> >> cost. After all, what happens if you don't pay?
>> >If you don't pay the cost, then you don't get the substitution. That is
>> >not an option evolutionary theory can be comfortable with.
>> I can. If you select slower then you don't pay more than you can afford.
>> No problem.
>In other words, Jonah agrees with me here -- the cost of substitution
>says you only get what you pay for.
I say you don't on average get more than you pay for, and sometimes you pay
in reduced population size.
>> >There are many reproductive costs involved in an evolutionary scenario.
>> >For example there are the following costs:
>> > (1) substitution
>> > (2) harmful mutation
>> > (3) heterozygote advantage
>> > (4) random death
>> > (5) recombination
>> >Even taken individually, costs 2, 3, & 4 can potentially be large,
>> >perhaps even overwhelming. Thus, even without substitutions, there are
>> >other costs to be paid if an evolutionary scenario is to be plausible.
>> Of course if the level of harmful mutations is too high, selection gets
>> swamped by them. Then the occasional favorable mutation will probably
>> carry a load of linked harmful mutations with it. Its selective value is
>> reduced by them. Selah.
>Jonah missed my point. The various costs 2 thru 5 (listed above) each
>take a bite out of the limited reproductive excess of the species,
>thereby reducing the amount available to pay for substitutions. The
>higher those costs, the lower the maximum plausible substitution rate.
You missed _my_ point. What beneficial mutations _do_ is sidestep your
costs 2-4 and sometimes 5. For the big one, when unavoidable random
deaths are prevalent, the maximum beneficial mutation is weakly selected
-- individuals carrying it are quite likely to suffer unavoidable random
death that they can do nothing about. For example, suppose you grow a
bacterial population as follows: You grow the population to size ten
billion, and then you remove one hundred individuals to a new environment
where you let them grow to size ten billion, and then you remove one
hundred individuals etc. How beneficial would a mutation have to be, to
be selected in that scenario? If you were to count reproductive excess
in terms of the 100 cells -> 100 cells cycle, the reproductive excess is
roughly ten billion, but it's all taken by unavoidable random death with
none left for selection.
On the other hand, suppose you grow the same population in continuous
culture, removing half the population each generation. So long as no
selection is going on, you get 5 billion random deaths each generation.
But as soon as a selected mutation gets established, it _takes_ from the
random death component. The difference is, that in the perodic transfer
environment the beneficial mutations can't take over from the random
death, and in the continuous culture they can. This difference isn't
something that Haldane's Dilemma can predict, it's a result of the
particular environment and sometimes on the nature of the selection on
the particular genes that are being selected. Sometimes the random death
can be avoided and sometimes it can't. You have no basis to estimate in
general how much of the reproductive excess it will unavoidably consume.
>> Species where an
>> individual can produce a million eggs have a much greater reproductive
>> excess than those like humans where an individual woman produces only 15
>> or so children, and can potentially evolve much faster. OK, I have no
>> problem with that.
>In other words, Jonah agrees with me on a key point that began this
>thread. The cost of substitution is real -- Joe Felsenstein is
>mistaken.
What exactly did Felsenstein say that was wrong?
wjre...@mmm.com
Donal Hickey wrote:
> I thought we all agreed on this, ever since Darwin first proposed it
> (reproductive excess) as a prerequisite for natural selection.
Yes. There is general agreement that reproductive excess is required
for something to go from 'few' to 'many', as repeatedly required by the
the evolutionary model. I regard it as almost true by definition, it's
that obvious.
> This discussion seems to risk degenerating into a
> discussion about the definition of various words,
> ....
Joe Felsenstein and I are momentarily debating whether a stochastic form
of reproductive excess exists (as I claim it does) at the level of the
gene, and that it can pay for neutral substitutions.
Beyond that there is another simple step in our argument. Reproductive
excess is not merely 'required' for substitutions -- its magnitude (or
lack thereof) limits the *rate* of beneficial substitution. In other
words, there is a link between reproductive excess and the speed of
beneficial evolution. This link is so direct it even so up in computer
simulations of evolution.
(NOTE: The beneficial substitution rate can be mutation-limited or
cost-limited, whichever gives the LOWER rate. That is, the rate can be
limited by mutation/creation rate of beneficial mutations, and by the
limits of Haldane-style costs and payments -- whichever is lower.)
> My impression is that your implied conclusion is that
> the semantic confusion of biologists can be taken as
> evidence against evolution in this case. Is
> that true?
No, that would be mistaken. I do not regard the semantic confusion of
biologists (on issues such as 'cost of substitution' and 'reproductive
excess') as evidence against evolution. Rather, it is evidence (and by
no means the only evidence) that Haldane's Dilemma was never solved, the
problem was merely obscured and brushed aside -- that is my claim.
I would go further. Let me repeat my stance from my earlier response to
Wirt Atmar:
I say the standard model of genetic evolution (the
one model prominent in all evolution books) cannot solve the problems
arrayed before it, of which Haldane's Dilemma is an historic example.
The standard model has failed, the key data needed to see this were
available decades ago -- and it is time for evolutionary geneticists to
address the matter. I believe they will (per force) replace that model
with 'something' different. In the mean time, I point out that
evolutionists and their textbooks continue to sell as true a model many
of them know to be false. In this context I need only site Wirt himself
(with his curiously backwards reference to "honesty").
> If there were any part of evolutionary biology
> that I wish we could roll the clock back on and
> start over, it would mathematical genetics. For
> the most part, it misconstrues and misrepresents
> the evolutionary process -- although at
> least it does it honestly.
-- Walter ReMine
Robert Williams
[This is actually a reply to a post by Walter Remine from 12/03/97 -
that post is no longer "visible" to me for my reply.]
Walter wrote:
>For ease of discussion (and solely for ease of discussion) let us
>suppose the population size remains constant. Suppose that in a given
>generation 100 individuals with the old trait meet their genetic deaths
>-- the end of a line of inheritance -- finito. Over that generation
>there are now 100 fewer individuals with the old trait. If the
>population is to remain the same size, then these must be replaced. By
>what? By individuals with the new trait, and this requires genetic
>births -- excess births by individuals with the new trait.
>Devastatingly simple, yes?
>Next suppose the generation began with only 2 individuals with the new
>trait. This scenario would require them to have a reproductive excess
>of 50 (=100/2). This is the cost of substitution incurred for that
>generation. If the species cannot supply that level of reproductive
>excess, then the scenario is not plausible. Indeed, the scenario is not
>plausible for higher mammals.
Who ever said that 100 of the individuals with the old trait had to die
when there were only 2 individuals with the new trait? I carefully
worked out equations to show that this was not the case - that
individuals carrying the old trait didn't start dying until there were
sufficient numbers of individuals bearing the new trait to produce
competitive pressure. If it weren't for the fact that I imposed density
dependent selection to hold the population constant, none of the
individuals carrying the old trait would have died (genetically). The
only condition under which 100 individuals with the old trait would die
when there are only 2 individuals carrying the new trait is in the case
of a deteriorating environment as described by Haldane in "The Cost of
Natural Selection".
I don't know where you came up with your definition for cost, but I have
been using the definition proposed by Haldane. On page 511 of "The Cost
of Natural Selection", Haldane states:
"In what follows, I shall try to estimate the effect of natural
selection in depressing the fitness of a species."
Further, on page 516 of this paper ("The Cost of Natural Selection"), he
states:
"The cost of changing q from q1 to q2 is
[the integral from q1 to q2 of] dq/(1-q) + O(k) = ln[(1 - q2)/(1
- q1)] + O(k),
which is nearly independent of k."
(The above was quoted to the best of my ability using a simple font -
i.e. not very well.)
k is the selection coefficient of the favorable allele, q1 is the
initial frequency of the allele for the old trait, and q2 is the final
frequency of the allele for the old trait. We are interested in fixation
from a low frequency (p0) to 1 for the new allele, so q1 is very near 1
( 1 - p0 to be exact), and q2 = 0. Therefor, the cost of substitution is
ln[ (1 / p0)] + O(k). This is equivalent to -ln(p0) + O(k), which is
precisely what Haldane had calculated on the previous page as D, the
cumulative fraction of selective deaths that were required for a
substitution. This is the number that Haldane estimated to be typically
30 times the population size. It is simply the summation of k*q for each
generation as q goes from 1 - p0 (almost 1) to 0. This could be a large
number in a deteriorating environment, but this is not the case for a
beneficial allele, as I showed in my previous post.
Walter, if you have a different definition for the cost of natural
selection than the one by Haldane, would you please provide references
for it?
Walter also wrote:
>Haldane understood (correctly) that a species' entire fecundity could
>not all be used to pay the cost of substitution. Only a portion of it
>could. He estimated that higher mammals have a reproductive excess of
>ten percent (0.1) that can be applied to substitutions. Robert used a
>figure fully 30 times higher, thereby achieving a substitution rate
>nearly 30 times faster. That's all Robert did. He did not reduce the
>cost of substitution one whit. He merely artificially increased the
>reproductive payments.
As for only 10% of the fecundity being applied to selection, I don't
think Haldane made a very good case for this. On page 520 and 521 of
"The Cost of Natural Selection", Haldane states :
"Suppose then that selection is taking place slowly at a number of loci,
the average rate being one gene substitution in each n generations, the
fitness of the species concerned will fall below the optimum by a factor
of about 30/n, so long as this is small. If the depression is larger, we
reason as follows. If a number of loci are concerned, the ith depressing
fitness by a small quantity di, the mean number of loci transformed per
generation is 1/D * [the summation of all]di, or about 1/30 * [the
summation of all]di. The fitness is reduced to [the product of all](1 -
di), or about exp(-[the summation of all]di). But n = 30 * [the
summation of all]di, roughly. Thus, the fitness is about exp(-30 / n),
or the intensity of selection I = 30 / n."
Haldane continues a little further down:
"I think n = 300, which would give I = 0.1, is a more probable figure.
Whereas, for example, n = 7.5 would reduce the fitness to exp(-4), or
0.02, which would hardly be compatible with survival."
Once again, Haldane is working from his model of common genes becoming
deleterious because of a change in the environment. This is not at all
the same thing as the case of new beneficial genes arising which leads
to an increase (not a reduction) of overall fitness. Please note that
this was Haldane's only justification for using a minimum of 300
generations for a substitution to occur. His estimate of 300 generations
was based solely upon keeping the overall fitness at a reasonable level
in a deteriorating environment - it had nothing to do with an estimate
"that higher mammals have a reproductive excess of
>ten percent (0.1) that can be applied to substitutions." I don't know where Walter is coming from with that claim.
Robert Williams
Donal Hickey
Walter,
Thank you for your extensive answer to my question. I'm still not sure
that I understand your position. Let me summarize what I think you are
saying. You can correct me if I'm wrong.
It seems to me that you believe:
(i) evolution did occur;
(ii) The "standard genetic model" that describes the evolutionary
process is incorrect.
(iii) evolutionary biologists continue to promulgate this erroneous
model. (Why?)
This leads me to further questions.
1. If you believe that evolution did occur, do you think it happenned by
the mechanisms of natural selection, as outlined by Darwin? I assume you
do - otherwise you wouldn't be worrying about the nitty-gritty
quantitifaction of the process.
2. What do you mean by the "standard genetic model"? Do you include all
of population genetics theory in this?
3. If you believe that the standard genetic model is inadequate, do you
have an alternative to offer? In most debates - be they scientific,
political or otherwise - criticism is usually a prelude to delivering
the "right" answer.
Thank you.
Donal.
===============================================================
wjre...@mmm.com wrote:
Donal Hickey
> Robert Williams wrote:
> but I also believe that the cost is non-existant in the case of a
>new, beneficial allele in a constant population size. Note that the
>density dependant selection that I will be talking about here is not an
>effort to side-step the cost of natural selection - it is simply a
>device to maintain a constant (not increasing) population. Let's look at
>what happens for the haploid case.
I see what you are doing in your model. The population has the potential
to expand by a factor of F every generation, but the constraints imposed
by the environmental carrying capacity prune the numbers back every
generation, by a process of non-selective deaths. By introducing a
genetic variance, one has the possibility of changing these
non-selective deaths into selective deaths, without increasing the total
number of deaths. In other words, selection does not increase the total
"load" in this case. It simply converts non-selective deaths into
selective deaths. The limitation, it would seem, is the number of
non-selective deaths that are available for such conversion.
>At any rate, what I am really interested in is what is the maximal
>substitution rate under these conditions? The maximal (theoretical)
>value of s is F - 1 ( as I believe Dr. Felsenstein pointed out (in
>1971!) in one of the papers mentioned earlier in this thread). This is
>because the fitness of an organism cannot be greater than its fecundity,
>and we have imposed the condition of constant population size, so we
>cannot increase F to increase the substitution rate.
This summarizes the core of the problem very nicely, and gets back to
Haldane's point that these considerations are most relevant to organisms
with long generation time and low fecundity, such as cattle. During the
evolution of artiodactyls from their early mammalian ancestors,
generation times have probably increased and fecundity decreased. One
reading of Haldane's theory would lead us to conclude that these
lineages risk losing the potential to adapt rapidily to future selective
pressures. Alternatively, we might be able to show that, although
lowered fecundity places more stringent limits on the theoretical,
maximal rates of evolutionary change, this does not, in fact, pose a
problem for any real species. In other words, fecundity - even in those
species with relatively low fecundity - may not be the limiting factor
in adaptive evolution. Your simulations might help shed some light on
the situation.
Donal.
wjre...@mmm.com
Per Erik Jorde wrote:
> There is no "doubling" involved in this scenario: at the haploid stage
> there are 2N gametes (sperm/egg) with one gene each; at the diploid
> stage there are N zygotes with 2 genes each. The number of genes, 2N,
> is the same at all stages.
The way Erik tabulated the genes, yes, "The number of genes, 2N, is the
same at all stages". But they are typically NOT all the same genes with
the same gene frequencies as before. Some of the genes increase, and
some decrease -- randomly, through the process I described previously.
Examine this stochastic reproductive excess further. Imagine one new
mutation that exists only in one individual, say a male. That gene has
a 50% probability of making it into a given sperm. Nonetheless, by
random chance, that gene can end up in all his progeny. That is
reproductive excess! It exists in this case, at the level of the gene,
even if each couple has exactly TWO children (so there is no
reproductive excess at the level of the individual).
After a generation or so, let's say this same gene has worked its way
into males and females. Now the gene exists in sperms and eggs. We
then have, conceptually, another version of stochastic reproductive
excess. Remember to take this from the gene's eye-view. This time
imagine there is one copy of the gene in an individual, the individual
happens to be an unfertilized egg. A moment later (after sperm and egg
join) there are TWO copies of that same gene in the individual. From
the gene's eye-view this is a source of stochastic reproductive excess.
It went from one to two. This occurred via a random process that tends
on average to leave the gene frequency unchanged, but which has
short-term fluctuations.
> An heterozygote individual, Aa, may produce the following sets of two
> gametes: {A,A} {A,a} {a,A} and {a,a}; all with equal probability.
> There are no "reproductive excess" involved here, yet two of the
> outcomes do result in change in the allele frequencies, even if
> the alleles are selectively neutral. Hence, all species can bear
> this "cost", because there is no cost.
Erik says there is "no reproductive excess" in his example. He is
mistaken. It contains the same stochastic reproductive excess I
described previously and above.
Erik makes a second mistake. He started by (mistakenly) claiming there
is "no reproductive excess." From that he concludes "there is no
cost". That is erroneous logic. It does not follow. The two are
different. The absence of reproductive excess would not mean there is
an absence of cost.
Joe Felsenstein
>Yes. There is general agreement that reproductive excess is required
>for something to go from 'few' to 'many', as repeatedly required by the
>the evolutionary model. I regard it as almost true by definition, it's
>that obvious.
>
>> This discussion seems to risk degenerating into a
>> discussion about the definition of various words,
>> ....
>
>Joe Felsenstein and I are momentarily debating whether a stochastic form
>of reproductive excess exists (as I claim it does) at the level of the
>gene, and that it can pay for neutral substitutions.
It is a matter of taste whether you choose to say that Mendelian segregation
creates a reproductive excess. I choose not to, ReMine chooses to. Donal
Hickey is right that this is about word definitions, and is not worth
worrying about.
I don't think that's what I am disputing with ReMine. The issue is not what
happens in the case of deleterious changes of environment, where everyone
since Haldane has agreed that there is a cost (imposed by the change of
environment, as I emphasized in 1971), and that too many such changes will
exhaust the reproductive excess and lead to extinction.
The issue is not (in spite of what ReMine says) what happens in cases of
neutral mutation. Even ReMine acknowledges that there is not limit
on their rate (aside from the limit set by the number of such mutations).
One can play semantic games about defining a reproductive excess but it
does not limit anything.
The issue is ReMine's claim that
>Beyond that there is another simple step in our argument. Reproductive
>excess is not merely 'required' for substitutions -- its magnitude (or
>lack thereof) limits the *rate* of beneficial substitution.
... and whether there is some limit that reproductive excess places on the rate
of substitution due to advantageous mutations. Once can calculate a cost,
but the catch is that each mutant not only imposes a cost, it also adds to
the reproductive excess available to pay the cost, so the population ends
out better off for the advantageous mutant having occurred. The "cost"
and "excess" do not, in this case, limit the rate of substitution.
ReMine has not yet grappled with this issue. The other issues are
not controversial, and I am certainly not going to spend time worrying about
whether there is or is not a "stochastic form of reproductive excess" as it
has no consequences worth worrying about.
wjre...@mmm.com
Robert Williams wrote:
> I don't know where you came up with your definition for cost,
For sake of discussion, let's use Robert's definition of cost, which he
gets (appropriately enough) from Haldane. The formula Robert cites is
for haploid organisms, where all genes are effectively dominant.
> "The cost of changing q from q1 to q2 is
>
> [the integral from q1 to q2 of] dq/(1-q) + O(k)
> = ln[(1 - q2)/(1 - q1)] + O(k),
> which is nearly independent of k."
>....
> k is the selection coefficient of the favorable allele, q1 is the
> initial frequency of the allele for the old trait, and q2 is the final
> frequency of the allele for the old trait.
(Note: the above error term "O(k)" disappears for small selective values
k.)
Focus on the integrand above:
#1) Cost of substitution for a given generation = dq/(1-q)
That value is summed (or integrated) every generation as q goes from its
starting value (near 1) to its final value (near 0). This particular
equation also assumes a constant population size, which means the
following identities hold true.
#2) 1-q = p
#3) dq = -dp
Identity #3 indicates that any decrease in q must perforce be balanced
by an identical increase in p.
Lastly, we replace the limits of integration (in terms of q) with their
equivalents (in terms of p). This reverses the order of integration.
(The original integration order was from high-to-low values of q. This
gets replaced by an integration whose order is from low-to-high values
of p). This reversal of the integration order introduces a change of
sign into the result, which cancels the negative sign that came from
identity #3.
The above changes were simple identities -- nothing that affects the
cost. We now see:
#4) Cost of substitution for a given generation = dp/p
That quantity is summed (or integrated) every generation to give the
total cost of substitution. This is nothing new, this same cost formula
shows up often in papers on Haldane's Dilemma.
But what is dp/p ? It is the excess birth rate (specifically for
individuals possessing the new mutation under substitution). That is
what the cost of substitution is. It is the reproductive excess
required by a given scenario.
For example, if the new trait is claimed to increase by five percent in
a generation, then these individuals must be capable of producing five
percent excess reproduction for this task. If they cannot, then the
scenario is not plausible. The logic is very direct.
As I said before, the genetic deaths are just a way to tally the genetic
births required by a scenario. Genetic births -- excess reproduction --
is the central issue.
Lastly, the result of the above integration gives the total cost of
substitution.
#5) Cost = ln( 1/ p0 )
where: ln( ) is the natural log,
and p0 is the starting frequency of the new mutation.
This happens to be the lowest cost for any single substitution under any
and all circumstances. It is for a dominant mutation (or for a haploid
species, where all mutations are effectively dominant). It requires the
substitution to proceed monotonically upward and infinitely slowly.
This optimally low cost requires very small values of selective
advantage to achieve.
Especially notice that the formula (and its derivation) has NOTHING to
do with the old trait, or how they die. One can jump into the derivation
at formula #4, and calculate the cost of substitution (#5) without ever
mentioning the individuals with the old trait, or the many other
confusion factors so common in the literature.
******
> I carefully worked out equations to show that ...
> individuals carrying the old trait didn't start dying until there were
> sufficient numbers of individuals bearing the new trait to produce
> competitive pressure. If it weren't for the fact that I imposed density
> dependent selection to hold the population constant, none of the
> individuals carrying the old trait would have died (genetically).
Robert here makes a small conceptual error. He says individuals with
the old trait "didn't start dying until there were sufficient numbers of
individuals bearing the new trait". He is mistaken. For a constant
population size, every increase in the new trait must perforce be
matched by an equal decrease in the old trait (and vice-versa).
Density-dependent selection is irrelevant to that dynamic.
More importantly, Robert's example of density-dependent selection is
irrelevant to the cost of substitution. In his example (which involves
a dominant substitution), it doesn't matter how (or when) the
individuals with the old trait die out. They are goners. Forget 'em.
The cost of substitution can be calculated without referring to them.
Again, the central issue is the growth of the new trait, and that is
limited by the specie's finite reproduction.
******
> Haldane is working from his model of common genes becoming
> deleterious because of a change in the environment. This is not at all
> the same thing as the case of new beneficial genes arising which leads
> to an increase (not a reduction) of overall fitness.
Why did Haldane focus on substitutions that resulted from changes in the
environment? That is the query Robert began this thread with. The
answer is cost -- Haldane was (artificially) trying to reduce it.
Haldane saw (correctly) that the cost of substitution is lower when the
new trait has less distance to increase. He therefore sought to
decrease the cost by giving the substitution a head-start. That is, he
suggested a near neutral mutation enters the population and makes its
way upward to modest frequencies either via drift or mutation pressure.
Then the environment changes, and (Shazam!) the near-neutral mutation
gets converted to a beneficial mutation (either directly, or merely
relative to the old trait which is suddenly rendered disadvantageous).
>From that point onward the cost of substitution is incurred. That is
what Haldane was up to with his environmental-change scenario -- he was
trying to (artificially) reduce the cost of substitution.
The cost of substitution doesn't depend on whether the old trait becomes
harmful (say, due to an environmental change). All that matters is that
the new trait goes from 'few' to 'many' -- and that absolutely requires
reproductive excess.
> Please note that this [environmental-change scenario]
> was Haldane's only justification for using a minimum of 300
> generations for a substitution to occur. His estimate of 300 generations
> was based solely upon keeping the overall fitness at a reasonable level
> in a deteriorating environment
Robert is attempting to brush off Haldane's results as applying "only"
to the situation of a deteriorating environment. Robert is mistaken.
The environmental-change scenario was nothing more than an attempt to
reduce the cost of substitution. Haldane based his cost estimate on his
environmental-change scenario, which is one of the reasons why his cost
estimate may be said to be too *low*. The cost is higher, and Haldane's
Dilemma even more acute, when the scenario does not apply.
(Note: My book specifically discusses why the environmental-change
scenario cannot plausibly increase the effective substitution rate.
Briefly, it is like trying to get a free-lunch from nature, and on
average, nature cannot give a free-lunch. When fully tallied, the
environmental-change scenario actually worsens Haldane's Dilemma. See
my book for detailed arguments on the environmental-change scenario.)
wjre...@mmm.com
The exchange with Jonah Thomas now has a high thrashing-to-insight
ratio, and I am not likely to pursue it further, as I doubt most readers
will either. I'll confine myself to the main point.
Jonah claims the cost of substitution predicts extinction. I say it
does not -- it is not a theory of extinction, it is a criterion of
plausible substitution rates.
To make his point, Jonah offers a scenario where the entire population
has a reproduction rate of .99 offspring per individual or less. There
is no reproductive excess, in fact there is a reproductive deficit. In
other words, the population is predicted to go extinct -- and that
prediction is obvious before any considerations about the cost of
substitution. The prediction of extinction is given entirely by Jonah's
special situation -- not by the cost of substitution.
Per Erik Jorde
wjre...@mmm.com writes:
>
> Examine this stochastic reproductive excess further. Imagine one new
> mutation that exists only in one individual, say a male. That gene has
> a 50% probability of making it into a given sperm. Nonetheless, by
> random chance, that gene can end up in all his progeny. That is
> reproductive excess! It exists in this case, at the level of the gene,
> even if each couple has exactly TWO children (so there is no
> reproductive excess at the level of the individual).
>
I take it that you mean that in order for genetic drift to happen you
need an excess production of gametes, only some of which make it into
the zygotes, and that it is this "reproductive excess" you are
referring to when stating (previously in this thread):
"To go from 'few' to 'many', a reproductive excess is
required -- absolutely, positively, no exceptions. The formulas for
cost of substitution calculate just how much reproductive excess is
required for a given scenario. If the species is incapable of supplying
the necessary level of reproductive excess, then the given scenario is
not plausible."
Here, you clearly imply that this required "reproductive excess" may
place a limit on the amount of genetic change that the species can
tolerate. Considering genetic drift this is nonsense. First, AFAIK all
species produce an excess of gametes above the required 2. Second,
given such an excess of gametes there is no limit to the number of
loci whose frequencies can change because of drift: a large number of
loci does not require any more "excess" than a single one.
Per Erik Jorde p.e....@bio.uio.no
--
wjre...@mmm.com
Joe Felsenstein wrote:
> So apparently ReMine wants to redefine reproductive excess ...
Reproductive excess has the same old, straightforward meaning it always
did. If an entity is reproduced once, that is required just to purchase
its continuity into the next generation. Reproduction above and beyond
that amount is reproductive EXCESS. It is required in order to pay the
reproductive costs of various evolutionary scenarios.
I do not redefine reproductive excess, I merely claim it exists in more
than one form, and at more than one level. There is reproductive excess
at the level of individual bodies -- that is how we traditionally
thought of the term. But there is also stochastic (random) reproductive
excess that exists in several forms covered in my book. For example, it
occurs at the level of the gene. From a gene's eye-view there can be
(and *is* in Felsenstein's earlier example) stochastic reproductive
excess at the level of the gene.
<continuing>
> (proclaiming all the while that he and he
> alone has understood the concept)
No, I didn't say 'I and I alone' understand the concept. That is
needlessly inflammatory Joe. But I can defend my material as a new
contribution to our understanding of Haldane-style cost/payment theory,
and as something for which no one ought be made to feel ashamed. :-P
******
> In fact, ReMine concedes that the reproductive excess
> does not set any limit on the rate of neutral substitution:
....
> So the cost does not place any limit on the
> rate of neutral substitution.
Let me expand on that. Two separate arguments set limits on
substitution rates -- (1) the mutation rate, and (2) cost-payment
analysis, whichever gives the LOWER rate is the one that prevails.
Concerning *neutral* substitutions, special mechanisms come into play
which automatically increase the rate given by cost-payment analysis
until it exactly matches the rate set by the neutral mutation rate.
There are still costs, and they are still paid, but in the end the
neutral mutation rate is what sets the limit on the neutral substitution
rate.
Again, there are special mechanisms that affect a cost-payment of
neutral substitutions. My book identifies what they are. (They had
never been identified before, because previous commentators mistakenly
viewed neutral substitutions as having "no cost".) My book also
identifies why those same mechanisms cannot help the beneficial
substitution rate.
******
> OK, is there any limit set in the case of advantageous mutation? I would
> have said no, as each advantageous mutation increases the fitness of
> the population, in effect creating extra reproductive excess.
Felsenstein here gives a very different argument (almost contradictory)
from his earlier one that began this thread. Earlier he argued that
beneficial substitutions have "no cost" because they provide a benefit.
Now he implicitly accepts that they have a cost but claims they make up
for it by creating "extra reproductive excess."
We already accept the idea that a beneficial substitution can sometimes
increase reproductive excess. But that does not change the fact that a
specie's reproductive excess is limited -- reproductive excess cannot
increase in perpetuity. Haldane's Dilemma does not require us to track
instantaneous rates, instead it is about long-term averages over the
range of situations the species is likely to encounter. That is:
Haldane's Dilemma is about long-term average costs,
and long-term average rates of reproductive excess
-- which allow us to calculate
the maximum plausible long-term average rate of substitution.
So the instantaneous reproductive excess can be bobbing up and down a
bit, for whatever reasons, just as Joe suggests. That does not change
the fact that the long-term average reproductive excess is limited, and
that limits the substitution rate.
Let's take a specific example. Suppose a new mutation increases its
numbers by five percent in one generation. This requires that the
species be capable of supplying a reproductive excess of five percent to
pay for this. Now let's assume Joe's idea, that this five percent
increase in reproduction is caused **by the new mutation itself.** That
scenario is not remotely plausible over the long-term, because
reproduction rates cannot increase ad infinitum.
In fact, Felsenstein's idea can worsen the problem. In Haldane's
Dilemma we assess the reproductive excess of known species, and project
that back into the past. To apply Felsenstein's idea, we must
extrapolate it *downward* in the past to account for the lower
reproduction his scenario claims organisms had in the past. That would
*reduce* the substitution rate in the past.
Over the long-haul, nothing comes for free in Haldane's Dilemma. People
often invent special scenarios in an effort to ease the problem, but
when fully tallied over the long-haul, one finds they tend to make the
problem worse. That is the case here with Felsenstein's scenario. It
does not, even slightly, reduce the problem of Haldane's Dilemma.
In the end, there is still the cost of substitution (which is
unavoidable, and Joe has not reduced it), and the specie's reproductive
excess (which is limited, and Joe has not increased it), and these limit
the beneficial substitution rate. Joe has not altered that dynamic even
a little. I emphasize again, this dynamic is so unavoidable it even
shows up in computer simulations of evolution.
******
> I would have said that my 1971 paper has been relatively little-noticed
> since then, and the whole discussion of cost of natural selection subsided
> soon after, and has attracted little attention since.
Above Joe confirms key points of what I've been saying:
One cannot find in the literature any evolutionists
directly challenging Felsenstein's solution to Haldane's
Dilemma. They allowed Felsenstein's mistaken notion to
thrive for decades unchallenged, (even while some proposed
their own solutions that implicitly contradicted Felsenstein).
Haldane's Dilemma has been obscured and brushed aside, it was
never solved.
wjre...@mmm.com
Per Erik Jorde wrote:
> I take it that you mean that in order for genetic drift to happen you
> need an excess production of gametes, only some of which make it into
> the zygotes,
Close, but not quite. The excess production of gametes is one source of
stochastic (random) reproductive excess. It is as the level of the
gene. I also said there are other sources of stochastic reproductive
excess -- and some of these occur at the level of the individual. So,
there are stochastic sources at the level of the gene and at the level
of the individual. We can conduct thought experiments (as Joe
Felsenstein did) where we artificially eliminate one of the sources, and
the other is still sufficient to produce an increase in a neutral
mutation (i.e. genetic drift).
> you clearly imply that this required "reproductive excess" may
> place a limit on the amount of genetic change that the species can
> tolerate. Considering genetic drift this is nonsense.
I emphasize again that my discussion about stochastic reproductive
excess and genetic drift was concerned with the rise of *neutral*
mutations. (In response to a question from Joe Felsenstein.) I also
said there are special mechanisms operating that effectively remove the
cost/payment limits from *neutral* substitutions, and that these
mechanisms are not available to help the beneficial substitution rate.
The Haldane-style cost limitations apply specifically to *beneficial*
substitutions.
wjre...@mmm.com
Joe Felsenstein wrote:
> It is a matter of taste whether you choose to say that
> Mendelian segregation creates a reproductive excess.
> I choose not to, ReMine chooses to. Donal Hickey is
> right that this is about word definitions, and is not worth
> worrying about.
> I am certainly not going to spend time worrying about whether
> there is or is not a "stochastic form of reproductive excess"
> as it has no consequences worth worrying about.
Joe Felsenstein indicates his strong dis-interest in worrying about an
issue that, in fact, he did worry about, and bothered us all to worry
about too. It was he who raised the issue via his (mistaken) challenge
concerning neutral mutations. Recall that he conducted a thought
experiment where he claimed to remove all the reproductive excess yet
the neutral mutations could still rise to fixation. He said this
countered my claims about reproductive costs and payments. I responded
by pointing out his mistake: There still is a source of reproductive
excess -- it is stochastic and (in his example) exists at the level of
the gene.
Felsenstein is further mistaken that this is merely a "semantic game" in
which one may arbitrarily "choose" word definitions. The truth of the
matter is that there *is* stochastic reproductive excess -- that is a
fact. Moreover, it is responsible for the rise of neutral
substitutions. This is not a matter of choice, or flimsy semantics.
My excursion into neutral substitutions shows (as I argue here and in my
book) a coherent, consistent approach to the Haldane-style cost-payment
theory. That is worthwhile simply for the clarity, unity, and coherence
it brings to the field. The cost-payment theory reaches a conclusion
about the neutral substitution rate that happens to coincide with the
traditional claims -- but does so via a mutually-exclusive explanation.
They cannot both be correct explanations, because they contradict each
other. (The traditional approach claimed neutral substitutions have "no
cost". I claim they individually have a high cost, and I identify
specific means by which it is abundantly paid.)
After raising the issue himself, Felsenstein now says the issue is "not
worth worrying about" because "it has no consequences". That is a
lamentable position to take, especially for a professor and educator.
The correct explanation is worth worrying about simply for the sake of
truth and because it clarifies our theoretical understanding.
******
Compare the following two statements:
> .... everyone since Haldane has agreed that there is a cost
> (imposed by the change of environment, as I emphasized in 1971),
> and that too many such changes will exhaust the reproductive excess
> and lead to extinction.
> One can play semantic games about defining a reproductive excess but it
> does not limit anything.
Joe just contradicted himself. In the first statement his says
reproductive excess sets a limit on something, in the second he says it
does not.
>From the context let me interpret what he is up to, because he does not
make it explicit. We both agree that *neutral* substitutions are not
limited by reproductive excess, they are limited by mutation-rate.
Felsenstein, I think, is attempting to toss beneficial substitutions
into that same boat with the neutrals. But I say the boat they belong
in is the one identified in his 1971 paper.
Let me describe that paper. He takes a situation where the population
is repeatedly experiencing harmful change (like harmful mutations,
except produced by random changes in the environment). The harmful
changes make the predominant old alleles disadvantageous, and this
repeated deteriorative process would inevitably lead to extinction (much
like an overwhelming rate of harmful mutation). What can save the
species from extinction? Felsenstein's scenario assumes that at moments
of harmful environmental change a rare near-neutral mutation suddenly
becomes advantageous by comparison. This begins a substitution process,
and the question is: Can the population make these beneficial
substitutions at a rate sufficient to avert the predicted extinction?
Felsenstein concludes that if the species lacks sufficient reproductive
excess, then the necessary substitution rate is not plausible, and the
species cannot avert the predicted extinction. I agree with that
conclusion. Let me repeat: Felsenstein agrees that the beneficial
substitutions achieved by his scenario are cost-limited.
However, Felsenstein claims this cost limitation does not apply to
directly-beneficial mutations, those received in the absence of harmful
environmental change. I claim that the cost of substitution is IDENTICAL
in both cases. The *source* of the beneficial mutation does not matter.
All that matters is that it goes from 'few' to 'many' -- and thereby
incurs a cost of substitution. Moreover, because it is not a neutral
substitution, the special mechanisms that remove cost-limitations for
neutral substitutions are not available to it. I say the limitations to
substitution rate that Felsenstein agrees to in his paper apply to ALL
beneficial substitutions, not just those created by environmental
change.
In other words, reproductive excess does limit something, and
Felsenstein (and least partly) identified it in his 1971 paper -- it
limits the beneficial substitution rate.
******
In the following section Joe and I discuss 'directly' beneficial
mutations (not those converted by environmental-change, which we already
agreed are cost-limited).
> One can calculate a cost, but the catch is that each
> [beneficial] mutant not only imposes a cost, it also adds to
> the reproductive excess available to pay the cost, so the population ends
> out better off for the advantageous mutant having occurred. The "cost"
> and "excess" do not, in this case, limit the rate of substitution.
Felsenstein's above statement is (or seems to be) opposite of his
earlier claims (and the claims from his 1971 paper) where he said
beneficial substitutions "do not impose any cost." Now he explicitly
acknowledges that beneficial substitutions do have a cost and it can be
calculated, but he says they pay for themselves by producing higher
reproductive excess. That precise posture is nowhere visible in his
1971 paper. Is he now contradicting his earlier idea? Or is this
merely a more refined articulation of his earlier idea? I am not
concerned with sorting that out. The literature on Haldane's Dilemma is
rife with ambiguous, sloppy, and mistaken usages of the cost concept,
and that has much to do with why the problem was never solved. I flag
it as a matter of historical, though only passing, interest. I am far
more concerned with where all this leads.
So let me congratulate Joe Felsenstein for his clearest statement so far
of our central issue. He is definitely getting clearer, perhaps as a
result of our dialog. That is a key purpose of scientific dialog, and I
respect him for sticking with it.
I will argue that his above idea does not even slightly ease Haldane's
Dilemma.
Some beneficial substitutions will increase the reproductive excess of
the species, while some will reduce it (say, in favor of increased
probability of survival). Haldane's Dilemma does not require us to
identify the one from the other, nor must we track specific mutations to
measure the reproductive excess that they specifically produce. All of
that is washed away by one overwhelming set of facts: A specie's
reproductive excess is limited and we can measure it.
Haldane's Dilemma is concerned with long-term averages. That is:
Long-term average costs of substitution, and
long-term average rates of reproductive excess,
allow calculation of the maximum plausible
long-term rate of beneficial substitution.
This does not mean the calculated substitution rate is actually
achieved, since the contour of the fitness terrain offers many other
additional obstacles to the evolutionary process. The calculated
substitution rate is merely the maximum plausible rate given the average
limitations of cost and reproduction.
Felsenstein's argument does not ease that dynamic one bit. A specific
beneficial mutation can alter the reproductive excess, just as
Felsenstein claims. But that has precious little bearing on the
problem. He must make a case for credible rates of reproductive excess,
and he has not even attempted to do so. He merely alludes to
unsustainable, ever increasing rates of reproductive excess, that have
no basis in observation.
Robert Williams
wjre...@mmm.com wrote:
>=20
> Robert Williams wrote:
>=20
> > I don't know where you came up with your definition for cost,
n
for the selective deaths (in a deteriorating environment) as a valid
definition for the substitution cost. ]
Well, Walter, dp/p is a perfectly valid statement of the selective
deaths in a generation in a deteriorating environment, and -ln(p0) is
the summation of those deaths over the course of substitution, as per
Haldane's "The Cost of Natural Selection". No one is disputing that
here. But, my question all along (and my reason for starting this
thread) is : is the substitution cost (the total number of selective
deaths) as calculated by Haldane for a deteriorating environment (i.e. a
common allele has become disadvantageous) the same as the substitution
cost for the fixation of a rare, beneficial allele? I have given
equations, derivations, and simulations in my post of 12/01/97 under
this thread as to why I believe the two costs are not the same.
In fact , it's becoming very clear to me that the problem rests solely
on the number of selective deaths in a generation. In a deteriorating
environment, the selective deaths are s*q (s =3D selection coefficient, q
is frequency of gene being replaced) generation after generation after
generation. But in the case of a population of constant size with a
rare, beneficial allele being fixed, as long as the beneficial allele is
rare, the selective deaths are rare. In this case, the selective deaths
are s*p*q/(1 + s*p) per generation - remember the equation I derived on
12/01:
(1/F) * p + s*q*p / [ F * (1 + s*p)] + (1/F) * q - s*q*p / [ F *(1
+ s*p)] =3D 1/F
If you multiply through by F, you get:
P + s*q*p/(1 + s*p) + q - s*q*p/(1 + s*p) =3D 1
Notice that q is reduced by s*q*p/(1 + s*p) each generation, not s*p!
Notice further that p is increased by exactly the same amount, as you
and I agree must be the case for the population to remain constant.
Guess what the summation of s*q*p/(1 + s*p) over the course of fixation
is. It's 1, regardless of the values of p, q, s, N( the population
size), or F(the fecundity) so long as s <=3D F - 1. I know this because
I've calculated the cost a hundred times or more. Here's a simulation
program for anyone who wants to try the calculations for themselves -
just run it in your favorite BASIC interpreter such as QBASIC that comes
with Windows on PCs:
10 mod1 =3D 1
20 N =3D 100000
30 p =3D 1 / N
40 q =3D 1 - p
50 s =3D .01
60 gen =3D 0
65 COST1 =3D 0
67 COST2 =3D 0
70 gen =3D gen + 1
80 p =3D (1 + s * q / (1 + s * p)) * p
90 qnew =3D 1 - p
92 COST1 =3D COST1 + q - qnew
95 q =3D qnew
96 COST2 =3D COST2 + s * p * q / (1 + s * p)
100 IF gen MOD mod1 =3D 0 THEN PRINT "N - "; gen, "p is : "; p, "q is: ";
q, "COST is "; COST1
110 IF p < .99 THEN 70
120 PRINT "p is : "; p, "n is: "; gen, "COST1 is "; COST1, "COST2 is ";
COST2
(We have such a huge advantage over Haldane with modern computers - we
can check our results!)
I also know that the cost is always 1 under these conditions because if
the selective deaths each generation is s*p*q, then the proper integral
to use is the integral from q0 (essentially 1) to 0 of dq (NOT
dq/(1-q)). Obviously the solution to this is always (almost) 1 (NOT the
ln(p0) as per Haldane for the case of a deteriorating environment). =20
> > I carefully worked out equations to show that ...
> > individuals carrying the old trait didn't start dying until there wer=
e
> > sufficient numbers of individuals bearing the new trait to produce
> > competitive pressure. If it weren't for the fact that I imposed densi=
ty
> > dependent selection to hold the population constant, none of the
> > individuals carrying the old trait would have died (genetically).
>=20
> Robert here makes a small conceptual error. He says individuals with
> the old trait "didn't start dying until there were sufficient numbers o=
f
> individuals bearing the new trait". He is mistaken. For a constant
> population size, every increase in the new trait must perforce be
> matched by an equal decrease in the old trait (and vice-versa).
> Density-dependent selection is irrelevant to that dynamic.
>=20
For a little bit Walter, I could get really annoyed over that passage.
You have carefully excised the very telling question I asked you in that
paragraph. Here it is in full:
-----------
Who ever said that 100 of the individuals with the old trait had to die
when there were only 2 individuals with the new trait? I carefully
worked out equations to show that this was not the case - that
individuals carrying the old trait didn't start dying until there were
sufficient numbers of individuals bearing the new trait to produce
competitive pressure. If it weren't for the fact that I imposed density
dependent selection to hold the population constant, none of the
individuals carrying the old trait would have died (genetically). The
only condition under which 100 individuals with the old trait would die
when there are only 2 individuals carrying the new trait is in the case
of a deteriorating environment as described by Haldane in "The Cost of
Natural Selection".=20
--------------
I stand by the statement that "individuals carrying the old trait didn't
start dying until there were
sufficient numbers of individuals bearing the new trait to produce
competitive pressure." Since the selective deaths for a given generation
are s*p*q, as long as s < F -1 (the fundamental limitation to the
substitution rate for a single gene under these conditions), since p and
q are both guaranteed to be less than 1, the selective deaths will
always be less than the reproductive excess of the p individuals.
Furthermore, are you going to answer the question, or not? Under the
scenario I have laid out, exactly when would 2 individuals with the
favorable trait going to have to "make up" for the deaths of 100
individuals with the old trait. This never happens under the conditions
of selection for a favorable allele, and I have produced the equations
and simulations to prove it. Stop waving your arms and plugging your
book and either show me where I am wrong or retract the statement. If
you have visited my web site recently, you know that if I make a
mistake, I will admit it, but so far you haven't uncovered any flaws in
my arguments on this topic.
> More importantly, Robert's example of density-dependent selection is
> irrelevant to the cost of substitution. In his example (which involves
> a dominant substitution), it doesn't matter how (or when) the
> individuals with the old trait die out. They are goners. Forget 'em.
> The cost of substitution can be calculated without referring to them.
> Again, the central issue is the growth of the new trait, and that is
> limited by the specie's finite reproduction.
I agree that the rate of substitution is limited by the species
reproduction rate. I just don't believe that you have shown that the
rate is 1 substitution per 300 generations as per Haldane. Nobody here
is claiming that a beneficial allele instantly becomes fixed. =20
>=20
> ******
>=20
> > Haldane is working from his model of common genes becoming
> > deleterious because of a change in the environment. This is not at al=
l
> > the same thing as the case of new beneficial genes arising which lead=
s
> > to an increase (not a reduction) of overall fitness.
>=20
> Why did Haldane focus on substitutions that resulted from changes in th=
e
> environment? That is the query Robert began this thread with. The
> answer is cost -- Haldane was (artificially) trying to reduce it.
> Haldane saw (correctly) that the cost of substitution is lower when the
> new trait has less distance to increase. He therefore sought to
> decrease the cost by giving the substitution a head-start. That is, he
> suggested a near neutral mutation enters the population and makes its
> way upward to modest frequencies either via drift or mutation pressure.
> Then the environment changes, and (Shazam!) the near-neutral mutation
> gets converted to a beneficial mutation (either directly, or merely
> relative to the old trait which is suddenly rendered disadvantageous).
> >From that point onward the cost of substitution is incurred. That is
> what Haldane was up to with his environmental-change scenario -- he was
> trying to (artificially) reduce the cost of substitution.
>=20
> The cost of substitution doesn't depend on whether the old trait become=
s
> harmful (say, due to an environmental change). All that matters is tha=
t
> the new trait goes from 'few' to 'many' -- and that absolutely requires
=D8 reproductive excess
Yes, a reproductive excess is required, but nothing like that required
in the case of a deteriorating environment.
>=20
> > Please note that this [environmental-change scenario]
> > was Haldane's only justification for using a minimum of 300
> > generations for a substitution to occur. His estimate of 300 generati=
ons
> > was based solely upon keeping the overall fitness at a reasonable lev=
el
> > in a deteriorating environment
>=20
> Robert is attempting to brush off Haldane's results as applying "only"
> to the situation of a deteriorating environment. Robert is mistaken.
> The environmental-change scenario was nothing more than an attempt to
> reduce the cost of substitution. Haldane based his cost estimate on hi=
s
> environmental-change scenario, which is one of the reasons why his cost
> estimate may be said to be too *low*. The cost is higher, and Haldane'=
s
> Dilemma even more acute, when the scenario does not apply.
>=20
Show me, Walter. So far all that I've seen is that Haldane raised the
number of deaths required for a substitution by a factor of 10, 30, or
even 100; leading to an increase in the number of generations for the
substitution to occur.
Robert Williams
jeth...@ix.netcom.com
In article <66heob$ltg$1...@nntp6.u.washington.edu>,
wjre...@mmm.com wrote:
>The exchange with Jonah Thomas now has a high thrashing-to-insight
>ratio, and I am not likely to pursue it further, as I doubt most readers
>will either. I'll confine myself to the main point.
I gave more-or-less real-life examples that demonstrated my points, and you
decided to quit. You have to avoid any sort of reality or else face the
utter irrelevance of your calculations. I'm done with this.
wjre...@mmm.com
Take the following two types of "beneficial" mutations:
1) A mutation that is beneficial from the moment of its inception.
2) An environmental change that renders the old allele disadvantageous
and a rare near-neutral mutation suddenly beneficial RELATIVE to the old
one.
To compare the two, let us stipulate that:
a) They have the same starting frequency at the
beginning of the substitution process, that is,
at the time they become "beneficial".
b) They have the same selective advantage
RELATIVE to the old allele.
We have two "beneficial" mutations differing in how they were created.
In case #1, it was created directly by a mutation event. In case #2,
there was some delay between the mutation event and when the mutation
actually became beneficial (via environmental change).
Robert Williams asks: Is the cost of substitution the same in both
cases? The answer is yes, their cost is the same. In fact, the
substitution process, the cost formulas, and the derivations of the cost
formulas are not merely equal -- they are one and the same. There is no
difference. They must both rise from 'few' to 'many', at the same
speed, with the same starting and ending points -- they require
precisely the same reproductive excess -- their cost is the same.
******
Robert claims:
> I have given equations, derivations, and simulations
> in my post of 12/01/97 under this thread as to why
> I believe the two costs are not the same.
Robert has done no such thing. I showed in a previous post that his
computer simulation achieved a rate 30 times faster than the Haldane's
rate simply by arbitrarily using a reproductive excess that is fully 30
times greater than Haldane allotted. Robert did not reduce the cost at
all.
Robert did a lot of symbol juggling, but he never derived, or
calculated, the cost of substitution. In a previous post, Robert gave a
detailed "derivation"! Over two pages long! Involving TWO
partial-fraction expansions! He is back now to repeat the conclusion of
his derivation. He waves it at us menacingly:
> - remember the equation I derived on 12/01:
>
> (1/F) * p + s*q*p / [ F * (1 + s*p)] + (1/F) * q - s*q*p / [ F *(1
> + s*p)] = 1/F
>
> If you multiply through by F, you get:
>
> p + s*q*p/(1 + s*p) + q - s*q*p/(1 + s*p) = 1
By simple addition that reduces to:
p + q = 1
In other words, Robert has spent a great deal of time "deriving" the
starting assumption he began with -- that the gene frequencies sum to
one. That could hardly be less enlightening.
I repeat. Robert has not calculated or derived the cost of
substitution. As best I can tell, he doesn't understand what it is, as
we'll see next.
******
In our immediately previous exchange of posts, Robert approvingly gave
Haldane's definition for the cost of substitution. It involves the
integral of:
dq/(1-q)
Now, Robert is back to repudiate that, in effect claiming that Haldane's
cost definition is WRONG:
> ... the proper integral to use [for the cost of substitution]
> is the integral from q0 (essentially 1) to 0 of dq
>(NOT dq/(1-q) ).
Robert is clearly moving into new, uncharted orbits now. I know of no
other evolutionist making such a proposal. It's unique. And considering
his super-duper "derivation" it could go far. One can only hope the good
doctor Felsenstein, or one of the many other capable evolutionary
scientists present, would step in to help square away this gentleman.
But I fear that would be hoping too much. You see Haldane's Dilemma has
no such history. Any answer seems good enough. Vague, wrong, and
mutually contradictory answers are allowed to languish and linger for
decades, with virtually no challenge from the evolutionary fraternity.
In fact, I know of only one case where an evolutionist has challenged
his fellow's answers to the problem, and you rarely even hear about that
one. Other than me, Robert's raw proposal goes unchallenged in this
forum.
Donal Hickey
Robert Williams wrote:
> I agree that the rate of substitution is limited by the species
> reproduction rate. I just don't believe that you have shown that the
> rate is 1 substitution per 300 generations as per Haldane.
Does everybody else in this discussion agree with the first statement
above? If so, perhaps we could all move on to the quantitative arguments
referred to in Robert's second sentence. I have two problems with
Walter's arguments. First, he implies that nobody, other than himself,
recognizes that the rate of substitution is limited by the species
reproduction rate. This does not seem to be true, given Robert's
statement above. Secondly, he implies that Haldane's calculations pose
some insurmountable problem for evolutionary theory. This is also not
true. First, as pointed out by Felsenstein and others, the constraint is
not always as severe as in the scenario outlined originally by Haldane,
i.e., species with low fecundity where most selection occurs by
selective juvenile deaths. Indeed, Haldane himself was well aware that
he was presenting a "worst case" scenario. Nevertheless, his conclusion
was that his calculation "accords with the observed slowness of
evolution". I find it curious that Walter now implies that Haldane's
calculations do NOT accord with the observed rates of evolution. Am I to
conclude that Haldane had the wit to do the correct calculation but
lacked the smarts to draw the proper conclusion?
Joe Felsenstein
In article <66jtk9$198i$1...@nntp6.u.washington.edu>, Walter ReMine
<wjre...@mmm.com> has found what he thinks are problems with my replies to
him:
Let's remember that there is no disagreement (that I can see) about
the case where a change of environment renders one allele disadvantageous
and allows another that restores the fitness to be selected. Haldane,
ReMine, and I seem not to be saying anything different there.
For the neutral case, ReMine feels he has corrected me by saying that there
is a "stochastic reproductive excess" whereas I said there was no cost.
We both agree that no excess offspring number, offspring of individuals, is
required to substitute a neutral mutant. We both agree that there is in
that case also no limit to the number of such mutants that could substitute,
aside from limits set by the rate of mutation.
However he wants to calculate a cost based on saying that the reduction
division of meiosis, followed by fertilization, represents a reproductive
excess. I prefer not to compute excess that way. But whether one calls
that an excess or not, it doesn't matter and is just a matter of
which convention you want to use. If he wants to consider me to have
"pointed out [my] mistake", well I disagree. There are stochastic
forces, and they do of course account for the substitution, but whether
one calls them a "cost" or "reproductive excess" is a matter of
favorite definitions which does not affect anything, that I can see.
ReMine declares that "My excursion into neutral substitutions shows (as I
argue here and in my book) a coherent, consistent approach to the
Haldane-style cost-payment theory. That is worthwhile simply for the clarity,
unity, and coherence it brings to the field."
Fine, now lets see what happens to all that "clarity, unity, and
coherence" when we get to the case of advantageous mutants that occur in
the absence of any changed environment. Here ReMine declares flatly that
there is a cost, and it limits the rate of subtitution:
After discussing my 1971 analysis of cost of natural selection in the
deleterious-environmental-change case, and agreeing with it, ReMine says:
> However, Felsenstein claims this cost limitation does not apply to
> directly-beneficial mutations, those received in the absence of harmful
> environmental change. I claim that the cost of substitution is IDENTICAL
> in both cases. The *source* of the beneficial mutation does not matter.
> All that matters is that it goes from 'few' to 'many' -- and thereby
> incurs a cost of substitution. ...
> .... I say the limitations to
> substitution rate that Felsenstein agrees to in his paper apply to ALL
> beneficial substitutions, not just those created by environmental
> change.
> In other words, reproductive excess does limit something, and
> Felsenstein (and least partly) identified it in his 1971 paper -- it
> limits the beneficial substitution rate.
> ... . He must make a case for credible rates of reproductive excess,
> and he has not even attempted to do so. He merely alludes to
> unsustainable, ever increasing rates of reproductive excess, that have
> no basis in observation.
Now it should be obvious to anyone who has achieved "clarity, unity and
coherence" that if a population is sitting there, with a certain reproductive
excess, and a beneficial mutation occurs (in the absence of any deterioration
of the environment), this is hardly a disaster but rather a Good Thing.
It increases the reproductive excess (or it can, as Walter points out, also
increase the viability too). If so, it makes life more bearable, right?
And having two such mutants substituting at the same time is no dilemma.
Or three, or four, or a hundred. One might make a formal exercise of
computing a cost, by comparing mean fitness to the fitness of the best
genotype. But each new mutant raises the standard! So no matter how big
the number gets, it does not cause a problem for the next beneficial
mutation.
So how is there then any limit set by the _initial_ reproductive excess?
In fact, there is none in the beneficial mutant case. If he is
saying that the reproductive excess initially present makes a high
rate of beneficial substitutions impossible to sustain, that that is
simply, plainly, flatly wrong.
ReMine concludes that evolution won't work because it would impose too
high a reproductive excess for the population to sustain. I can't see that
there is anything to that argument, as he has not made any logical argument
that the reproductive excess present in the population limits future
beneficial substitutions. At all.
I hope that ReMine will enlighten us all how this limit works in the
beneficial case.
Robert Williams
Quite right, Donal. Walter clearly has no intentions of fairly
considering anything anyone else has to say on this topic, so I'm not
going to waste much more time arguing with him.
What quantitative arguments would you like to consider now? Do you think
that:
[(1 + s)*p]/(1 + s*p) + q/(1 + s*p) = 1
is a reasonable description of the substitution of one allele for
another with constant population size? Please let me know if you have
any problems with this eqation, or the alternative form that clearly
shows the substitutional births / deaths for each generation:
( 1/F + s*q/[F*(1 + s*p)]) * p + (1/F - s*p/[F*(1 + s*p)]) * q = 1/F
If so, you will remember that I have already generated a table of the
number of generations for fixation for various values of s and
population sizes (from 10,000 to 1 billion in my post of 12/01/97.
Here it is again:
s N # of Generations
Until p = 0.99
------- ---------------- --------------------
0.01 10,000 1388
0.01 100,000 1619
0.01 1,000,000 1851
0.01 1,000,000 2545
0.1 10,000 145
0.1 100,000 170
0.1 1,000,000 194
0.1 1,000,000,000 266
1 10,000 20
1 100,000 24
1 1,000,000 27
1 1,000,000,000 37
2 10,000 13
2 100,000 15
2 1,000,000 17
2 1,000,000 24
3 10,000 10
3 100,000 12
3 1,000,000 14
3 1,000,000,000 19
4 10,000 9
4 100,000 11
4 1,000,000 12
4 1,000,000,000 16
The above was calculated with this program:
10 mod1 = 1
20 N = 100000
30 p = 1 / N
40 q = 1 - p
50 s = .01
60 gen = 0
65 COST1 = 0
67 COST2 = 0
70 gen = gen + 1
80 p = (1 + s * q / (1 + s * p)) * p
90 qnew = 1 - p
92 COST1 = COST1 + q - qnew
95 q = qnew
96 COST2 = COST2 + s * p * q / (1 + s * p)
100 IF gen MOD mod1 = 0 THEN PRINT "N - "; gen, "p is : "; p, "q is: ";
q, "COST is "; COST1
110 IF p < .99 THEN 70
120 PRINT "p is : "; p, "n is: "; gen, "COST1 is "; COST1, "COST2 is ";
COST2
Where would you like to go from here?
Robert
==============================================
Donal Hickey wrote:
>
> Robert Williams wrote:
>
> > I agree that the rate of substitution is limited by the species
> > reproduction rate. I just don't believe that you have shown that the
> > rate is 1 substitution per 300 generations as per Haldane.
>
Joe Felsenstein
In article <66pqca$1fg8$1...@nntp6.u.washington.edu>,
Donal Hickey <dhi...@uottawa.ca> wrote:
>Robert Williams wrote:
>
>> I agree that the rate of substitution is limited by the species
>> reproduction rate. I just don't believe that you have shown that the
>> rate is 1 substitution per 300 generations as per Haldane.
>
>above? If so, perhaps we could all move on to the quantitative arguments
>referred to in Robert's second sentence.
I do _not_ agree with the first statement, at least not for advantageous
mutant that occur in the absence of an environmental deterioration,
at least not limited by the species reproduction rate that exists
before the advantageous mutation.
Robert Williams
Walter,
I just have two questions for you.
1.) Do you, or do you not agree with Haldane when he defines the cost
of natural selection as the number of selective deaths required for a
substitution of one allele for another?
2.) Are you going to explain how this scenario that you worked out could
possibly apply to any of the situations I have described regarding the
substitution of a rare beneficial allele for a common less fit allele?
You and I both know that I have never called for the genetic deaths of
100 individuals bearing the old trait when only 2 individuals with the
new trait exist. This is my third time asking you about this, so if you
wish to retain any shred of credibility in this forum, I suggest that
you acknowledge the question.
Donal Hickey
Joe Felsenstein wrote:
> I do _not_ agree with the first statement, at least not for advantageous
> mutant that occur in the absence of an environmental deterioration,
> at least not limited by the species reproduction rate that exists
> before the advantageous mutation.
>
Joe,
I didn't think you agreed (although Robert does), so I asked the
question to clarify your position for myself. I must say that I hadn't
thought about making the distinction between reproductive output of
mutants and non-mutants, and I agree that it is the reproductive rate of
the new nutants that is relevant to calculating future maximum rates of
evolutionary change. That would mean that we can't really predict future
rates of change (since the mutations haven't happened yet), but we
should be able to estimate the past rates - because the organisms we
observe now are descended from the beneficial mutants. Right?
Donal Hickey
Joe Felsenstein wrote:
> Let's remember that there is no disagreement (that I can see) about
> the case where a change of environment renders one allele disadvantageous
> and allows another that restores the fitness to be selected. Haldane,
> ReMine, and I seem not to be saying anything different there.
>
Does environmental change include both abiotic and biotic changes? For
instance, can one consider increasing intensity of interspecific
competition as a deteriorating biotic environment? If so, subscribers to
the Red Queen school of evolutionary thinking would say that the area of
agreement referred to above is not insignificant.
> There are stochastic
> forces, and they do of course account for the substitution, but whether
> one calls them a "cost" or "reproductive excess" is a matter of
> favorite definitions which does not affect anything, that I can see.
My impression is that the argument about beneficial mutations is also,
at least partly, about favorite definitions of what constitutes a "cost"
or a "Good Thing".
> Now it should be obvious to anyone who has achieved "clarity, unity and
> coherence" that if a population is sitting there, with a certain reproductive
> excess, and a beneficial mutation occurs (in the absence of any deterioration
> of the environment), this is hardly a disaster but rather a Good Thing.
> It increases the reproductive excess (or it can, as Walter points out, also
> increase the viability too). If so, it makes life more bearable, right?
I totally agree here. Such mutations are certainly a "good thing" and
any attempt to label them as a "load" or a "cost" which might lead to
extinction is clearly ridiculous. The question that one could ask is how
frequent is this class of mutations. If they have formed an important
component of all selected mutations, should we see evidence for
constantly increasing levels of reproductive excess? One type of
beneficial mutation which may not fit this scenario (it seems to me) is
one that would increase intra-specific competitive ability.
> So how is there then any limit set by the _initial_ reproductive excess?
Indeed, if the mutation increases the reproductive excess (either by
affecting viability or fecundity), the INITIAL reproductive excess is a
poor predictor of the maximum evolutionary rate. Could one avoid a lot
of the arguments if we could agree that the reproductive rate of the new
mutant genotypes would be a more reliable guide to evolutionary rates,
until another mutation occurred that increases that upper limit still
more? Again, this gets back to the question of whether reproductive
rates have, in fact, been increasing during the course of evolution.
> ReMine concludes that evolution won't work because it would impose too
> high a reproductive excess for the population to sustain. I can't see that
> there is anything to that argument, as he has not made any logical argument
> that the reproductive excess present in the population limits future
> beneficial substitutions. At all.
>
I agree with Walter that the amount of reproductive excess is relevant
to calculations of the rates of evolution by natural selection, although
Joe points out quite rightly that the pre-mutation excess may not be the
right one to use. It seems that we still have some serious quibbles
about how the maximum rate might be most accurately calculated. What I
totally disagree with is Walter's implied conclusion (assuming that I
understand his arguments) that natural selection for beneficial
mutations would place some insurmountable cost on the population. As
pointed out by Joe, beneficial mutations are essentially a "good thing",
in the sense that the population would be worse off without them. There
are limits, based on the magnitude of the reproductive excess, on how
quickly this benefit can be propagated throughout the entire population
by natural selection. But, even if the reproductive excess is very
modest, the beneficial mutations still increase - although at a slower
rate. They act like evolutionary "checks in the mail", assuming a
Canadian postal system. In both cases, the benefits eventually show up
but it takes time.
Donal Hickey
Robert,
This is a response to your previous post which, through my computer
clumsiness, I deleted. You asked if I had a problem with your
calculations. The simple answer is that I do not; they seem perfectly
logical to me, given the model that you have set up. The model itself,
of course, could be debated. Essentially, you have defined a population
in which there is a given amount of reproductive excess already present,
and you point out that this amount of reproductive excess is available
for positive Darwinian selection without incurring any EXTRA "cost". To
me, it seems that you calculate a "cost" but then say it's NOT a cost
because that reproductive excess was there in the first place although
it was serving no purpose. I think that is debatable.
Donal Hickey
Walter wrote:
If the species cannot supply that level of reproductive
>excess, then the scenario is not plausible. Indeed, the scenario is
>plausible for higher mammals.
Walter,
I have two questions:
First, what do you mean by not plausible? I take it that you mean the
gene frequency would not jump from 1% to 50% in one generation. I think
most people would agree that is not plausible. My question is what do
you think IS plausible in such a case?
My second question is about the scenario you describe. The outcome may
not be plausible but is the scenario itself realistic? Maybe we should
confine ourselves to debating the possible outcomes of realistic
scenarios.
wjre...@mmm.com
Of the people I've seen on the net so far, Dr. Joe Felsenstein handles
Haldane's Dilemma the best. Yet he (with ability and grace) also
represents the traditional confusions that kept this problem obscured
and unresolved. If you have time to track only one Internet discussion
on this issue, then this one with Felsenstein is the one I would
recommend.
Felsenstein's latest post is less clear than his previous, as he
introduces many confusion factors that we must now eliminate
one-by-one. This exercise is worthwhile because he is a very capable
man -- if he can be confused on these points, then so can many other
people.
******
Cost and payment are not the same. They are as different as the cost of
a car versus the payments you make on it. Of course they must have the
same units (such as dollars), but the similarity ends there. A given
evolutionary scenario has a 'cost' that we can calculate, and the
'payment' is the reproductive excess the species actually possesses. In
several places Felsenstein wrongly interchanges the two:
> However he wants to calculate a cost based on saying that the reduction
> division of meiosis, followed by fertilization, represents a reproductive
> excess. I prefer not to compute excess that way. But whether one calls
> that an excess or not, it doesn't matter and is just a matter of
> which convention you want to use.
Felsenstein is confusing cost with payment. He said I calculate cost
based on meiosis. I did no such thing. Cost has nothing to do with
meiosis. Rather meiosis is one form of reproductive 'payment'. Meiosis
is a source of stochastic reproductive excess which pays for the rise of
neutral mutations to fixation.
> There are stochastic forces, and they do of course
> account for the substitution, but whether one calls
> them a "cost" or "reproductive excess" is a matter of
> favorite definitions ...
Joe is again confusing cost with payment. They are not interchangeable,
and the word "cost" has no proper business in his above statement.
> For the neutral case, ReMine feels he has corrected me
> by saying that there is a "stochastic reproductive excess"
> whereas I said there was no cost.
Felsenstein misrepresents our previous posts. In actual fact, he did not
say neutral substitutions have no cost. Rather, his posts (which
involved his thought-experiment) were entirely about payment. They
focused on zero reproductive excess and zero reproductive payment --
not zero cost.
The above three examples of cost-payment confusion are all employed
toward the same end: By means of confusion they obscure a point that
Felsenstein and I had recently spent time debating and settling:
Stochastic reproductive excess exists and is responsible for the
rise of neutral substitutions. This is a fact -- not a matter of
arbitrary
choice, preference, convention, or semantics.
******
> ReMine concludes that evolution won't work because it would impose too
> high a reproductive excess for the population to sustain. I can't see that
> there is anything to that argument, ...
That is untrue. In his 1971 paper, Felsenstein himself used the above
argument to identify when a substitution rate is implausible. But he
seeks to confine his conclusion to ONLY beneficial mutations that are
**created via environmental change.** I say his analysis applies to ALL
beneficial mutations regardless of their origin. Why?
Other things being equal, the *origin* of a beneficial
mutation makes no difference whatever to its cost of
substitution.
Therefore, to be consistent, Felsenstein ought apply his
same conclusion to all beneficial mutations -- Their
maximum plausible substitution rate is determined by
the specie's reproductive excess.
******
> Now it should be obvious ...
> that if a population is sitting there, with a certain reproductive
> excess, and a beneficial mutation occurs (in the absence of any deterioration
> of the environment), this is hardly a disaster but rather a Good Thing.
> It increases the reproductive excess (or it can, as Walter points out, also
> increase the viability too). If so, it makes life more bearable, right?
Felsenstein says a beneficial mutation is "hardly a disaster but rather
a Good Thing" that "makes life more bearable". But that cannot reduce
the cost of substitution. If something is to go from 'few' to 'many',
then a reproductive cost is absolutely unavoidable, and the more "Good"
a beneficial mutation is, the *higher* its cost of substitution.
Substitutions with a *low* selective advantage have the lowest cost.
The only thing in his statement worth focusing on is his new claim that
a beneficial mutation "increases reproductive excess". (That idea was
nowhere visible in his 1971 paper.) My previous posts argued that his
idea does not, even slightly, reduce the problem. Rather than
responding to my points, Felsenstein misrepresents them:
> So how is there then any limit set by the _initial_ reproductive excess?
> In fact, there is none in the beneficial mutant case. If he is
> saying that the reproductive excess initially present makes a high
> rate of beneficial substitutions impossible to sustain, that that is
> simply, plainly, flatly wrong.
Felsenstein misrepresents what I said. I never once focused on the
"initial" reproductive excess. Rather, I specifically emphasized that
Haldane's Dilemma is concerned with long-term averages, and, if
anything, it is the 'final' reproductive excess (of living organisms
today) that is directly observable and which terminates Felsenstein's
claims of every increasing reproduction rates.
> [ReMine] has not made any logical argument that the reproductive
> excess present in the population limits **future** beneficial
> substitutions. [WR: My emphasis added.]
Felsenstein's point is irrelevant. The beneficial substitution rate at
a given time, is limited by the reproductive excess available at that
same time -- not by some future or past time. But Haldane's Dilemma
does not require us to track the instantaneous reproduction of a species
for each separate mutation. Instead, long-term averages are sufficient
and accurate for calculating the long-term substitution rate.
******
> One might make a formal exercise of computing a cost,
> by comparing mean fitness to the fitness of the best
> genotype. But each new mutant raises the standard!
> So no matter how big the number gets, it does not cause
> a problem for the next beneficial mutation.
Felsenstein is here inserting the substitutional load argument. It
occurs nowhere in his 1971 paper, nor within Haldane's infamous 1957
paper. It was created by Motoo Kimura in response to Haldane's
Dilemma. Then it was adopted by modern commentators, where it remains a
leading source of confusion. It creates confusion by over-emphasizing
what is virtually irrelevant to the problem -- fitness values, mean
fitness, fitness of the best genotype, fitness normalization, and a
fitness "standard". Substitutional load thoroughly obscures the central
issue of Haldane's Dilemma, which is the indelible link between speed of
growth and reproductive excess.
Jonah Thomas
In article <676ds8$25ba$1...@nntp6.u.washington.edu>,
wjre...@mmm.com wrote:
>> ReMine concludes that evolution won't work because it would impose too
>> high a reproductive excess for the population to sustain. I can't see
>> that there is anything to that argument, ...
>That is untrue. In his 1971 paper, Felsenstein himself used the above
>argument to identify when a substitution rate is implausible. But he
>seeks to confine his conclusion to ONLY beneficial mutations that are
>**created via environmental change.** I say his analysis applies to ALL
>beneficial mutations regardless of their origin. Why?
> Other things being equal, the *origin* of a beneficial
> mutation makes no difference whatever to its cost of
> substitution.
> Therefore, to be consistent, Felsenstein ought apply his
> same conclusion to all beneficial mutations -- Their
> maximum plausible substitution rate is determined by
> the specie's reproductive excess.
>> Now it should be obvious ...
>> that if a population is sitting there, with a certain reproductive
>> excess, and a beneficial mutation occurs (in the absence of any
>> deterioration of the environment), this is hardly a disaster but rather
>> a Good Thing. It increases the reproductive excess (or it can, as
>> Walter points out, also increase the viability too). If so, it makes
>> life more bearable, right?
>Felsenstein says a beneficial mutation is "hardly a disaster but rather
>a Good Thing" that "makes life more bearable". But that cannot reduce
>the cost of substitution. If something is to go from 'few' to 'many',
>then a reproductive cost is absolutely unavoidable, and the more "Good"
>a beneficial mutation is, the *higher* its cost of substitution.
>Substitutions with a *low* selective advantage have the lowest cost.
It looks like a fundamental part of your confusion comes from trying to
reason using the English language, in ways it wasn't designed for. People
haven't had much success discussing the math with you. Let's try
metaphor.
Imagine the following economic scenario: You're running a very large
factory. You have 10,000 machines of the same type that occasionally
wear out. You keep 200 replacements on hand, and when a machine wears
out you take one of the stock of replacements and use it. You've
calculated that you need to order a 100 new replacements each month.
A salesman comes to you with the claim that his machine lasts much longer
than the kind you're already buying. You decide to try it. So you buy 100
of them and that month you replace 100 of the regular kind with the new
kind. Each month after that, you buy replacements in proportion. If there
are still 100 of the new machines out there, you buy 1 new machine and 99 of
the old kind. Then if 100 of the old machines fail and none of the new ones
do, the number of the new kind goes up. Eventually you'll be buying 2 of
the new ones each month.
Say you're doing this and somebody tells you that on average you're going
to replace more than 100 of the old ones with new ones each month. You
can tell them without a second thought that it's implausible. There's no
way you can replace more than 100 unless you change your procedure and
_order_ more than 100. Well, but suppose they say the new ones are going to
increase in frequency by more than 1%. They could do that only if the
number in use went down. If you only kept 5,000 machines going then you
could replace 100 of them each month and replace at 2%. If you only kept
100 machines going you could replace them all in one month. "Implausible"
says you can't do that much replacement without changing something. That's
all it says.
OK, so what's the cost here? Why is there any extra cost to making the
change? Well, the manufacturer of the old kind of machine loses sales.
The better the new machine is, the faster he loses sales. Every time a
new machine replaces an old one, the cost is that there are fewer of the
old type and fewer replacements sold of the old type. Why should you
care? Why indeed, I don't see that you should.
This model supposes the population size is fixed and the replacement rate
is fixed. If the new machines really do last longer, things will be out
of balance. When you order 100 of them each month some of the
replacements won't get used. You could replace some machines early, or
you could throw away some replacements, or you could reduce the number
you order, or you could increase the number of machines in use. You get
to choose. In biological populations that's handled by default. Like,
if the only reason the factory didn't expand was lack of capital, as the
more reliable machines come on line it makes sense to increase the number
in use. Or it might make sense to reduce the size of the orders and use
the savings elsewhere. That corresponds to an increase in K versus r
strategy. Etc.
Calling the thing a "cost" brings up a lot of inappropriate associations
in English and they confuse you.
Here is one that isn't a metaphor:
Take a population of 10^10 E coli. Dump a lot of streptomycin on them,
enough to kill 10^9 of them. The ten remaining cells are streptomycin
resistant mutants. Their frequency has increased 10,000,000 percent in
one generation. It happens.
But it doesn't happen two generations in a row. Next generation if you kill
more than 95% of them the population is extinct. It will take about 30
generations without deaths for the population to get back to 10^10. But
during those 30 generations there can be a lot of selection. If one of the
strR mutations grows twice as fast as the others it will totally dominate
the population, and nobody has to die to get that result.
Donal Hickey
wjre...@mmm.com wrote:
> and the more "Good"
> a beneficial mutation is, the *higher* its cost of substitution.
> Substitutions with a *low* selective advantage have the lowest cost.
I don't understand your argument here. Do you mean cost per generation
or the total cost of the substitution? Haldane (1957) suggested that in
most cases "the number of deaths needed to secure the substitution, by
natural selection, of one gene for another at a locus, is independent of
the intensity of selection." You obviously disagree with Haldane on
this. Is this why you refer to his paper as "imfamous".
> Substitutional load thoroughly obscures the central
> issue of Haldane's Dilemma, which is the indelible link between speed of
> growth and reproductive excess.
>
"Speed of growth"? Surely, you mean rate of change in gene frequency.
I'm sorry to be picky about terminology, but you have gone to some
length to chastise Felsenstein about what you see as the sloppy use of
technical terminology (costs, payments, loads etc.).
wjre...@mmm.com
Robert Williams is back to taunt us with his diabolical equations:
> Do you think that:
>
> [(1 + s)*p]/(1 + s*p) + q/(1 + s*p) = 1
>
> is a reasonable description of the substitution of one allele for
> another with constant population size? Please let me know if you have
> any problems with this equation, or the alternative form that clearly
> shows the substitutional births / deaths for each generation:
>
> ( 1/F + s*q/[F*(1 + s*p)]) * p + (1/F - s*p/[F*(1 + s*p)]) * q = 1/F
Recall that those equations are his result of more than TWO-PAGES of
"derivation", including TWO partial-fraction expansions. Lots of
razzle-dazzle! Lots to distract and confuse the unwary.
Yet with a few simple steps of arithmetic, each of those equations
reduces to:
p + q = 1
In other words, Robert spent a lot of time "deriving" his
starting-assumption, that the gene frequencies sum to one. He begins
with his starting-assumption, then by a most circuitous route he ends up
back with his starting-assumption -- only this time in disguise!
Robert masquerades his equations as far more than what they are. They
are not remotely about "substitutional births / deaths for each
generation". He is wrong to pretend they represent anything other than
p+q=1. The words farce and sham come to mind.
I noted this all in my previous post, yet he is back to press his
masquerade upon us again -- for the third time! Worse still, not one
evolutionist here on sci.bio.evolution posted any objection to his
flim-flam!
Dr. Felsenstein specifically responded to Robert's post, but not to
eliminate the above red-herring. Instead he had a completely different
target in mind. He noticed Robert had endorsed something that put
Haldane's Dilemma more in the 'problem' category:
Robert wrote:
> I agree that the rate of substitution is
> limited by the species reproduction rate.
That was about the only straight-on correct thing in Robert's post, yet
Dr. Felsenstein was moved to announce his disagreement of it.
Robert then responded with, well, nothing. Not a question, not a
challenge. Just nothing.
This demonstrates EXACTLY what I have been saying. Among evolutionists,
any so-called "answer" to Haldane's Dilemma goes virtually unchallenged
-- and any confusion, even of the raw-est kind, gets a free-pass and is
allowed to thrive. Sadly, this lamentable dynamic displayed here on
sci.bio.evolution is even *better* than what exists in the literature.
-- Walter ReMine
The Biotic Message
Guy A. Hoelzer
> Felsenstein says a beneficial mutation is "hardly a disaster but rather
> a Good Thing" that "makes life more bearable". But that cannot reduce
> the cost of substitution. If something is to go from 'few' to 'many',
> then a reproductive cost is absolutely unavoidable, and the more "Good"
> a beneficial mutation is, the *higher* its cost of substitution.
> Substitutions with a *low* selective advantage have the lowest cost.
As a voyeur to this thread, it seems to me that much of this debate has
centered on a simple miscommunication about the relevance of "costs" and
"payments" (to use ReMine's distinction) to the evolution of populations.
Please correct me if I am wrong, but I think that ReMine has focused only
on costs of substitution while Felsenstein has included potential benefits
in his analysis. Assuming for the moment that this is a valid contrast, I
think it is elementary to favor Felsenstein's argument. The net effect of
a substitution on a population must reflect both the costs and benefits it
imposes. By definition, an advantageous mutation (i.e., one that improves
mean population fitness) has a cost to benefit ration <1. Granted, mean
population fitness can be maximized with some alleles at intermediate
frequencies, but in simpler cases complete substitution will maximize the
benefits accrued by the population. By limiting exploration of Haldane's
dilemna to the costs of mutation and/or substitution, I expect that one's
understanding of evolution will be limited and biased.
--
Guy Hoelzer e-mail: hoe...@med.unr.edu
Department of Biology phone: 702-784-4860
University of Nevada Reno fax: 702-784-1302
Reno, NV 89557
Robert Williams
8bit
[moderator's note: Autoconversion of this article from 8-bit to
quoted-printable left a few control characters in it; I have edited
these out for readability. - JAH]
Walter has made some pretty serious accusations regarding the derivation
I have provided in my post of 12/01/97 for the substitution of a rare
beneficial allele for a common less fit one. The equation of concern is:
(1 + s)*p/[F*(1 + s*p)] + q/[F*(1 + s*p)] = 1/F
which can be manipulated to show that:
[1/F + s*q/[F*(1 + s*p)]] * p + [1/F - s*p/[F*(1 + s*p)]] * q = 1/F
Walter then multiplies the second form through by F and adds to achieve
the result:
p + q = 1
With this, he thinks he has shown some fatal flaw in my derivation. He
wants us to think that I have done nothing more than derive one of my
assumptions.
Obviously, any equation that describes the substitution of one allele
for another at a two allele locus had
_better_ show that p + q = 1. I have already pointed out the benefits o=
f
the equation in my 12/01 post - it allows us to track the numbers of
selective births and deaths for any given generation, it allows us to
see that selective births and deaths are equal (in this situation), and
it allows us to calculate the value of p (and hence q) for each
successive generation. That is:
p' = (1 + s) * p/(1 + s*p)
where p' is the new frequency of p after a round of selection.
This is not a substantive criticism, but rather a rhetorical trick on
Walter's part. I can't believe that he is so inattentive as to have
missed all the above points. I also can't believe that he thinks anyone
in this forum is so na=EFve as to fall for such a simple ploy on his part.
Walter has demonstrated no problems whatsoever with the equations.
Walter throws around a lot of emotion laden phrases to describe this
derivation, such as "Robert Williams is back to taunt us with his
diabolical equations", elsewhere he calls the equation "menacing". Well,
Walter, nobody but you finds the equation to be menacing or diabolical.
Everyone else seems to think that it is simply an attempt on my part to
quantify the course of substitution of a beneficial mutation. That is
exactly what it is. If you (or anyone else) has any bonafide criticism
of the equation, please let me know. I want it to be correct.
As to differences between Dr. Felsenstein and myself regarding the cost,
we are examining different situations - I am looking at mutations that
do not lead to changes in the overall population numbers or to increases
in the species fecundity, Dr. Felsenstein is looking at changes that
affect both of those. I do not yet understand all of the points he made
in his 1971 paper, I hope to do so in the near future. On the other
hand, it's a little difficult for me to discuss my differences with Dr.
Felsenstein when we are constantly having to answer your fallacious
claims regarding the material we post.
Now Walter, I ask you for the FOURTH time (and I'm not the only one):
where does this equation EVER require 2 individuals with the beneficial
mutation to produce offspring to replace 100 individuals lost due to
selection. You made this claim in your post of 12/03/97, and you
continue to ignore the question. I am referring to the following quote:
Walter wrote:
>Next suppose the generation began with only 2 individuals with the new
>trait. This scenario would require them to have a reproductive excess
>of 50 (=100/2). This is the cost of substitution incurred for that
>generation. If the species cannot supply that level of reproductive
>excess, then the scenario is not plausible. Indeed, the scenario is not
>plausible for higher mammals.
Your failure own up to your mistake in this case demonstrates the
fraudulent nature of your claims. How ironic from the man who has
accused every other person involved in this thread (not to mention
pretty much the entire scientific community) of intellectual sloppiness
or worse.
Also, are you ever going to answer this simple question: Did Haldane
define the cost of substitution as the total sum of selective deaths
(normalized to the population size) over that substitution? Why do you
continue to ignore this question, Walter?
Robert Williams
wjre...@mmm.com
Donal Hickey writes:
> My second question is about the scenario you describe. The outcome may
> not be plausible but is the scenario itself realistic? Maybe we should
> confine ourselves to debating the possible outcomes of realistic
> scenarios.
The scenario I described is plausible (and realistic) -- or not --
depending on the reproductive excess of the species. That is precisely
the point of the cost of substitution, it discriminates between
plausible and implausible scenarios.
Let me state my example again. Suppose a trait increases in number by
100 individuals in one generation, and that there were at the beginning
of that generation only 2 individuals with the trait. In other words,
the scenario requires that the two individuals replace themselves, plus
100 more. This scenario requires them to have a reproductive excess of
50 (=100/2). For that generation alone, this scenario has a cost of
50. It is plausible, or not, depending on the reproductive excess of
the species. For some species it is plausible, for mammals it is not.
The argument is utterly simple and general. Just plug-in the data from
your scenario, then ask: Does the species have enough reproductive
excess to pay the 'cost'?
The cost of substitution is merely the total cost of an entire
substitution, and this typically requires many generations. Thus, it
merely sums the above costs over all the generations of the
substitution. From there we ask the same question as before: Does the
species have enough reproductive excess to pay the 'cost' of a given
scenario?
******
> My impression is that the argument about beneficial
> mutations is also, at least partly, about favorite
> definitions of what constitutes a "cost" or a "Good
> Thing".
Many confusions about the cost of substitution arise from informal,
loose, and mistaken interpretations of the word cost. The concept is
actually precise and narrowly defined.
Beneficial mutations may be a "Good Thing" but that does not even
slightly reduce their cost of substitution. The cost of substitution is
highest when the substitution occurs in one generation. The cost goes
down when the substitution is slower and occurs over more generations.
The cost reaches its absolute lowest value (under the most optimal
conceivable conditions), when the trait increases monotonically and
infinitely slowly. When a mutation is a "Good Thing" we can take that
to mean it increases FASTER, and therefore has a HIGHER cost. The
slower the substitution -- such as when a mutation has a low selective
advantage -- the lower the cost. (This is opposite of what Felsenstein
suggests.)
Haldane recognized the connection between high-speed and high-cost. He
also saw the cost is lowest and *approximately* constant when the
selective advantage is ten percent or less (s < 0.1), which is said to
be typical of evolution. Haldane correctly understood that in *most*
cases the cost of substitution is (to good approximation) independent of
selective value. Haldane then used that assumption (s < 0.1) to
calculate the average cost of substitution, and this gave nearly the
lowest conceivable cost.
At this point in Haldane's Dilemma, selective value has dropped out as
unimportant. Haldane made it so. To get low cost he emphasized low
selective values, and in the bargain one obtains an approximately
*constant* cost of substitution. Under those terms of the problem, the
selective value is nearly irrelevant. But one would never get that
impression from the literature on the problem -- it focuses maniacally,
almost exclusively on fitness values, especially in the "substitutional
load" argument. In other words, the least significant part of the
problem gets most of the traditional attention, and that obscures the
central issues.
If evolutionists want to play with fitness values (via "substitutional
load" arguments, or soft selection), then it can only result in (1) no
substantial affect (for s < 0.1), or (2) it will make Haldane's Dilemma
worse by raising the cost of substitution (for s > 0.1).
******
> Such [beneficial] mutations are certainly a "good thing"
> and any attempt to label them as a "load" or a "cost"
> which might lead to extinction is clearly ridiculous.
That is one of the great classic confusions about the cost of
substitution. It goes like this:
Step 1) First, claim (mistakenly) that the cost of
substitution leads to extinction.
Step 2) Then point out that the notion of beneficial
mutations leading to extinction is
"clearly ridiculous".
That argument is often given in an attempt to brush aside the cost of
substitution as nonsense. It is decades old, and never once have I seen
it challenged by an evolutionist. The confusion starts at Step 1 -- for
in truth the cost of substitution NEVER predicts extinction. A
prediction of extinction, when actually made, is always made by outside
circumstances that have little to do with the cost of substitution.
For example, take Joe Felsenstein's 1971 paper "On the biological
significance of the cost of gene substitution". He examines a situation
where a species is undergoing harmful random change, and deteriorating
toward extinction. The species needs beneficial substitutions just to
break even, just to stay running in the same place. Can the species
undergo beneficial substitutions at a rate sufficient to avert the
predicted extinction? Felsenstein (correctly) concludes that it depends
on the specie's reproductive excess. But the cost of substitution did
not predict extinction -- a prediction of extinction was clear long
before any considerations about the cost of substitution.
The cost of substitution is merely a criterion of plausibility for
substitution rates, not a theory of extinction.
******
I wrote:
Substitutional load thoroughly obscures the
central issue of Haldane's Dilemma, which
is the indelible link between speed of
growth and reproductive excess.
Donal responds:
> "Speed of growth"? Surely, you mean rate of change in gene frequency.
> I'm sorry to be picky about terminology, ...
I am picky about terminology, especially in Haldane's Dilemma where
every conceivable confusion has been amplified and the central issues
obscured for decades.
Donal believes a central issue is "change in gene frequency". That
mistaken belief is key to one of the traditional confusions. In
practice it goes like this: There is a population of one million
bacteria, then you add penicillin which kills off all but one cell that
happened to be resistant. That resistance went from super-rare to a
frequency of "1" in one generation. 'See it didn't take 300 generations
as Haldane said. See, there is no cost of substitution!' says the
evolutionist.
There is still a cost of substitution, but it has not been included
within the scope of the scenario. The cost is incurred when a trait
goes from 'few' to 'many'.
The "gene frequency" confusion runs parallel to another classic -- the
"constant population size" confusion. Some evolutionists claim a cost
of substitution only applies when the population is a constant size.
That is untrue. It applies anytime a trait goes from 'few' to 'many' --
and that is unavoidable in the evolutionary account.
> First, what do you mean by not plausible? I take it that
> you mean the gene frequency would not jump from 1%
> to 50% in one generation. I think most people would
> agree that is not plausible. My question is what do
> you think IS plausible in such a case?
Donal asks: Is it plausible for a gene frequency to jump from 1% to 50%
in one generation? Answer: The central issue is growth (not gene
frequencies) and Donal left out the key data that would get at that.
So, to get anywhere we must supply an assumption. Let us therefore take
a case of frequent interest to us, and assume the population size
remains constant. In this case, the 1% of the population must, on
average, each reproduce themselves plus 49 more. In other words, the
cost for this one generation scenario is 49. The scenario is plausible
if the species has a reproductive excess greater than 49, otherwise it
is implausible.
[The above are my responses to three recent posts from Donal Hickey.]
-- Walter ReMine
The Biotic Message -- the book
wjre...@mmm.com
Guy A. Hoelzer wrote:
> The net effect of a substitution on a population must
> reflect both the costs and benefits it imposes. By
> definition, an advantageous mutation (i.e., one that improves
> mean population fitness) has a cost to benefit ratio <1.
Hoelzer invents a "cost to benefit ratio" (an item not seen before in
discussions of Haldane's Dilemma) that underscores his misunderstanding
of the cost issue. He also speaks (mistakenly) of a "net effect" of
costs versus benefits (that is, costs *minus* benefits). (The correct
issue is costs versus payments. No, this is not just a semantic
difference.) He never once used the cost concept correctly. Instead, he
misinterprets it as a 'bad thing' that can be offset by beneficial
mutations which are a 'good thing.' That is not remotely what the cost
of substitution is. The cost of substitution is absolutely unavoidable
and is HIGHER the more beneficial the substitution.
Let's take an example. Suppose a scenario claims a trait increases its
numbers by 5 percent in one generation -- the cost is then 0.05 for this
one generation. If the species cannot supply 5 percent reproductive
excess for this generation to pay the cost, then the scenario is not
plausible. The logic is direct.
Next let's say the beneficial mutation is even better, even more of a
'Good Thing', say increasing its numbers by 7 percent in one generation
-- the cost of this scenario is GREATER than the previous one, it is now
0.07. If the species cannot supply 7 percent reproductive excess for
that generation, then this scenario is not plausible. In other words,
pointing out the "benefits" of a substitution does not even slightly
reduce the problem. Nothing comes for free in Haldane's Dilemma.
It boils down to this:
1) There is a cost of substitution,
it is unavoidable, and
nothing Hoelzer said reduces it.
2) The reproductive excess of the species is
limited, observable, and measurable,
and nothing Hoelzer said changes that.
3) These set a limit on the maximum plausible
beneficial substitution rate.
-- Walter ReMine
The Biotic Message -- the book
Don Cates
On 20 Dec 1997 00:24:37 GMT, wjre...@mmm.com wrote:
[snip]
>The scenario I described is plausible (and realistic) -- or not --
>depending on the reproductive excess of the species. That is precisely
>the point of the cost of substitution, it discriminates between
>plausible and implausible scenarios.
>Let me state my example again. Suppose a trait increases in number by
>100 individuals in one generation, and that there were at the beginning
>of that generation only 2 individuals with the trait. In other words,
>the scenario requires that the two individuals replace themselves, plus
>100 more. This scenario requires them to have a reproductive excess of
>50 (=100/2). For that generation alone, this scenario has a cost of
>50. It is plausible, or not, depending on the reproductive excess of
>the species. For some species it is plausible, for mammals it is not.
>The argument is utterly simple and general. Just plug-in the data from
>your scenario, then ask: Does the species have enough reproductive
>excess to pay the 'cost'?
>The cost of substitution is merely the total cost of an entire
>substitution, and this typically requires many generations. Thus, it
>merely sums the above costs over all the generations of the
>substitution. From there we ask the same question as before: Does the
>species have enough reproductive excess to pay the 'cost' of a given
>scenario?
I want to get this clear. Assuming a fixed population size and the
minimum necessary reproductive excess, The number of generations for
complete substitution would be log(popsize)/log(1+cost per generation)
and the total cost would be # of generations*(cost per generation).
Rigth?
So total cost has a floor of about 2.3*log(popsize) or about 20 for a
population of 1,000,000,000. With a cost/generation of 0.1 has a total
cost of about 21 and even a cost/gen of 2 only has a total cost of
about 38. These have a corresponding number of generations of 217 and
19 respectively. The numbers for a population of 1,000,000 are 13.8
for the floor, 14.5 and 145 for 0.1, and 25.2 and 12.6 for 2. None of
these numbers seem to me to be either unreasonable or onerous.
Am I missing something?
[snip]
>Beneficial mutations may be a "Good Thing" but that does not even
>slightly reduce their cost of substitution. The cost of substitution is
>highest when the substitution occurs in one generation. The cost goes
>down when the substitution is slower and occurs over more generations.
Why, if you sum it over all the generations?
>The cost reaches its absolute lowest value (under the most optimal
>conceivable conditions), when the trait increases monotonically and
>infinitely slowly. When a mutation is a "Good Thing" we can take that
>to mean it increases FASTER, and therefore has a HIGHER cost. The
>slower the substitution -- such as when a mutation has a low selective
>advantage -- the lower the cost. (This is opposite of what Felsenstein
>suggests.)
[big snip]
Perhaps you could critique the following scenario to help me
understand just what a 'cost of substitution' is?
Assumptions:
1. A stable population limited by the rate of food availability.
2. On average, each individual has 3 offspring of which one per
generation survives to reproduce.
3. The offspring scatter widely and are randomly mixed in the
population.
If I understand you correctly, this is a reproductive excess of
2/generation but no 'cost' involved.
4. A mutation occurs which allows two mutants to survive in a
population of non-mutants. This is balanced (because of a fixed rate
of food supply) by a corresponding decrease in the number of
non-mutants surviving.
So initially the number of mutants increases exponentially. As the
proportion of mutants rises, the average number surviving begins to
drop and, as they approach complete substitution, approachs one, as in
the original population of non-mutants.
At no time does the number of offspring/individual change, nor the
average number of survivors, nor the total population.
What are the costs and why?
What is the total cost and why?
Thank you.
Donal Hickey
wjre...@mmm.com wrote:
>
> Donal Hickey writes:
>
> > My second question is about the scenario you describe.
Walter,
I had posed my two questions in the order of their importance to me. You
have made comments on my second, general question/comment. Why did you
ignore my more particular first question? The answer to that question is
important to me. I would like to distinguish between maximum cost per
generation and total cost of a substitution, summed over many
generations. For instance, the example you provide gives the impression
that substitutions happen in a single generation of intense selection.
That is a scenario that I agree is implausible. My point is that neither
is it particularly relevant to any realistic model of evolution. In
other words, you have built in the "implausability" by using totally
unrealistic starting assumptions about the intensity of selection per
generation (see below).
> Let me state my example again. Suppose a trait increases in number by
> 100 individuals in one generation, and that there were at the beginning
> of that generation only 2 individuals with the trait. For some species it is plausible, for mammals it is not.
>
> The argument is utterly simple and general. Just plug-in the data from
> your scenario, then ask: Does the species have enough reproductive
> excess to pay the 'cost'?
>
But it is important to remember that if you are to learn anything useful
from this comparison of the actual amount of reproductive excess to the
"cost" demanded by "your scenario", the scenario itself must be as
realistic as we can make it. You seem to ignore this constraint.
Walter wrote:
The cost of substitution is
> highest when the substitution occurs in one generation. The cost goes
> down when the substitution is slower and occurs over more generations.
This is certainly true for the cost of that particular substitution in
that particular generation. But what about the total cost of a
substitution summed over all generations?
>
> At this point in Haldane's Dilemma, selective value has dropped out as
> unimportant. Haldane made it so. To get low cost he emphasized low
> selective values, and in the bargain one obtains an approximately
> *constant* cost of substitution. Under those terms of the problem, the
> selective value is nearly irrelevant. But one would never get that
> impression from the literature on the problem -- it focuses maniacally,
> almost exclusively on fitness values, especially in the "substitutional
> load" argument. In other words, the least significant part of the
> problem gets most of the traditional attention, and that obscures the
> central issues.
>
But, with all due respect, are you not in danger of falling into the
trap yourself by focussing (unmaniacially of course) on extreme
scenarios using unrealistically high selection intensities?
Walter wrote:
> The cost of substitution is merely a criterion of plausibility for
> substitution rates, not a theory of extinction.
>
I agree with this. The reason that I raised the issue was that all of
your own examples refer to massive killing of over ninety percent of the
population in a single generation.
> Donal believes a central issue is "change in gene frequency". That
> mistaken belief is key to one of the traditional confusions. In
> practice it goes like this: There is a population of one million
> bacteria, then you add penicillin which kills off all but one cell that
> happened to be resistant.
Walter,
I know that there are people who may offer such scenarios (or any other
scenarios). I am not one of them and I can't help getting a little
annoyed when you presume to tell me what I think. In fact, in my first
post I did discuss a scenario involving cattle breeding because I
thought it was more relevant to discussions of susbtitution rates in
mammals.
> Donal asks: Is it plausible for a gene frequency to jump from 1% to 50% in one generation?
Perhaps I should rephrase my question. My question was about your
starting assumptions, not about the mechanisms. More specifically, is it
a reasonable model of mammalian evolution to expect such rapid changes
in gene frequency. Has anyone ever proposed such rapid rates for
mammals? If so, I'd certainly like to see the reference.
Walter, I have to say that I admire your debating skills. They are
excellent. One technique you use, which has been noted already, is the
selective answering of questions. You are also well aware that attack is
the best method of defense and I have to admire how smoothly you achieve
a debating manouvre that somebody once told me was the debating
equivalent of "switching the gun to the other shoulder". In closing, I
would like to reiterate another of my questions that you haven't
answered; that is, do you think the conserved rates of substitutional
change during the course of mammalian evolution are, or are not,
plausible given your own interpretations of Haldane's arguments?
Donal.
Guy A. Hoelzer
> Guy A. Hoelzer wrote:
> > The net effect of a substitution on a population must
> > reflect both the costs and benefits it imposes. By
> > definition, an advantageous mutation (i.e., one that improves
> > mean population fitness) has a cost to benefit ratio <1.
[SNIP]
> Let's take an example. Suppose a scenario claims a trait increases its
> numbers by 5 percent in one generation -- the cost is then 0.05 for this
> one generation. If the species cannot supply 5 percent reproductive
> excess for this generation to pay the cost, then the scenario is not
> plausible. The logic is direct.
Someone is very confused here. Let's see if we can determine who it is.
It seems to me that this "scenario" is self-contradictory. You start by
saying that a beneficial mutation caused a 5% increase in population size
(N). Population growth obviously requires the average individual to pass
on more than one complete copy of his/her genome to the next generation,
but does not require producing more offspring than will survive.
Producing some offspring that will not reproduced is nearly universal, but
not necessary in this example. You then say that this is an implausible
scenario if the population cannot grow by 5% in the unspecified time
frame. The problem here is that the population already grew by 5%, so we
know that it could.
> pointing out the "benefits" of a substitution does not even slightly
> reduce the problem. Nothing comes for free in Haldane's Dilemma.
I agree that pointing out the benefits does not reduce the costs, but it
certainly can reduce the problem. As I said originally, the "problem"
depends on the difference between the costs and benefits (or the C/B
ratio); not on either the costs or benefits alone.
> It boils down to this:
> 1) There is a cost of substitution,
> it is unavoidable, and
> nothing Hoelzer said reduces it.
I never suggested that the benefits of advantageous mutations reduced the costs.
> 2) The reproductive excess of the species is
> limited, observable, and measurable,
> and nothing Hoelzer said changes that.
Again, this is completely irrelevant to the point I made. I agree with
this statement.
> 3) These set a limit on the maximum plausible
> beneficial substitution rate.
I disagree with this conclusion. I believe it results from ignoring the
benefits of advantageous mutation.
Jonah Thomas
Since you don't even try to answer my compelling objections to your
confused ideas, I must follow your lead and conclude that you implicitly
agree that I'm right and you're wrong. 8-)
In article <67f385$2dnc$1...@nntp6.u.washington.edu>,
wjre...@mmm.com wrote:
wjre...@mmm.com
Guy A. Hoelzer writes:
> It seems to me that [ReMine's] "scenario" is self-contradictory.
> You start by saying that a beneficial mutation caused a 5%
> increase in population size (N).
Hoelzer makes a minor misinterpretation there. I didn't say the
population size increases. Rather, I posed a scenario where "a trait
increases its numbers by 5 percent in one generation" -- as in an
evolutionary substitution where a new rare trait rises from 'few' to
'many'. The population size can (and in most cases nearly does) remain
constant. It is the sub-population, comprised of the new trait, that
grows in size.
Hoelzer also makes a deeper error. To show it I must first make his
argument explicit -- he uses the following mistaken reasoning.
If we pose that a population did something,
then we automatically "know that it could"
and it is "self-contradictory" to argue that it
couldn't.
Here it is in his words:
>The problem here is that the population already
>grew by 5%, so we know that it could.
In other words, Hoelzer failed to differentiate between a scenario and
how we test it. Specifically he failed to differentiate between cost
and payment. There is a difference between the cost of a scenario, and
the specie's actual reproductive excess. They are not the same thing.
One is a cost, the other is a payment. They are as different as the
cost of a car versus the payments you make on it. A scenario might
'claim' a new trait grew in numbers by 5% per generation, but that does
NOT mean we therefore "know that it could". The species might not have
the reproductive excess necessary to make the scenario plausible. That
is precisely the point of cost arguments -- they identify implausible
scenarios.
> I agree that pointing out the benefits
> does not reduce the costs, ...
Excellent! We are making headway. Remember this thread began with Joe
Felsenstein erroneously claiming (as in his 1971 paper) that beneficial
substitutions "do not impose a cost".
Hoelzer's post explicitly acknowledges that his discussion has not
changed the costs or payments, yet he denies these set a limit on the
maximum plausible beneficial substitution rate. To see his error, let
me offer again the central premise of the cost of substitution:
Speed of growth is limited by the available reproductive
excess. It doesn't matter what the trait is. It can be
super-beneficial, slightly-beneficial, converted-beneficial,
neutral, or even harmful, and the following point still holds
true. If you claim a trait increases by X percent in a given
generation, then those individuals must supply at least
X percent excess reproduction in that generation,
or else the scenario is not plausible -- absolutely,
positively, no exceptions.
Cost arguments (such as Haldane's Dilemma) merely apply the same above
logic continuously over many generations. There is no way around it: If
you don't pay the cost, you don't get the substitution.
-- Walter ReMine
The Biotic Message -- the book
Jonah Thomas
In article <67ou6v$16vc$1...@nntp6.u.washington.edu>,
wjre...@mmm.com wrote:
> Speed of growth is limited by the available reproductive
> excess. It doesn't matter what the trait is. It can be
> super-beneficial, slightly-beneficial, converted-beneficial,
> neutral, or even harmful, and the following point still holds
> true. If you claim a trait increases by X percent in a given
> generation, then those individuals must supply at least
> X percent excess reproduction in that generation,
> or else the scenario is not plausible -- absolutely,
> positively, no exceptions.
This is simply wrong. I can give an example in which the trait increases
by a hundred billion percent in a given generation, and the individuals
involved have no excess reproduction in that generation. You have given
no argument against similar examples except that you dislike them.
You consistently pretend that your simplifying assumptions are reality.
>Cost arguments (such as Haldane's Dilemma) merely apply the same above
>logic continuously over many generations. There is no way around it: If
>you don't pay the cost, you don't get the substitution.
The logic is slightly better applied over many generations. On average,
selection requires that those selected must more than replace themselves;
otherwise the population size will decrease.
You might become less confused about this if you used a name that lacked
these irrelevant economic associations. I suggest that you replace "cost"
with "substitution". That will reveal a lot about your arguments. Thus:
Substitution arguments (such as Haldane's Dilemma) merely apply the same
above logic continuously over many generations. There is no way around it:
If you don't make the substitution, you don't get the substitution.
Joe Felsenstein
>Haldane's Dilemma the best. Yet he (with ability and grace) also
>represents the traditional confusions that kept this problem obscured
>and unresolved.
ReMine has persistently called everyone but himself confused and wrong.
Perhaps he should consider that some of the differences between himself
and others is a matter of using different definitions. Or failing to care
about some of the distinctions he makes.
>Cost and payment are not the same.
And so on, with a lot of emphasis on what is cost, what is payment,
and how terribly wrong I am about all that.
>Felsenstein misrepresents our previous posts. In actual fact, he did not
>say neutral substitutions have no cost. Rather, his posts (which
>involved his thought-experiment) were entirely about payment. They
>focused on zero reproductive excess and zero reproductive payment --
>not zero cost.
Let's get to the nitty-gritty.
>> ReMine concludes that evolution won't work because it would impose too
>> high a reproductive excess for the population to sustain. I can't see that
>> there is anything to that argument, ...
>
>That is untrue. In his 1971 paper, Felsenstein himself used the above
>argument to identify when a substitution rate is implausible. But he
>seeks to confine his conclusion to ONLY beneficial mutations that are
>**created via environmental change.** I say his analysis applies to ALL
>beneficial mutations regardless of their origin.
...
> Therefore, to be consistent, Felsenstein ought apply his
> same conclusion to all beneficial mutations -- Their
> maximum plausible substitution rate is determined by
> the specie's reproductive excess.
In my 1971 paper I asked what reproductive excess was necessary to
keep the population from going extinct, in the face of a certain rate
of substitution. The substitutions were induced by environmental changes,
each of which reduced the fitness of one allele from 1 to 1-s while
leaving the other allele, whose initial frequency was p0, having fitness
1. The substitutional load was imposed by these environmental changes.
If you ask the same question about beneficial mutations, you get a very
different answer. We could either be talking about a new beneficial mutant
arising in the absence of environmental change, leaving the fitness of the
other allele unchanged, or an environmental change that benefits one allele
while not penalizing the other. In either case the answer is the same --
you don't need any reproductive excess. The substitution increases
fitnesses.
(Notice I didn't use the words "cost" or "payment" but am discussing
whether there is some dilemma for evolution. There is not, in the second
case.)
So why is ReMine saying that? Well, he could be confused himself, but
perhaps he is not asking what reproductive excess is needed to keep the
species in existence. For when I asked:
>> So how is there then any limit set by the _initial_ reproductive excess?
>> In fact, there is none in the beneficial mutant case. If he is
>> saying that the reproductive excess initially present makes a high
>> rate of beneficial substitutions impossible to sustain, that that is
>> simply, plainly, flatly wrong.
>
>Felsenstein misrepresents what I said. I never once focused on the
>"initial" reproductive excess. Rather, I specifically emphasized that
>Haldane's Dilemma is concerned with long-term averages, and, if
>anything, it is the 'final' reproductive excess (of living organisms
>today) that is directly observable and which terminates Felsenstein's
>claims of every increasing reproduction rates.
...
>Felsenstein's point is irrelevant. The beneficial substitution rate at
>a given time, is limited by the reproductive excess available at that
>same time -- not by some future or past time. But Haldane's Dilemma
>does not require us to track the instantaneous reproduction of a species
>for each separate mutation. Instead, long-term averages are sufficient
>and accurate for calculating the long-term substitution rate.
OK, so does that mean ReMine isn't saying that a population will get into
trouble if too many favorable mutants arise? But instead is he saying that
the empirically observed reproductive excess is not large enough to
be consistent with the number of substitutions observed to have occurred?
Here we have to worry about where these observations came from, but also
we have to realize that the final reproductive excess will be the net
effect of
(1) deleterious environmental changes that are compensated for by
substituting an allele that copes with them,
(2) deleterious environmental changes that are uncompensated for,
(3) favorable environmental changes that do not induce any substitution,
(4) favorable environmental changes that do induce a substitution,
and (5) advantageous mutants that occur in the absence of environmental
change,
plus even (6) deleterious mutations that get fixed by genetic drift.
It seems to me that in view of events like (2) the occurrence of a
stream of advantageous mutants (of type 4) that substitute need not drive
the reproductive excess up to heights inconsistent with observation.
Sorry for the slow response but I've been busy.
Robert Williams
There has been a lot of discussion here regarding the definition of the
cost of substitution. Regardless of what any of us thinks that
definition is (or should be), I think it's clear what Haldane had to say
about it.
I believe that Haldane defined
the cost of natural selection as the number of selective deaths required
for a substitution. This is from very careful reading and rereading of
his paper. Here are some excerpts from "The Cost of Natural Selection"
that led me to this conclusion.
"The principal unit process in evolution is the substitution of one
gene for another at the same locus. ... I shall show that the number of
deaths needed to carry out this unit process by selective survival is
independent of the intensity of selection over a wide range." page 511
"It is convenient to think of natural selection provisionally in terms
of juvenile deaths. If it acts in this way, by killing off the less fit
genotypes, we shall calculate how many must be killed while a new gene
is spreading through a population." page 512
"[Haldane is speaking about the process of natural selection in a
deteriorating environment]... But meanwhile, a number of deaths, or
their equivalents in lowered fertility, have occurred. If selection at
the ith selected locus is responsible for di [that is, d subscript i] of
these deaths in any generation the reproductive capacity of the species
will be [the product of](1 - di) of that of the optimal genotype , or
exp(-[summation of]di) nearly, if every di is small. Thus the intensity
of selection approximates to [the summation of]di." page 514
"Let Di [that is D subscript i] be the sum of the values of di over all
generations of selection, ..." page 514
[moderator's note: Oh Jesus, not Princess Di again... - JAH]
Haldane then goes on to discuss the calculation of D for many different
cases - haploid, diploid, etc. On page 516, summing up the haploid case,
he says:
"We may, therefor, take it that when selection is fairly slow, the
total number of selective deaths over all generations is usually 5-15
times the total number in the population in each generation, 10 times
this being a representative value."
There are lots of other quotes in the paper along this line. Haldane
clearly defined the cost of natural selection to be the cumulative total
of all selective deaths in the course of a gene substitution. Obviously,
for the population size to remain constant, there
must be an equivalent number of surplus births somewhere. Therefor, the
cost can also be said to represent the amount of reproductive excess
required to keep the population from declining . Perhaps this is what
Walter means by "payments" for the "cost" of substitution. We may not be
disagreeing
on this specific issue, just talking about two sides of the same coin.
Well Walter, I ask you yet again, do you, or do you not accept Haldane's
definition for the cost of a substitution?
Robert
wjre...@mmm.com
Joe Felsenstein writes:
<snip>
> If you ask the same question about beneficial mutations, you get a very
> different answer. We could either be talking about a new beneficial mutant
> arising in the absence of environmental change, leaving the fitness of the
> other allele unchanged, or an environmental change that benefits one allele
> while not penalizing the other. In either case the answer is the same --
> you don't need any reproductive excess. The substitution increases
> fitnesses.
Here Felsenstein displays the central error of his 1971 paper (and much
of the literature on Haldane's Dilemma). He says a beneficial
substitution "increases fitness", and therefore "you don't need any
reproductive excess" to achieve it. But the increased fitness is
virtually irrelevant. The cost of substitution has virtually NOTHING to
do with the fact that a substitution increases the fitness of the
population. Rather, it is about that fact that anytime a given trait
goes from 'few' to 'many', the rate at which it does so is limited by
the specie's reproductive excess. There is no way around it.
******
Felsenstein recently acknowledged that beneficial substitutions do
indeed have a cost and it can be calculated, but he claimed this is made
up by the increased reproductive excess they provide. I pointed out
(among other things) that his scenario of ever increasing reproduction
is not realistic -- a specie's reproduction is limited. Felsenstein now
responds: (If you are short on time, jump below to "+++")
> we have to realize that the final reproductive excess will be the net
> effect of
> (1) deleterious environmental changes that are compensated for by
> substituting an allele that copes with them,
> (2) deleterious environmental changes that are uncompensated for,
> (3) favorable environmental changes that do not induce any substitution,
> (4) favorable environmental changes that do induce a substitution,
> and (5) advantageous mutants that occur in the absence of
> environmental change,
> plus even (6) deleterious mutations that get fixed by genetic drift.
>
> It seems to me that in view of events like (2) the occurrence of a
> stream of advantageous mutants (of type 4) that substitute need not drive
> the reproductive excess up to heights inconsistent with observation.
Felsenstein makes the following argument. He identifies six things that
affect a specie's final reproductive excess. Some of them (such as type
2) decrease it, while others (such as type 4) increase it. (Note: In
actual fact, "deleterious" and "favorable" changes are not tightly bound
to 'decreased' or 'increased' reproduction, respectively, so that
complicates the picture a bit. But let's follow his argument
nonetheless.) The decreases offset the increases, and therefore he
feels a stream of advantageous substitutions "need not drive the
reproductive excess up to heights inconsistent with observation."
+++ In short, Felsenstein is agreeing with me (from my previous
posts), that observations today put an end to (his) claims of ever
rising reproduction. A specie's reproduction is limited. It cannot
increase ad infinitum. So he now interjects a number of mechanisms that
REDUCE reproductive excess in order to keep it within plausible bounds
consistent with observation. This is ironic because an easing of
Haldane's Dilemma requires MORE reproductive excess, not less --
Felsenstein is going in precisely the wrong direction. He does that in
order to make his previous claims of ever increasing reproduction less
preposterous. But that move simultaneously eliminates his scenario from
easing Haldane's Dilemma.
Haldane's Dilemma is based on long-term average costs and payments.
These two factors -- unavoidable cost and limited payment -- set the
maximum plausible beneficial substitution rate. Felsenstein has not
reduced the cost of substitutions, nor increased the average
reproductive excess of the species, so he has not even slightly reduced
the problem. He has not set beneficial substitutions free from these
limitations.
-- Walter ReMine
The Biotic Message -- the book
Guy A. Hoelzer
In article <688rmo$r0i$1...@nntp6.u.washington.edu>, wjre...@mmm.com wrote:
> [Felsenstein] says a beneficial
> substitution "increases fitness", and therefore "you don't need any
> reproductive excess" to achieve it. But the increased fitness is
> virtually irrelevant. The cost of substitution has virtually NOTHING to
> do with the fact that a substitution increases the fitness of the
> population. Rather, it is about that fact that anytime a given trait
> goes from 'few' to 'many', the rate at which it does so is limited by
> the specie's reproductive excess. There is no way around it.
I think that I will agree to a limited interpretation of this statement.
That is, if reproduction is associated with parental death, then
individuals must (on average) produce more than one offspring if the
population is to increase. This statement can apply to any definable
population (e.g., the population of a new allele), and I think defines the
reproductive excess described by ReMine. However, it is astonishing to me
that ReMine says "increased fitness is virtually irrelevant" when fitness
is essentially defined as lifetime reproductive output. If a species
[note the spelling -- there is no such word as specie in the biological
lexicon] or any other population can be said to have an inherent
reproductive excess (=max. population growth rate?) that might limit its
rate of evolution, then that value itself must increase in response to a
beneficial mutation. In any case, such an inherent maximum is clearly not
a biologically relevant limiting factor under most conditions. I cannot
think of a natural situation in which this factor would affect rate of
evolution. Let's take a case where selection pressures are extreme, way
beyond the normal range: the introduction of a new antibiotic in a
hospital. Imagine that a new mutation arises that permits the mutant
pathogen to thrive despite the antibiotic. This mutation will spread
quickly throughout the pathogen population and its rate of spread might
seem to be limited only by its rate of reproduction, which I believe is
identical to ReMine's reproductive excess in this case. The net effect,
however, will depend on the population substructure. That is, within the
initially infected individual the new mutation will probably spread
unimpeded by anything other than reproductive rate. This spread will
likely not proceed in the same way throughout the hospital because other
factors will quickly reduce the rate of spread of the new mutation.
Transmission to other patients will be limited by chances of contact,
etc.. Therefore, the net rate of pathogenic evolution in the hospital, or
throughout the world, will be limited primarily by factors other than
reproductive excess.
I purposely chose an example that I think should maximize the influence
of reproductive excess; yet it seems clear to me that reproductive excess
fails to limit evolution in any meaningful way, even in this example.
Perhaps ReMine could provide a counter example of a hypothetical natural
population where reproductive excess is actually responsible for limiting
rate of evolution.
wjre...@mmm.com
Guy A. Hoelzer wrote:
<snip>
> ... it is astonishing to me that ReMine says "increased
> essentially defined as lifetime reproductive output.
Cost and payment are different, but Hoelzer confused the two. I was
speaking of cost. Hoelzer presumed I was talking about payment (i.e.
the species' reproductive output). Hoelzer misinterpreted what I was
saying.
Here is the context. Joe Felsenstein argued that a beneficial
substitution "increases fitness", and therefore "you don't need any
reproductive excess" to achieve it. In other words, Felsenstein was
reverting back to the mistake he made in his 1971 paper of claiming that
beneficial substitutions have no cost. I pointed out his mistake -- The
fact that a substitution is beneficial does NOT eliminate nor even
reduce its cost. Hoelzer misinterpreted our conversation as being about
reproductive payment.
******
Hoelzer makes another mistake of confusing "fitness" with reproductive
excess. Though one can affect the other, they are not the same. The
cost of substitution is concerned with costs and payments (of
reproductive excess), and neither of those is fitness.
> If a species ... or any other population can be said to have an inherent
> reproductive excess (=max. population growth rate?) that might limit its
> rate of evolution, then that value itself must increase in response to a
> beneficial mutation.
A beneficial substitution need not increase reproductive excess, and
indeed can often reduce it. Hoelzer should modify his above statement
from "must increase" to "might increase".
******
> In any case, such an inherent maximum [reproductive excess]
> is clearly not a biologically relevant limiting factor under
> most conditions. I cannot think of a natural situation
> in which this factor would affect rate of evolution.
Hoelzer cannot think of any natural situations where limited
reproduction limits the rate of substitution? Surely he is kidding us,
for even Doctor Felsenstein advertised here in this forum (and in his
1971 paper) that such a limitation exists, (though he mistakenly tries
to confine the limitation to situations of repetitive deleterious
environmental change).
So let's get back on track with an easy example. Suppose someone claims
that in a population of 100,000 asexual organisms there is one with a
beneficial mutation, and this substitutes in one generation. This
scenario has a cost of 99,999. In other words, the species must be
capable of supplying a reproductive excess of at least 99,999 or else
this scenario is not plausible. (Indeed it is not plausible for any
species I know of.) These cost arguments are potent.
******
Hoelzer gives an example involving the spread of a newly mutated
bacteria in a hospital. He points out that there are many obstacles to
its spread:
> This spread will likely not proceed in the same
> way throughout the hospital because other factors
> will quickly reduce the rate of spread of the
> new mutation. Transmission to other patients will
> be limited by chances of contact, etc.
> Therefore, the net rate of pathogenic evolution
> in the hospital, or throughout the world, will be
> limited primarily by factors other than
> reproductive excess.
Hoelzer is correct, there are many ADDITIONAL obstacles to evolutionary
substitutions beyond those identified in the Haldane-style cost-payment
arguments, and those obstacles operate to further SLOW the
substitutions. The actual rate of substitution will be SLOWER than what
is given by cost-payment arguments alone. Haldane's Dilemma is even
more severe than the cost-payment arguments indicate by themselves.
-- Walter ReMine
The Biotic Message -- the book
Joe Felsenstein
newsreaders]
We seem to have come down to a rather simple set of points. I argued
that beneficial mutations that occur in the absence of environmental
change do not create a problem for the species. ReMine seems to agree
(though he doesn't say so very clearly). He argues instead that they
create a "cost".
The crux of his argument appears to be that this cost creates a need for
a reproductive excess, not because there is some threat to the survival
of the species, but because the empirical absence of this reproductive
excess would be evidence against the advantageous mutations having
occurred. If a population substitutes 100 advantageous mutations, each
raising the fitness by 1%, we expect that the fitness ends up a factor of
2.7048 higher (readers may be tempted to expect 100%, but this is compound
interest).
I pointed out that there were other factors at work, such as changes of
environment, that could leave the population with not that much increase
of fitness, even though the advantageous mutations had occurred. Thus
in the absence of comprehensive information about genetics and environment,
the resulting fitness is unlikely to provide a strong argument limiting how
many advantageous mutants have occurred.
And there we stand. ReMine has no argument to counter this, though he
continues to engage in triumphalist rhetoric. His arguments play to
another audience, one that wants to believe that ReMine has uncovered some
major flaw in evolutionary genetic theory, one that us stuffy, pompous,
arrogant, confused academics have missed. He therefore announces that
> Felsenstein displays the central error of his 1971 paper (and much
> of the literature on Haldane's dilemma)
(There is no such error. The question of whether one should book-keep a
"cost" in the case of advantageous mutation is debatable but has largely
been ignored in the literature, and properly so, as it has no consequences.)
The issue that ReMine is actually raising is whether there is a prediction
about reproductive excess that springs from evolutionary theory, a prediction
which can be refuted by observations about the fitness of the resulting
organisms. When I make the argument that other changes can obscure the
fitness effects of the beneficial mutations, he says
>I pointed out
>(among other things) that his scenario of ever increasing reproduction
>is not realistic -- a specie's reproduction is limited.
...
>In short, Felsenstein is agreeing with me (from my previous
>posts), that observations today put an end to (his) claims of ever
>rising reproduction.
My claims of _what_? I talked of the consequences of beneficial substitutions
but never imagined that those would be the only events happening in real
species. I was talking about whether his "cost" was a problem for the
continued existence of the species, and raised beneficial substitutions
as a counterexample, as they clearly do not threaten the species.
It was me, not ReMine, who mentioned the events that reduce fitness. But
things, of course, appear far more dramatic to ReMine:
>A specie's reproduction is limited. It cannot
>increase ad infinitum. So he now interjects a number of mechanisms that
>REDUCE reproductive excess in order to keep it within plausible bounds
>consistent with observation. This is ironic because an easing of
>Haldane's Dilemma requires MORE reproductive excess, not less --
>Felsenstein is going in precisely the wrong direction. He does that in
>order to make his previous claims of ever increasing reproduction less
>preposterous. But that move simultaneously eliminates his scenario from
>easing Haldane's Dilemma.
I think this is precisely backwards. ReMine is saying that all substitutions
require reproductive excess, and that there is insufficient reproductive
excess for those substitutions to have actually occurred. I pointed out
that other changes, such as environmental changes, may eliminate much
of the reproductive excess that ReMine would predict. So ReMine says
aha, you therefore make Haldane's Dilemma worse.
The question is, whose Dilemma? It is not, in this argument, a Dilemma
for the species. Its continued existence is not threatened by the Dilemma.
ReMine's Dilemma is his claim that species don't have enough reproductive
excess to have evolved. That is not how he says but that is what it
boils down to. I suggested why they don't _appear_ to have the reproductive
excess, and ReMine says that this is a problem for _me_! No, it is a
problem for _him_. It vitiates his claim to have an observation
incompatible with evolution.
He needs to be asked: if a mix of beneficial mutations and (say)
unknown deteriorations of the environment are occurring, do you still claim to
have a way of predicting the final reproductive excess?
We need him to answer that.
wjre...@mmm.com
Let's get to the interesting new stuff first.
Joe Felsenstein wrote:
> ReMine is saying that all substitutions
> require reproductive excess, and that there is insufficient reproductive
> excess for those substitutions to have actually occurred. I pointed out
> that other changes, such as environmental changes, may eliminate much
> of the reproductive excess that ReMine would predict. So ReMine says
> aha, you therefore make Haldane's Dilemma worse.
Felsenstein misrepresents the situation. He claims I "would predict"
high reproductive excess -- (I would make no such prediction). Then he
races to "eliminate much of the reproductive excess". He thereby
(unintentionally) makes Haldane's Dilemma worse. How? Because the
lower the reproductive excess, the lower the substitution rate. I
pointed that out in my previous post.
So, next Felsenstein back-pedals, trying yet another approach. He
claims his arguments that "eliminate much of the reproductive excess"
give only the false APPEARANCE of lower reproductive excess. This is a
whopper, so here it is in his own words:
> I suggested why they don't _appear_ to have the reproductive
> excess, and ReMine says that this is a problem for _me_!
> No, it is a problem for _him_. It vitiates his claim to have an
> observation incompatible with evolution.
>
> He needs to be asked: if a mix of beneficial mutations and (say)
> unknown deteriorations of the environment are occurring, do you
> still claim to have a way of predicting the final reproductive
> excess?
I do not "predict" a species' final reproductive excess -- we need
merely observe it and measure it. It is fairly straightforward.
Felsenstein pretends there are too many factors, too many complications
to do this. He pretends that reproductive excess is actually much
higher than it "appears". He is thoroughly in error. The species'
reproductive excess is observable, and that's all there is. There ain't
no more.
Moreover, the many factors that he himself identified ACTUALLY DO REDUCE
the reproductive excess. They don't just "appear to", they actually
do. When Felsenstein argued for lower reproduction, he made Haldane's
Dilemma worse.
Next we must eliminate a number of misrepresentations and confusion
factors. I covered most in previous posts, but they are back again, so
we here eliminate them again.
******
> We seem to have come down to a rather simple set of points. I argued
> that beneficial mutations that occur in the absence of environmental
> change do not create a problem for the species. ReMine seems to agree
> (though he doesn't say so very clearly).
No, the cost of substitution never creates "a problem for the species",
it creates a problem for a given evolutionary *scenario*. If the
species cannot pay the cost of the scenario (by supplying the required
level of reproductive excess), then the scenario is not plausible. I
clearly stated this from the beginning.
******
> The crux of his argument appears to be that this cost creates a need for
> a reproductive excess, not because there is some threat to the survival
> of the species, but because the empirical absence of this reproductive
> excess would be evidence against the advantageous mutations having
> occurred.
The cost of substitution is not fundamentally an argument "against the
advantageous mutations having occurred." Rather, it is -- first and
foremost -- a method for identifying when a given beneficial
substitution rate is implausible.
The speed of growth of a trait -- the substitution rate -- cannot
proceed faster than the species' limited reproductive excess will
allow. The central issue is the indelible connection between growth
rate and reproductive excess.
A species' limited reproductive excess places
a firm limit on the rate at which a new rare
trait can go from 'few' to 'many' --
absolutely, positively, no exceptions.
******
Next we have several cases where Felsenstein mistakenly focuses on
"fitness". I have repeatedly pointed out that fitness is virtually
irrelevant to the problem of Haldane's Dilemma. Felsenstein didn't
respond to those arguments, nonetheless he continues to interject
fitness into the discussion as though it were a central issue. Worse
still, he misrepresents *my* position as focusing on fitness.
> If a population substitutes 100 advantageous mutations,
> each raising the fitness by 1%, we expect that the
> fitness ends up a factor of 2.7048 higher (readers
> may be tempted to expect 100%, but this is compound
> interest).
ALL of the above is irrelevant to Haldane's Dilemma and the cost of
substitution. The fact that a substitution increases fitness does not
reduce its cost of substitution.
> I pointed out that there were other factors at work, such as changes of
> environment, that could leave the population with not that much increase
> of fitness, even though the advantageous mutations had occurred. Thus
> in the absence of comprehensive information about genetics and environment,
> the resulting fitness is unlikely to provide a strong argument limiting how
> many advantageous mutants have occurred.
Felsenstein again focuses (mistakenly) on the "increase of fitness" and
"the resulting fitness".
> The issue that ReMine is actually raising is whether there is a prediction
> about reproductive excess that springs from evolutionary theory, a prediction
> which can be refuted by observations about the fitness of the resulting
> organisms. When I make the argument that other changes can obscure the
> fitness effects of the beneficial mutations, he says ...
Felsenstein misrepresented my argument as being about fitness.
******
> The question of whether one should book-keep a "cost"
> in the case of advantageous mutation is debatable but has
> largely been ignored in the literature, and properly so, as
> it has no consequences.
Felsenstein is partially correct: Yes, the cost issue is abundantly
"debatable", and "has largely been ignored in the literature" under the
(mistaken) belief that "it has no consequences". It has big
consequences, of course it does, there is something serious at stake.
Haldane's Dilemma was obscured and brushed aside as 'solved', but
evolutionary geneticists themselves do not remotely agree on the
solution.
-- Walter ReMine
The Biotic Message -- the book
wjre...@mmm.com
Let's get to the interesting new stuff first.
Joe Felsenstein wrote:
> ReMine is saying that all substitutions
> require reproductive excess, and that there is insufficient reproductive
> excess for those substitutions to have actually occurred. I pointed out
> that other changes, such as environmental changes, may eliminate much
> of the reproductive excess that ReMine would predict. So ReMine says
> aha, you therefore make Haldane's Dilemma worse.
Felsenstein misrepresents the situation. He claims I "would predict"
high reproductive excess -- (I would make no such prediction). Then he
races to "eliminate much of the reproductive excess". He thereby
(unintentionally) makes Haldane's Dilemma worse. How? Because the
lower the reproductive excess, the lower the substitution rate. I
pointed that out in my previous post.
So, next Felsenstein back-pedals, trying yet another approach. He
claims his arguments that "eliminate much of the reproductive excess"
give only the false APPEARANCE of lower reproductive excess. This is a
whopper, so here it is in his own words:
> I suggested why they don't _appear_ to have the reproductive
> excess, and ReMine says that this is a problem for _me_!
> No, it is a problem for _him_. It vitiates his claim to have an
> observation incompatible with evolution.
>
> He needs to be asked: if a mix of beneficial mutations and (say)
> unknown deteriorations of the environment are occurring, do you
> still claim to have a way of predicting the final reproductive
> excess?
I do not "predict" a species' final reproductive excess -- we need
merely observe it and measure it. It is fairly straightforward.
Felsenstein pretends there are too many factors, too many complications
to do this. He pretends that reproductive excess is actually much
higher than it "appears". He is thoroughly in error. The species'
reproductive excess is observable, and that's all there is. There ain't
no more.
Moreover, the many factors that he himself identified ACTUALLY DO REDUCE
the reproductive excess. They don't just "appear to", they actually
do. When Felsenstein argued for lower reproduction, he made Haldane's
Dilemma worse.
Next we must eliminate a number of misrepresentations and confusion
factors. I covered most in previous posts, but they are back again, so
we here eliminate them again.
******
> We seem to have come down to a rather simple set of points. I argued
> that beneficial mutations that occur in the absence of environmental
> change do not create a problem for the species. ReMine seems to agree
> (though he doesn't say so very clearly).
No, the cost of substitution never creates "a problem for the species",
it creates a problem for a given evolutionary *scenario*. If the
species cannot pay the cost of the scenario (by supplying the required
level of reproductive excess), then the scenario is not plausible. I
clearly stated this from the beginning.
******
> The crux of his argument appears to be that this cost creates a need for
> a reproductive excess, not because there is some threat to the survival
> of the species, but because the empirical absence of this reproductive
> excess would be evidence against the advantageous mutations having
> occurred.
The cost of substitution is not fundamentally an argument "against the
advantageous mutations having occurred." Rather, it is -- first and
foremost -- a method for identifying when a given beneficial
substitution rate is implausible.
The speed of growth of a trait -- the substitution rate -- cannot
proceed faster than the species' limited reproductive excess will
allow. The central issue is the indelible connection between growth
rate and reproductive excess.
A species' limited reproductive excess places
a firm limit on the rate at which a new rare
trait can go from 'few' to 'many' --
absolutely, positively, no exceptions.
******
Next we have several cases where Felsenstein mistakenly focuses on
"fitness". I have repeatedly pointed out that fitness is virtually
irrelevant to the problem of Haldane's Dilemma. Felsenstein didn't
respond to those arguments, nonetheless he continues to interject
fitness into the discussion as though it were a central issue. Worse
still, he misrepresents *my* position as focusing on fitness.
> If a population substitutes 100 advantageous mutations,
> each raising the fitness by 1%, we expect that the
> fitness ends up a factor of 2.7048 higher (readers
> may be tempted to expect 100%, but this is compound
> interest).
ALL of the above is irrelevant to Haldane's Dilemma and the cost of
substitution. The fact that a substitution increases fitness does not
reduce its cost of substitution.
> I pointed out that there were other factors at work, such as changes of
> environment, that could leave the population with not that much increase
> of fitness, even though the advantageous mutations had occurred. Thus
> in the absence of comprehensive information about genetics and environment,
> the resulting fitness is unlikely to provide a strong argument limiting how
> many advantageous mutants have occurred.
Felsenstein again focuses (mistakenly) on the "increase of fitness" and
"the resulting fitness".
> The issue that ReMine is actually raising is whether there is a prediction
> about reproductive excess that springs from evolutionary theory, a prediction
> which can be refuted by observations about the fitness of the resulting
> organisms. When I make the argument that other changes can obscure the
> fitness effects of the beneficial mutations, he says ...
Felsenstein misrepresented my argument as being about fitness.
******
> The question of whether one should book-keep a "cost"
> in the case of advantageous mutation is debatable but has
> largely been ignored in the literature, and properly so, as
> it has no consequences.
Felsenstein is partially correct: Yes, the cost issue is abundantly
"debatable", and "has largely been ignored in the literature" under the
(mistaken) belief that "it has no consequences". It has big
consequences, of course it does, there is something serious at stake.
Haldane's Dilemma was obscured and brushed aside as 'solved', but
evolutionary geneticists themselves do not remotely agree on the
solution.
-- Walter ReMine
The Biotic Message -- the book
Joe Felsenstein
In article <68h73g$oni$1...@nntp6.u.washington.edu>, <wjre...@mmm.com> wrote:
>Let's get to the interesting new stuff first.
ReMine has got very upset with my statements:
>Felsenstein misrepresents the situation.
...
>So, next Felsenstein back-pedals, trying yet another approach.
>... This is a whopper
...
>Next we must eliminate a number of misrepresentations and confusion
>factors.
...
>... Worse
>still, he misrepresents *my* position as focusing on fitness.
...
>Felsenstein misrepresented my argument as being about fitness.
Rather than trying to go over all these and see whether I did do all
these horrible things, perhaps we could go one step at a time and
see whether we can thrash them out. We can get back to my sins and
crimes later.
Point 1:
ReMine says that
>No, the cost of substitution never creates "a problem for the species",
>it creates a problem for a given evolutionary *scenario*. If the
>species cannot pay the cost of the scenario (by supplying the required
>level of reproductive excess), then the scenario is not plausible. I
>clearly stated this from the beginning.
So, (in 500 words or less), am I correct to interpret ReMine as saying
that if someone says that 100 substitutions of advantageous mutations
have occurred, each adding 1% fitness, that this can be checked by observing
something about the organism's reproductive excess afterwards? If so, exactly
what is it that can be oberved? The reproductive excess itself?
----
Donal Hickey
wjre...@mmm.com wrote:
>
> Joe Felsenstein writes:
> > If you ask the same question about beneficial mutations, you get a very different answer.
> Here Felsenstein displays the central error of his 1971 paper (and much
> of the literature on Haldane's Dilemma). He says a beneficial
> substitution "increases fitness", and therefore "you don't need any
> reproductive excess" to achieve it.
Re: Haldane's "The Cost of Natural Selection"
I thought I should start the new year by summarizing what I have learned
from this discussion.First of all, there is quite a lot of agreement
between all parties. The disagreement is most obvious in dealing with
beneficial mutations occurring in a more or less constant environment.
More particularly, the key argument is whether reasonable assumptions
about real levels of reproductive excess, especially in mammals, pose an
insurmountable cost in terms of the selective deaths that must be
invoked to account for the substitution of MULTIPLE beneficial
mutations. Everybody seems to agree that if beneficial mutations are
very rare, there is usually enough reproductive excess for them to chug
along, over many generations, from low initial frequencies to eventual
fixation in the population. But what happens if there are multiple
beneficial mutations that all "need"to be selected simultaneously?
Haldane envisaged that nature might be faced with the same problem as
the cattle breeder who wished to select his cows not only for higher
total milk yield, but also higher butterfat content (seen as positive
attribute back in the 1950's), ease of calving, docility, meat quality,
etc, etc. Obviously, the breeder runs out of calves to cull pretty
quickly since each cow produces only a single calf per year.
Intuitively, one can see that problem might not be so acute for the pig
breeder down the lane, since her sows would farrow a couple of times a
year, and each could produce more than a dozen piglets at each
farrowing. I don't
think the argument is really about the correlation between reproductive
capacity and speed of response to selection. Everybody recognizes that
as a fact - this is why population geneticists choose fast-reproducing
organisms such as Drosophila for their selection experiments. The
argument here is how natural selection (not artificial selection) can
cope with MULTIPLE beneficial mutations. Walter Remine claims that this
poses an insurmountable problem for evolutionary theory, at least as
applied to large mammals with small litter sizes and long generation
times. My impression of his view (and correct me of I'm wrong, Walter)
is that simultaneous selection on many favorable alleles is just not
sustainable in these populations; it would lead to a sort of
evolutionary gridlock and the population could well go extinct due to
the high "cost" in selective deaths. Joe Felsentstein presents a very
different perspective on the same situation. He asks us to imagine a
population of organisms that is well adapted to its environment,and in
no obvious danger of going extinct. He then asks how the addition of
mutation that INCREASES the adaption of some genotypes could possibly
make this population more vulnerable to extinction, or reduce its
fitness in any way. And if one mutation is a "good thing", surely more
mutations are even better. Both views seem pretty logical and coherent.
So who's right?
At the risk of playing the weasel of compromise who tries to
satisfy everyone and ends up satisfying nobody, let me try to explain
what I think happens. Up to now, I have confined myself to nipping at
the heels of other peoples' arguments, to get an idea where they were
coming from. So let's consider a population of, say, 10,000 well-adapted
individuals (pick a large mammal of your choice), all of which have a
finite amount of potential reproductive excess, and into which we
introduce one hundred "beneficial" mutations, while keeping the
environment constant. To keep everyone happy, let's say some of the
advantageous mutations increase juvenile viability, some increase female
fecundity, others augment male fertility, while still others are
favorable by providing advantages in terms of intraspecific competition
for limited resources. With a hundred different mutations to choose
from, we can fill lots of different "beneficial" categories. This new
population with 9,900 of the old genotype, along with 100 different
favorably mutant genotypes will not be in greater danger of extinction.
Also, I think everyone would probably agree that the mutant frequencies
might all tend to increase by natural selection, within the constraints
set by the amount of reproductive excess in this species. Initially,
when the mutations are very rare and the population is finite (10,000),
there won't be any appreciable interference between selection at one
locus and selection at the other 99 loci. The difficulties arise as the
gene frequencies at each of the selected loci increases. At some point
in time, a majority of individuals in the population will have at least
one copy of one of the hundred different favorable mutations, and many
individuals will have multiple mutations. Even if the reproductive rate
is increased due to the presence of these mutations, it is reasonable to
assume that it is still finite and, perhaps, not hugely different from
that in the original population. (We can argue about that later).
Consequently, we might conclude that the selective advance of any given
mutant allele will be impeded by the simultaneous selection acting at
all the other loci. This is because the reproductive excess is now being
"shared" by selection acting at several different loci. So what are the
consequences for a real population? Is it in danger of going extinct?
Will it simply stop evolving? I believe the answer is "no" to both of
these questions. First, if the environment has not deteriorated, and the
population now contains many fitter types than it did originally, the
probability of extinction will be decreasing rather than increasing.
This is, I believe, what Joe Felsenstein has been trying to get
across. But what about Haldane's analogy to trying to cull too many cows
for two many different traits at once. Here is where the analogy with
artificial selection becomes more of a hindrance than a help in
understanding the natural world. The two processes (artificial and
natural selection) are very similar in many respects but, in a breeding
experiment (or in a bacterial selection experiment), a certain outcome
is "demanded" within a certain time period. Meeting the demands (in
terms of
numbers of alleles substituted within a given time period) may place an
implausible "burden" or "cost" on the population, given the average
reproductive output (of any genotype). In other words, the impatient
breeder risks annihilating his breeding population by culling too many
individuals. Natural selection, however, does not have to meet pre-set
deadlines for genetic improvement. The available reproductive excess,
whatever it is, provides the fuel for gene frequency change. Even if
there are mutations at many different loci being substituted
simultaneously, there is no threat of extinction, or of a crash in
population size (again, assuming no deterioration in either the physical
or biotic environment). What IS affected is the rate of substitution of
ANY GIVEN mutation. Since the total amount of culling does not increase
drastically even when several beneficial mutations are undergoing
natural selection simultaneously, the amount of culling per locus, per
generation, has to decrease. To recap, the typical breeder would tend to
hold the time to fixation constant, thus requiring an exponentially
increasing amount of reproductive excess to fix many mutations
in a given time period; natural selection on the other hand has to work
with a (relatively) fixed amount of reproductive excess, resulting in
longer time periods for multiple substitutions. So it seems as though
I'm concluding that multiple beneficial substitutions do slow the rate
of evolution, even if they don't threaten the population with
extinction. Not so. The rate of EACH substitution is slowed compared the
case of single substitutions, but we must remember that the slower
process is resulting in many simultaneous substitutions. To take a
trivial example, if it takes a hundred times as long to substitute one
hundred mutations simultaneously, compared to the time it would take to
substitute a single mutation, there is still an average of one
substitution per unit time. Thus, at equilibrium, the average rate of
substitution can be independent of the number of mutations that are
being simultaneously substituted at any one time. This is reminiscent of
the equilibrium rate of substitution of neutral mutations, which is
independent of population size - despite the fact that the rate of
frequency change of any given neutral allele at a given moment in time,
is very dependent on population size.
To summarize, although the rate of response to natural selection is
constrained by the amount of reproductive excess, (i) beneficial
mutations cannot be seen to constitute any biological cost to the
population and (ii) multiple substitutions slow the rate of substitution
of particular individual alleles, but they do not affect on the average
rate of substitution. This leaves us with the question of how much
adaptive genetic change actually did occur in real populations over the
course of evolution. The answer to this question will depend more on the
empirical results from selection experiments and comparative genomics
than it does on any of the arguments presented here, including my own.
For what it's worth my hunch is that we will find that the amount of
adaptive genetic change that has actually occurred during the course of
evolution is only a fraction of what could have occurred, given the
available reproductive excess and the number of generations involved.
It's not so along ago since we worried that cells might not possibly be
able to contain enough DNA to code for their myriad genetic functions.
Then we discovered that there is not only enough DNA per eukaryotic
cell, but about two orders of magnitude more than enough. Likewise,
nineteenth century evolutionists worried that the age of the earth (then
estimated by some to be less than 10,000 years old) might not be great
enough to allow time for evolution by natural selection. Again, this
worry proved to be unfounded. So my hunch is that once we get some
reasonable quantitative estimates of the number of adaptive genetic
changes between species, we will see that the amount of time available
for the observed amount of adaptive evolutionary change is very ample
indeed. It's only a hunch, of course, but I don't see any convincing
evidence to the contrary. Is there some available that I'm not aware of?
Donal Hickey.
wjre...@mmm.com
Joe Felsenstein wrote:
> So, (in 500 words or less), am I correct to interpret ReMine as saying
> that if someone says that 100 substitutions of advantageous mutations
> have occurred, each adding 1% fitness, that this can be checked by
> observing something about the organism's reproductive excess
> afterwards? If so, exactly what is it that can be observed?
> The reproductive excess itself?
Felsenstein's latest post does not advance any viewpoint, it only asks
questions, questions about the 'observability' of reproductive excess.
If this issue was essential to solving Haldane's Dilemma, then it SHOULD
have been raised and addressed in Felsenstein's 1971 paper. But it was
not. His paper makes no mention of it. Felsenstein is increasingly
referring to matters not present in his paper -- and this illustrates my
claim that his paper does not solve Haldane's Dilemma.
His paper (correctly) concludes that the beneficial substitution rate is
limited by the species' limited reproductive excess, but it (mistakenly)
claims this limitation applies ONLY to those that originate through
environmental change. I say his conclusion applies to ALL beneficial
substitutions regardless of their origin. Why? (1) Other things being
equal, the 'origin' of a beneficial mutation makes no difference to its
cost of substitution. (2) A species' reproductive excess is always
limited. There is an unavoidable cost of substitution, and there are
limitations to a species' reproduction -- these limit the substitution
rate, and Felsenstein has not changed that dynamic. He has not freed
beneficial substitutions from these shackles that he admits exist.
Felsenstein's entire focus lately is on whether reproductive excess is
'observable'. Well, yes, it is observable, (even after 100 advantageous
substitutions). And. no, that doesn't change any of the above.
Joe Felsenstein
In article <68tug3$rqu$1...@nntp6.u.washington.edu>,
Donal Hickey <dhi...@uottawa.ca> wrote:
>... The disagreement is most obvious in dealing with
>beneficial mutations occurring in a more or less constant environment.
>My impression of [Walter ReMine's] view (and correct me of I'm wrong, Walter)
>is that simultaneous selection on many favorable alleles is just not
>sustainable in these populations; it would lead to a sort of
>evolutionary gridlock and the population could well go extinct due to
>the high "cost" in selective deaths.
>Even if the reproductive rate
>is increased due to the presence of these mutations, it is reasonable to
>assume that it is still finite and, perhaps, not hugely different from
>that in the original population. (We can argue about that later).
OK. It's later. Let's argue about it. If each mutant allele increases
the reproductive rate by 1% when homozygous, then (making them multiplicative)
100 of them will increase it by a factor of 2.7048. So it is _not_ reasonable
to assume this, unless you want to make the alleles interact
non-multiplicatively.
>... Natural selection, however, does not have to meet pre-set
>deadlines for genetic improvement.
...
>... What IS affected is the rate of substitution of
>ANY GIVEN mutation.
...
>... natural selection on the other hand has to work
>with a (relatively) fixed amount of reproductive excess, resulting in
>longer time periods for multiple substitutions.
...
>... The rate of EACH substitution is slowed compared the
>case of single substitutions,
Not unless we want to assume non-multiplicative interactions.
---
Joe Felsenstein
In article <68tuge$kr6$1...@nntp6.u.washington.edu>, <wjre...@mmm.com> wrote:
>Joe Felsenstein wrote:
>
>> So, (in 500 words or less), am I correct to interpret ReMine as saying
>> that if someone says that 100 substitutions of advantageous mutations
>> have occurred, each adding 1% fitness, that this can be checked by
>> observing something about the organism's reproductive excess
>> afterwards? If so, exactly what is it that can be observed?
>> The reproductive excess itself?
>
>Felsenstein's latest post does not advance any viewpoint, it only asks
>questions, questions about the 'observability' of reproductive excess.
>If this issue was essential to solving Haldane's Dilemma, then it SHOULD
>have been raised and addressed in Felsenstein's 1971 paper. But it was
>not. His paper makes no mention of it. Felsenstein is increasingly
>referring to matters not present in his paper -- and this illustrates my
>claim that his paper does not solve Haldane's Dilemma.
Nor was it intended to. It was intended to explain what (in one model case
where we could analyze it more exactly) Haldane's Dilemma was. It did that.
I don't know where ReMine gets the idea that my 1971 paper was trying to
"solve Haldane's Dilemma".
>His paper (correctly) concludes that the beneficial substitution rate is
>limited by the species' limited reproductive excess, but it (mistakenly)
>claims this limitation applies ONLY to those that originate through
>environmental change. I say his conclusion applies to ALL beneficial
>substitutions regardless of their origin. Why? (1) Other things being
>equal, the 'origin' of a beneficial mutation makes no difference to its
>cost of substitution. (2) A species' reproductive excess is always
>limited. There is an unavoidable cost of substitution, and there are
>limitations to a species' reproduction -- these limit the substitution
>rate, and Felsenstein has not changed that dynamic. He has not freed
>beneficial substitutions from these shackles that he admits exist.
>
>Felsenstein's entire focus lately is on whether reproductive excess is
>'observable'. Well, yes, it is observable, (even after 100 advantageous
>substitutions). And. no, that doesn't change any of the above.
So suppose that an organism starts out with 2.0 offspring per parent when
population density is low. 100 mutations, each with a 1% advantage when
homozygous, and multiplicative in their effects on fitness, substitute. When
all is over, we should see a fitness of 2 x 1.01^100 = 4.1496, right? Yes,
if that is all that is going on. No, if there are also some deteriorations of
the environment occurring, ones which are not related to the substitutions.
This is, I think, the crux of the disagreement between ReMine and me. He
is arguing that observing 2.0 offspring per parent is inconsistent
with having had those substitutions. He is wrong.
--
DJohn1117
You may want to reply to Donal Hickey's very long question rather than mine.
Mine is similar, but shorter. (After I finished typing this it turned out to
be longer than I meant it to be.)
I've got a copy of the Princeton paperback edition of Haldane's book The Causes
of Evolution and in a supplementary appendix written by Egbert Leigh, there's a
formula giving the time required to take a mutant allele with a positive
selection coefficient = k from an original frequency of x to a final frequency
of y. The formula is
n = (1/k) ln (y/x)
where n is the number of generations. He gets this by starting with a
difference equation that he approximates with the differential equation
du/dn = ku, where u is the gene frequency. (x is u(0) and y is u(final time).)
Now my question is how this formula changes if there are multiple beneficial
mutations that appear in the population simultaneously? Suppose they all
convey the same fitness advantage and that the fitnesses are multiplicative.
That is, one mutant allele will give the critter a relative fitness of 1+k and
having two mutant alleles will give a fitness of (1+k)^2, etc....
Also assume the mutants are at different loci and aren't linked. How many
generations would it take to bring the initial frequency of x up to a later
frequency of y? Has anyone worked this out?
My intuition is that intially, when all the beneficial mutations are rare, they
increase in frequency at the same rate as would happen if there were only one
beneficial mutation in the population. Later, when a significant fraction of
the population has one or more of these new alleles, they will start
interfering with each other and this will slow down the rate at which
individual alleles are substituted. I suppose it might also make a difference
as to whether the population size as a whole is increasing as a result of these
changes.
I think I have your 1971 paper somewhere, but I can't find it. (I'm not a
biologist, but I've been interested in this question even before I heard of the
Biotic Message argument. And no, I'm not a creationist. It seems like trying
to calculate the maximum possible rate at which genes could be substituted
would be one of the standard problems in population genetics, but it seems to
me that people in the field don't see it that way. Maybe the problem is in
general too complex to be solved except in special cases, which is why I'm
formulating what I hope is a simple version. Anyway, if I remember it
correctly, the impression that I took from your paper was that in the case
where the environment is deteriorating, and new alleles are needed simply to
prevent extinction, there was a limit to the rate at which genes could be
substituted, so if you had 100 new alleles in the population or just 1, the
maximum possible rate of substitution is the same--it depended on the
reproductive excess available. Is that right and does it hold if the
environment isn't deteriorating?
Donald Johnson
Donal Hickey
Joe Felsenstein wrote:
> OK. It's later. Let's argue about it. If each mutant allele increases
> the reproductive rate by 1% when homozygous, then (making them multiplicative)
> 100 of them will increase it by a factor of 2.7048. So it is _not_ reasonable
> to assume this, unless you want to make the alleles interact
> non-multiplicatively.
>
rate, and that interactions between loci are always multiplicative, then
I don't think we have anything to argue about. We could, however, argue
about those two assumptions. But I'm not sure how useful such an
argument would be in solving the issues raised in the current
discussion. The underlying assumption in Walter ReMine's arguments seems
to be that if biologists admitted that the amount of reproductive excess
in a species sets an upper limit to the rate of adaptive evolution, then
the Darwinian theory of evolution by natural selection would have to be
abandoned. He implies that Haldane's calculations pointed out some fatal
flaw in evolutionary theory, despite the fact that the closing sentence
in Haldane's paper is: "This accords with the observed slowness of
evolution". My reading of your own subsequent work is that you feel that
Haldane was probably too conservative in his estimates of maximal
evolutionary rates. He probably was. In any case, even Haldane didn't
think that evolution happened too fast to be explained by natural
selection. Neither do I. Do you? I suspect not. Obviously Walter does,
and I don't think that any arguments we could have about the relative
merits of multiplicative versus non-multiplicative models of fitness
interactions is going to change that belief.
Donal.
John Edser
One "substitution" of one allele at one single locus, after mutation has
occurred to creat it, is only possible if the *soma* that "contains" the
allele, replicates itself once.The soma must replicate once, NOT just the
allele. "Substitution" as used in this thread, just means, replication of
the mutant allele, into the next generation of *somas,* not into the next
generation of alleles.
ReMines costing concept, as I understand it, for one allele, at one locus,
is then, one *soma*.
Is this correct?
John Edser
Independent Researcher
ed...@atinet.com.au
Box 266 Church Point P.O.
Church Point
NSW 2105
Australia
Mobile:014 077 018
wjre...@mmm.com
Donal Hickey wrote:
> .... the key argument is whether reasonable assumptions about
> real levels of reproductive excess, especially in mammals, pose an
> insurmountable cost in terms of the selective deaths that must be
> invoked to account for the substitution of MULTIPLE beneficial
> mutations.
Hickey summarizes the discussion he has seen so far, saying the "key
argument" is about MULTIPLE substitutions. In actual fact we scarcely
mentioned it. So far it has not been the issue been Joe Felsenstein and
me. Rather, Felsenstein argues (here and in his 1971 paper) that
beneficial substitutions "do not impose a cost because they confer a
benefit", and therefore the beneficial substitution rate is not limited
by the species' limited reproduction. The key argument is this: Are
beneficial substitutions freed from the limitations of finite
reproduction simply because they are "beneficial"? Felsenstein says
yes. I say no, and repeatedly gave counter-examples to his argument. I
say his argument is thoroughly mistaken, and neither his argument nor
mine is about multiple substitutions.
Felsenstein now offers less and less defense of his original position.
He does not address my arguments. Instead, he increasingly interjects
extraneous matters that divert and confuse our discussion. Such as
substitutional load, fitness, multiple substitutions, and most recently,
multiplicative fitness models (as opposed to non-multiplicative fitness
models). He does not focus on those issues, he just casually drops them
into the debate, ***but they have no role whatever in defending his
original position.***
It seems that Felsenstein is wandering about, looking for a solution.
Donal Hickey apparently senses this too, as he suggests we move to focus
on 'multiple' substitutions.
******
> Everybody seems to agree that if beneficial mutations are very rare,
> there is usually enough reproductive excess for them to chug
> along, over many generations, from low initial frequencies to
> eventual fixation in the population.
No, we don't all agree on the above scenario. It really depends on a
given species' reproductive excess and the claimed substitution rate.
Depending on the figures, it might be plausible, or implausible -- one
cannot say without reference to those figures. We do not agree the
above scenario is *always* plausible.
******
> Walter ReMine claims that this poses an insurmountable
> problem for evolutionary theory, ...
No. To be precise, I claimed Haldane's Dilemma is a serious problem
that was never solved, it was merely obscured and brushed aside.
******
> My impression of [ReMine's] view ... is that simultaneous
> selection on many favorable alleles is just not sustainable
> in these populations; it would lead to a sort of evolutionary
> gridlock and the population could well go extinct due to
> the high "cost" in selective deaths.
Leave out extinction. The cost of substitution never was a theory of
extinction. This 'extinction' error occurs repeatedly in Hickey's
post. It is often used by people to confuse, obscure, and brush aside
Haldane's Dilemma.
******
> Joe Felsentstein presents a very
> different perspective on the same situation. He asks us to imagine a
> population of organisms that is well adapted to its environment,and in
> no obvious danger of going extinct. He then asks how the addition of
> mutation that INCREASES the adaption of some genotypes could possibly
> make this population more vulnerable to extinction, or reduce its
> fitness in any way. And if one mutation is a "good thing", surely more
> mutations are even better. Both views seem pretty logical and coherent.
> So who's right?
Hickey follows Felsenstein in misrepresenting our debate. The above
paragraph has nothing to do with the cost of substitution or Haldane's
Dilemma. It emphasizes the traditional confusions of extinction and
fitness.
******
Haldane's paper briefly discusses the artificial selection of cows.
Hickey sees how this can pose a limitation to the substitution rate,
just as Haldane described. But Hickey tries to brush this aside as
irrelevant to natural selection, claiming there is some key difference
between artificial and natural selection. He says in artificial
selection "a certain outcome is 'demanded' within a certain time
period", but "Natural selection, however, does not have to meet pre-set
deadlines for genetic improvement." Hickey misunderstands the
situation. An evolutionary scenario itself DEMANDS certain substitutions
within a certain time period. The scenario does NOT have the luxury of
claiming there are no deadlines for genetic improvement. If the species
does not have sufficient reproduction to pay the costs of the scenario,
then the scenario is not plausible. There is no difference between
artificial and natural selection on this count.
Here is Hickey's wording:
> But what about Haldane's analogy to trying to cull too many cows
> for two many different traits at once. Here is where the analogy with
> artificial selection becomes more of a hindrance than a help in
> understanding the natural world. The two processes (artificial
> and natural selection) are very similar in many respects but, in a
> breeding experiment (or in a bacterial selection experiment), a
> certain outcome is "demanded" within a certain time period.
> Meeting the demands (in terms of numbers of alleles substituted
> within a given time period) may place an implausible "burden" or
> "cost" on the population, given the average reproductive output
> (of any genotype). In other words, the impatient breeder risks
> annihilating his breeding population by culling too many
> individuals. Natural selection, however, does not have to meet
> pre-set deadlines for genetic improvement. The available
> reproductive excess, whatever it is, provides the fuel for gene
> frequency change.
wjre...@mmm.com
Donald Johnson wrote:
> It seems like trying to calculate the maximum possible
> rate at which genes could be substituted would be one
> of the standard problems in population genetics, but it
> seems to me that people in the field don't see it that way.
Johnson correctly observes the emperor's clothes are missing. What
ought to be an interesting, highly relevant, central issue in
evolutionary genetics is scarcely discussed by people in the field.
That issue is the maximum possible rate at which genes could be
substituted, the precise issue addressed by the cost of substitution and
Haldane's Dilemma. (Even then a number of false solutions and confusions
have been given a free pass in the literature and allowed to stand
unchallenged for decades.) This **key central issue** of evolutionary
genetics has been given astonishingly little scrutiny. Bravo to Donald
Johnson for confirming what I have been saying for years!
It's too bad that in this forum (sci.bio.evolution) Johnson couldn't
just speak the truth -- whatever it may be -- unashamed and confident
that his person would not be impugned. But alas, he was compelled to
add, "And no, I'm not a creationist." (If he has another incident like
this, he may wish to genuflect a little deeper next time. A more
fulsome denouncement would be expected.)
wjre...@mmm.com
Joe Felsenstein wrote:
> I don't know where ReMine gets the idea that my 1971 paper was trying to
> "solve Haldane's Dilemma".
Felsenstein's 1971 paper on the cost of substitution claims beneficial
mutations impose no cost because they confer a benefit. It claimed
there is no cost limitation to the beneficial substitution rate. In
other words, it (implicitly) claimed to offer a solution to Haldane's
Dilemma. Now Felsenstein pretends otherwise?
Below is the entirety of Felsenstein latest argument.
> So suppose that an organism starts out with 2.0 offspring per parent when
> population density is low. 100 mutations, each with a 1% advantage when
> homozygous, and multiplicative in their effects on fitness, substitute. When
> all is over, we should see a fitness of 2 x 1.01^100 = 4.1496, right? Yes,
> if that is all that is going on. No, if there are also some deteriorations of
> the environment occurring, ones which are not related to the substitutions.
> This is, I think, the crux of the disagreement between ReMine and me. He
> is arguing that observing 2.0 offspring per parent is inconsistent
> with having had those substitutions. He is wrong.
Recall that Felsenstein and I have been debating his thesis that
beneficial substitutions "impose no cost" and that the beneficial
substitution rate is therefore not limited by the species' finite
reproduction.
I gave two types of counter-examples to his thesis. For one, take the
following scenario. A population of 100,000 haploid individuals where
one has a new beneficial mutation that substitutes in one generation.
This scenario has a cost of substitution of 99,999. The species would
need a reproductive excess of 99,999 in order to make this scenario
plausible. In fact, it is not plausible for any species I know of.
Tack 100 of these substitutions end to end, and it's still implausible,
and for the same reason as before: the species lacks the required
reproductive excess. This simple example directly refutes Felsenstein's
paper. The fact that the mutation is beneficial, "good" for the
species, and increases its "fitness" does not even slightly ease the
problem. Something else must be brought to the table if the problem is
to be solved. The mere 'beneficiality' of a mutation is insufficient.
For another counter-example I gave Felsenstein's own (1971) paper, where
he correctly acknowledges that the beneficial substitution rate is
limited by the species' finite reproductive excess -- this shows that
Felsenstein himself accepts the logic of the cost argument. But he
seeks to confine that conclusion ONLY to beneficial mutations arising
through environmental change. So I argued that (other things being
equal) the 'origin' of beneficial mutations does not affect their cost
of substitution, therefore, Felsenstein has no logical basis for
withholding his own conclusion from ALL beneficial substitutions. The
argument is identical whatever the origin of the beneficial mutation:
There is an unavoidable cost of substitution, the available reproduction
is finite, and these combine to limit the substitution rate.
Felsenstein accepts each leg of my argument, and his own paper confirms
the logic of it. Felsenstein has not even tried to reconcile that
self-contradiction. (More on this below.)
I believe the argument was essentially lost for Felsenstein when he
acknowledged that beneficial mutations do have a cost of substitution
and we can calculate it. This effectively countered his own 1971 paper,
and ever since he has been trying to make up for it by exploring the
other leg of the argument -- reproductive excess. You remember the
various diversions: such as "initial" versus "final" reproductive
excess, and whether reproductive excess is "observable". (None of these
were mentioned in his 1971 paper.) But there is no way out.
Reproduction is finite.
Non-zero cost of substitution
+ Finite reproduction
+ The logic from Felsenstein's own paper
= a limitation on the substitution rate
Felsenstein has not responded to these key arguments. Instead he
increasingly offered diversions and confusion factors. Quite a few of
them. Go back and see for yourself.
Which brings us to his latest argument (exhaustively cited above).
Notice the following points:
1) He emphasizes the same old irrelevant issue -- fitness. (I've
already refuted the importance of fitness in Haldane's Dilemma. I did
that from several angles, using several types of examples. Felsenstein
has not even tried to counter it.)
2) He leaves out the central issues -- time and substitution rate.
(Surely Felsenstein knows this.)
3) He introduces new issues -- multiple substitutions, simultaneous
substitutions, and multiplicative fitness models. These new issues are
not relevant to a defense of his original thesis, they are merely
introduced as yet another diversion away from his thesis.
4) He does not even try to defend his original thesis that beneficial
mutations, solely by virtue of their beneficiality, do not impose a cost
of substitution.
5) He does not even try to reconcile the self-contradiction I
identified in his position.
In other words, Felsenstein gets plenty of diversion and confusion on
the table, hoping we will forget his original thesis. Well perhaps we
should, as Felsenstein no longer cares to defend it.
James G. Acker
I have been following this debate with interest, having
been aware of Remine's book for a couple of years. This is the
first time I have seen a discussion of some of his points. Unfortunately
for a layman in the field, it's truly hard to determine if Walter
is actually raising a true point of contention in evolutionary
biology. Joe Felsenstein continually notes that Remine's central
argument is not a true problem, and this seems confirmed by both
those to whom Walter responds and those he does not. What is
particularly difficult to see is any quantitative comparison.
However, others have given Walter the opportunity to define his
ideas quantitatively, and he does not appear to have done so to this
point. So how are we to judge a non-quantitative argument when
it is necessary to quantify the results?
In any case, it does seem to me that Walter could address
Felsenstein's 1971 paper in a journal article of his own. It is not
unprecedented for someone to discover a problem in a classical treatment
and point it out (this recently occurred in a relativistic physics
example). Walter has written a substantial book; he should take
his expertise to the journals so that his ideas can be thoroughly
examined.
(And what a coup it would be to be published critiquing
evolutionary theory.)
wjre...@mmm.com wrote:
: Joe Felsenstein wrote:
: Below is the entirety of Felsenstein latest argument.
:
: > So suppose that an organism starts out with 2.0 offspring per parent when
: > population density is low. 100 mutations, each with a 1% advantage when
: > homozygous, and multiplicative in their effects on fitness, substitute. When
: > all is over, we should see a fitness of 2 x 1.01^100 = 4.1496, right? Yes,
: > if that is all that is going on. No, if there are also some deteriorations of
: > the environment occurring, ones which are not related to the substitutions.
: > This is, I think, the crux of the disagreement between ReMine and me. He
: > is arguing that observing 2.0 offspring per parent is inconsistent
: > with having had those substitutions. He is wrong.
:
: Recall that Felsenstein and I have been debating his thesis that
: beneficial substitutions "impose no cost" and that the beneficial
: substitution rate is therefore not limited by the species' finite
: reproduction.
:
: I gave two types of counter-examples to his thesis. For one, take the
: following scenario. A population of 100,000 haploid individuals where
: one has a new beneficial mutation that substitutes in one generation.
: This scenario has a cost of substitution of 99,999. The species would
: need a reproductive excess of 99,999 in order to make this scenario
: plausible. In fact, it is not plausible for any species I know of.
Translation: in one generation, 100,000 individuals die off
and 100,000 new individuals descended from the lucky mutator take
their place. True, it's not plausible -- even I can see that.
So (plausibly) the descendants with the mutation have to slowly (over several
generations) increase in number relative to the non-mutated strain.
If the mutation is "beneficial", they should out-compete the non-
mutated individuals reproductively, correct?
Question: how can one quantitatively compare the reproductive
benefit to the substitional cost?
: Tack 100 of these substitutions end to end, and it's still implausible,
: and for the same reason as before: the species lacks the required
: reproductive excess.
Well of course it does! It's an implausible example, isn't it?
Shouldn't we be examining plausible examples? (That's why it seems
to me it is necessary to quantify the argument.)
: This simple example directly refutes Felsenstein's
: paper. The fact that the mutation is beneficial, "good" for the
: species, and increases its "fitness" does not even slightly ease the
: problem. Something else must be brought to the table if the problem is
: to be solved. The mere 'beneficiality' of a mutation is insufficient.
Dumb as I am, I can't see this. Beneficiality seems to
imply that the mutated strain competes at an advantage over the
non-mutated strain when it comes to reproduction. Over many
generations, that benefit should become apparent.
: For another counter-example I gave Felsenstein's own (1971) paper, where
: he correctly acknowledges that the beneficial substitution rate is
: limited by the species' finite reproductive excess -- this shows that
This makes sense to me. It will take time (generations) for a
beneficial mutation to propagate through a population.
: Felsenstein himself accepts the logic of the cost argument. But he
: seeks to confine that conclusion ONLY to beneficial mutations arising
: through environmental change. So I argued that (other things being
: equal) the 'origin' of beneficial mutations does not affect their cost
: of substitution, therefore, Felsenstein has no logical basis for
: withholding his own conclusion from ALL beneficial substitutions. The
Simple question, which I know has been raised before: how
does one define a mutation as "beneficial" without reference to
the environment? Even if it's just agar and a petri dish, something
is allowing the mutated bacteria to reproduce at a competitive advantage
against their non-mutated fellow bacteria.
(This point seems to me both basic and crucial to evolution.)
: argument is identical whatever the origin of the beneficial mutation:
: There is an unavoidable cost of substitution, the available reproduction
: is finite, and these combine to limit the substitution rate.
: Felsenstein accepts each leg of my argument, and his own paper confirms
: the logic of it. Felsenstein has not even tried to reconcile that
: self-contradiction. (More on this below.)
:
: I believe the argument was essentially lost for Felsenstein when he
: acknowledged that beneficial mutations do have a cost of substitution
: and we can calculate it. This effectively countered his own 1971 paper,
In all of this discussion, I never saw Felsenstein deny that
beneficial mutations have a cost of substition. He basically stated
that the benefit outweighs the cost. So if Remine calculates the cost
of substitution, does he claim that the benefit doesn't outweigh the
cost? Following along the line of argument, it would appear the
argument is thus:
1. Beneficial mutations incur a cost of substitution.
2. The cost of substitution is paid by reproductive excess.
3. There is insufficient reproductive excess in (some? most? all?)
species to allow a plausible rate of substitution for beneficial
mutations.
: and ever since he has been trying to make up for it by exploring the
: other leg of the argument -- reproductive excess. You remember the
: various diversions: such as "initial" versus "final" reproductive
: excess, and whether reproductive excess is "observable". (None of these
: were mentioned in his 1971 paper.) But there is no way out.
: Reproduction is finite.
:
: Non-zero cost of substitution
: + Finite reproduction
: + The logic from Felsenstein's own paper
: = a limitation on the substitution rate
Ah, so the whole point is: there is a limit on the substitution
rate. (See #3 above.) This doesn't seem like a remarkable insight.
The key question remains: do beneficial mutations substitute at a
plausible rate (given the likelihood that there are limits on the
rate of substitution)?
THAT requires quantification and modeling, I think. Otherwise,
the argument degenerates to "Is so/Is not" with no advancement of
knowledge.
: 1) He emphasizes the same old irrelevant issue -- fitness. (I've
: already refuted the importance of fitness in Haldane's Dilemma. I did
: that from several angles, using several types of examples. Felsenstein
: has not even tried to counter it.)
It seems relevant to me if reproduction is competitive.
: 2) He leaves out the central issues -- time and substitution rate.
: (Surely Felsenstein knows this.)
Those do indeed seem to be central issues. What model can
be used to examine them? Has a model been proposed?
: 3) He introduces new issues -- multiple substitutions, simultaneous
: substitutions, and multiplicative fitness models. These new issues are
: not relevant to a defense of his original thesis, they are merely
: introduced as yet another diversion away from his thesis.
:
: 4) He does not even try to defend his original thesis that beneficial
: mutations, solely by virtue of their beneficiality, do not impose a cost
: of substitution.
As stated previously, I thought he acknowledged the cost but
indicated that the benefits outweigh the cost.
So, those are my comments from the sidelines. Since I'm not
in the game, all I can do is comment on how I perceive the current
state of the discussion. Right now it looks like a rugby scrum on
a muddy field: no clear advantage but everybody is muddy.
Jim Acker
===============================================
| James G. Acker |
| REPLY TO: jga...@neptune.gsfc.nasa.gov |
===============================================
All comments are the personal opinion of the writer
and do not constitute policy and/or opinion of government
or corporate entities.
David L. Rosen
John Edser wrote:
>
> One "substitution" of one allele at one single locus, after mutation has
> occurred to creat it, is only possible if the *soma* that "contains" the
> allele, replicates itself once.The soma must replicate once, NOT just the
> allele. "Substitution" as used in this thread, just means, replication of
> the mutant allele, into the next generation of *somas,* not into the next
> generation of alleles.
>
> ReMines costing concept, as I understand it, for one allele, at one locus,
> is then, one *soma*.
>
> Is this correct?
>
> John Edser
correct, and you are possibly wrong. The example of parasitic wasps
with polydnaviruses. For a complete description of this symbiosis,
please read:
Nancy E. Beckage, "The Parasitic Wasps Secret Weapon," Scientific American
277, 82-87 (November 1997).
Some parasitic wasps inject their eggs into caterpillars, but
have to overwhelm the caterpillars immunodefense system as follows. Part
of one of the alleles of the wasp mother (which in wasps is inherited
strictly in a Mendelian fashion) is turned into a polydnavirus (author uses
it as one word, instead of polydna virus). .
The polydna virus reproduces independently, and is injected into the caterpillar with
the egg. The eggs hatch, the polydnaviruses continue to reproduce. The
virus attacks the blood cells that protect the caterpillar. The virus,
with recognizable wasp dna sequences, reproduces independent of the wasp
larvae inside the caterpillar. Soon, the wasp larvae overwhelms the
the caterpillar, the caterpillar and its polydnaviruses die, leaving a
lot of wasp pupae that become imagos that repeat the cycle.
Here is a case where the allele reproduces for a while independent of
soma. The allele is strictly Mendelian in the wasp soma, but in the caterpillar,
it reproduces as a virus. So the gene has a selective pressure, independent of
the wasp, inside the caterpillar.
You could call the adult wasp the "Selecton" and the virus an "integron."
However, it is conceivable that eventually, a mutant virus could spread without
the wasp. As I understand it, there is a theory that most viruses started as
alleles in complete cells. What happens to your "Selecton theory" then?
Repeat the arguement where New Zealand tribesmen replace the caterpillar,
and kuru prions replace the polydnavirus. Kuru prions DID once reproduce
independently of the tribesman, but a kuru-like prion-protein disease has
also been inherited by European families.
At least, the European families TELL us that it was inherited.
They may be secretly eating each others brains. The tribesmen were
open about it, while this funeral custom was around. Eating brains or getting
brains in a cut was the only way to get the disease. The European cases must
have been produced by the hosts body itself.
Am I correct by saying that the work by Pruisner strongly
suggests that prion diseases are analogous to the polydnaviruses?
wjre...@mmm.com
James Acker asks for "quantitative comparison" of our arguments. But
the key issues between Joe Felsenstein and me are predominantly
conceptual, not numerical or quantitative. Does a beneficial mutation
have a cost of substitution, or not? Do mutations, merely by their
beneficiality, get around the cost limitations on substitution rate?
Are they freed from the limitations imposed by a species' finite
reproduction? These issues are conceptual and do not require
quantitative numbers to resolve.
But quantitative (i.e. numerical) examples do help our understanding,
and I have provided several. Some of my examples use cost arguments to
show that a given evolutionary scenario is implausible. I use such
examples to show that cost arguments have teeth, they don't just let
everything pass as "plausible". Of course this frustrates some
evolutionist readers, such as Acker who exclaims,
> Shouldn't we be examining plausible examples? (That's why
> it seems to me it is necessary to quantify the argument.)
Acker feels we should examine only plausible examples, and he thereby
misses the whole point of the cost argument. The cost argument
differentiates between plausible and implausible scenarios -- that is
precisely its purpose. Acker complains that I have not quantified my
argument, when ironically the very example he refers to is one I
quantified with numbers. It seems he is unwilling to accept a
"quantitative comparison" unless it shows evolution as plausible.
Moreover, I specifically chose some of my quantified examples to be
borderline cases, depending on the reproductive excess of the species.
These examples show how cost arguments can actually differentiate
various levels of plausibility on the basis of reproduction.
******
Acker argues that in a beneficial substitution "the benefit outweighs
the cost". That misuses the word "cost", which has a very specialized
meaning in Haldane's Dilemma. Let me address it this time by analogy.
In this analogy a beneficial substitution is like a house.
You want a house that costs a certain amount. But you cannot have it
unless you make the payments. The house may "benefit" you in many
ways. You can eat there, sleep there, store yer stuff there. Lots of
"benefits". But if you don't make the payments you don't keep the
house. Period -- no exceptions. It is silly to brush aside this
problem saying "the benefit outweighs the cost". That wording is sloppy
and misrepresents the problem. No matter how "beneficial" the house, it
is never free, in fact it's beneficiality to you does not even slightly
lower the cost. And no matter how much money you make, it is always
finite. These two indelible facts limit the RATE at which you can pay
for your house.
Moreover, we do not need to know your precise income every instant of
every year. Your AVERAGE income will suffice to tell whether your house
purchase is plausible or not. Perhaps your income goes up through the
years, for whatever reasons. That's fine, we can roll that into the
calculations and still determine whether your house purchase is
plausible.
The cost of substitution makes an argument in that manner. (Except that
a species' reproduction is more openly observable than your income.) We
measure the species' reproductive excess, and appropriately assess its
average-rate back into the past. (Under Felsenstein's scenario of ever
increasing reproduction, we would have to figure species typically had
LOWER reproduction in the past, and roll this into our calculations.)
>From there we calculate the rate at which the species can pay the cost
of substitution. And that gives the maximum plausible substitution
rate. (The actual rate will be lower because there are many additional
obstacles to the process.)
NOTE: The *difference* in reproductive excess between the old and new
trait is not relevant here. Some readers seem confused on this point.
The key data is the species' long-term average reproductive excess.
******
> : Non-zero cost of substitution
> : + Finite reproduction
> : + The logic from Felsenstein's own paper
> : = a limitation on the substitution rate
>
> Ah, so the whole point is: there is a limit on the substitution
> rate. ... This doesn't seem like a remarkable insight.
Acker says my point isn't a remarkable insight. (In other words, he
feels my point is fairly obvious!) Well, it remains a key point of
dispute between Felsenstein and me.
> The key question remains: do beneficial mutations substitute at a
> plausible rate (given the likelihood that there are limits on the
> rate of substitution)?
That question (along with all my material) is addressed in my book, and
quantified using data supplied by evolutionary geneticists themselves.
******
One other point about "quantifying" our arguments. Computer simulations
of evolution demonstrate the phenomena I am talking about. Most all of
them will, especially if they closely mimic the present evolutionary
model, offhand I can't think of any exceptions. My book uses the most
widely known simulation as an example: Dawkins's "METHINKS IT IS LIKE
A WEASEL" simulation from his book _The Blind Watchmaker_. The computer
program simulates random mutation followed by selection. As you turn
the reproduction rate up and down, it visibly raises and lowers the
substitution rate -- in accordance with a Haldane-style cost-payment
limitation on the substitution rate.
In other words, Felsenstein's claims are refuted not just by my
arguments, but also by the logic of his own 1971 paper, and by computer
simulations.
Donal Hickey
James G. Acker wrote:
>
> Well of course it does! It's an implausible example, isn't it?
> Shouldn't we be examining plausible examples? (That's why it seems
> to me it is necessary to quantify the argument.)
>
try to stick to realistic examples. He simply ignores this, along with
many other points. This is why I believe that any further discussion
with him on this topic is a waste of everybody's time.
> Ah, so the whole point is: there is a limit on the substitution
> rate. (See #3 above.) This doesn't seem like a remarkable insight.
> The key question remains: do beneficial mutations substitute at a
> plausible rate (given the likelihood that there are limits on the
> rate of substitution)?
> THAT requires quantification and modeling, I think. Otherwise,
> the argument degenerates to "Is so/Is not" with no advancement of
> knowledge.
>
I agree that it requires quantification and modelling. It also requires
some empirical data that can be used to test the models against. Walter
ReMine seems content to use rhetoric to solve the problem.
> So, those are my comments from the sidelines. Since I'm not
> in the game, all I can do is comment on how I perceive the current
> state of the discussion. Right now it looks like a rugby scrum on
> a muddy field: no clear advantage but everybody is muddy.
>
You may be on the sidelines, but you seem to understand the game. I
think many of the players, including myself, have been kicking up mud
in an effort to get the ball. One notable exception is the player who
has been kicking up mud, not to get the ball, but simply to get mud on
the faces of the other players. This, in my estimation, is not very
sportsperson-like behavior.
Donal.
DJohn1117
This is bizarre. My first message appeared; then, when Mr. ReMine took my
message as a blanket endorsement of his thesis and I wrote another one
pointing out that I wasn't intending to do that, the second one doesn't seem to
be anywhere in sight. So I'll repeat myself as best as I can.
I'm an amateur who occasionally reads a little bit of population genetics and
what I've noticed is that the books I've seen don't discuss what seems like a
basic and interesting question--what is the fastest rate at which genes can be
substituted into a population? Now maybe the answer is so model-dependent that
no one answer is meaningful, but in that case the books should present the
different models (I've read truncation selection is particularly efficient) and
explain their different predictions. They should also explain whether any of
these models with varying maximum rates would be fast enough to explain what
has actually happened.
Just to add a bit of confusion in my own mind (I'm hoping I'll be able to
figure this out, but anyone who wants to should feel free to enlighten me), M
Kimura in his book The Neutral Theory of Molecular Evolution uses Haldane's
dilemma to argue that most nucleotide substitutions must be neutral, because if
they were selective the required reproductive excess would be too great. Now I
think I can see how an allele can be substituted by drift with no reproductive
excess needed. And I understand the simple two line derivation for equating
the substitution rate of neutral alleles with the neutral mutation rate. But
I can't quite grasp the concept that neutral evolution should be able to
substitute alleles at a much greater rate than selection, when in an individual
case obviously selection will fix a beneficial mutation much faster than drift
will fix a neutral one. Maybe it'll hit me in another day or two. If not,
I'll post this particular question again sometime (assuming this post doesn't
make it either.)
My vanished message also said something about rates of phenotypic
evolution--how does the rate of evolution for a particular trait vary if other
traits are also being selected? I assume the quantitative geneticists and
plant and animal breeders care about that one. Are there realistic
mathematical models that try to answer that question?
Donald Johnson
Joe Felsenstein
In article <69dl04$eg0$1...@nntp6.u.washington.edu>, <wjre...@mmm.com> wrote:
[ReMine]
>Recall that Felsenstein and I have been debating his thesis that
>beneficial substitutions "impose no cost" and that the beneficial
>substitution rate is therefore not limited by the species' finite
>reproduction.
>
>I gave two types of counter-examples to his thesis. For one, take the
>following scenario. A population of 100,000 haploid individuals where
>one has a new beneficial mutation that substitutes in one generation.
>This scenario has a cost of substitution of 99,999. The species would
>need a reproductive excess of 99,999 in order to make this scenario
>plausible. In fact, it is not plausible for any species I know of.
>Tack 100 of these substitutions end to end, and it's still implausible,
>and for the same reason as before: the species lacks the required
>reproductive excess. This simple example directly refutes Felsenstein's
>paper. The fact that the mutation is beneficial, "good" for the
>species, and increases its "fitness" does not even slightly ease the
>problem. Something else must be brought to the table if the problem is
>to be solved. The mere 'beneficiality' of a mutation is insufficient.
Let's concentrate on this. It relates to ReMine's central thesis
about there being a limitation on how many mutations can have substituted,
even advantageous ones. That's why I want to concentrate on it.
If the population substitutes completely in one one generation, the mutant
would need a fitness (relative to the non-mutant allele) that is
infinite (not 99,999) as the nonmutant is still there too. In other
words if the alleles are a and A, and their haploid fitnesses were
W1 and W2, the new frequency of the mutant (A) is
W1 / (0.00001 W2 + 0.99999 W1)
(which can only be 1 if W1 is infinitely greater than W2). Now whatever
the advantageous mutation's fitness, it causes the rise in frequency and
there is no problem for the organism.
It might be thought to predict that after the substitution we will see
an implausibly high fitness, so that even if there is no problem for the
organism, there is a problem imagining this happening if we look and don't
see that high fitness. That is what I think ReMine is saying.
However if environmental deterioration is happening too the fitness that
results will be lower than the prediction we would make just from that
gene. And if we don't know what the environmental effects are, we can't
make a prediction of the resulting fitness. That makes it impossible
to know from the after-the-fact fitness what rate of gene substitutions
occurred.
I hope Walter ReMine will comment on this issue. It is the one I have
been trying to raise with him in recent postings.
John Edser
DJohn1117 <djoh...@aol.com> wrote in article
> My vanished message also said something about rates of phenotypic
> evolution--how does the rate of evolution for a particular trait vary if
other
> traits are also being selected? I assume the quantitative geneticists
and
> plant and animal breeders care about that one. Are there realistic
> mathematical models that try to answer that question?
JE:-
A higher quality question, that will I'm sure, produce a higher quality
answer IMHO. It was Fisher's simplification which removed epistasis between
loci, reducing all their relationships to simple additive compounding. This
was necessary to produce the gene pool concept, which effectively destroyed
the individual genome placing selection on "the gene" itself. We all know
that selection only operates on the phenotype, and we all know, that every
phenotype is a functional set of body parts, that relate together, more
than the sum of their particular parts.
Why can't population genetics use a two loci model, where the two loci are
linked to the studied natural history of a phenotypic set, in a non
additive way? This would mean, the actual set is inherited by two loci,
acting like a single genetic element, with the contained loci producing
variation. This reduces selection on each allele, to a relative measure,
where they don't compete against each other, but compliment each other, for
the sake of the set. Perhaps then, single allele substitution would not be
viewed as the most
important event in evolutionary history.
John Edser
Independent Researcher
ed...@atinet.com.au
Box 266 Church Point P.O.
Church Point
NSW 2105
Australia
Mobile:014 077 018
APLOLOGIES: The email ed...@brewery.net.au
is not operational but it refuses to be erased from
Explorer 3. Many thanks to Microsoft
wjre...@mmm.com
Donald Johnson wrote:
> what I've noticed is that the books I've seen don't discuss what seems like a
> basic and interesting question--what is the fastest rate at which genes can be
> substituted into a population? Now maybe the answer is so model-dependent that
> no one answer is meaningful, but in that case the books should present the
> different models (I've read truncation selection is particularly efficient) and
> explain their different predictions. They should also explain whether any of
> these models with varying maximum rates would be fast enough to explain what
> has actually happened.
That is exactly correct, and what I've been saying publicly for years!
The evolutionary genetics textbooks scarcely discuss what ought to be a
central issue -- the beneficial substitution rate. This is a scandal.
It is not the only one, as I will show below.
> M Kimura in his book The Neutral Theory of Molecular Evolution uses Haldane's
> dilemma to argue that most nucleotide substitutions must be neutral, because if
> they were selective the required reproductive excess would be too great.
That is exactly correct. Motoo Kimura used Haldane's Dilemma as his
leading evidence for his theory of neutral evolution. His second-up
evidence was a keen argument that rapid evolution in small populations
is implausible because the process starves for lack of beneficial
mutations. (Both arguments are elaborated in my book.) His two
arguments are independent and together covered the full range from small
to large population sizes. Kimura used these to show that selective
evolution is too slow to plausibly explain evolution. He was not
especially direct in making that argument, but that is what he was
doing.
In other words, Kimura used evidence AGAINST selective evolution as
evidence FOR neutral evolution. You see, evolutionists DO use a
two-model approach, when it suits them to do so. (In fact, Darwin
invented its use in the origins debate and evolutionists continue to use
it to this day.) In this example, evolution is taken as absolutely
true, then evidence 'against' one evolutionary mechanism is
automatically taken as evidence FOR another evolutionary mechanism.
This type of reasoning occurs often for evolutionists. My book quotes
examples (from Gould and others) where evidence against Lamarckian
mechanisms is taken as evidence "for" natural selection. And other
examples, where evidence against gradual evolution or against phyletic
evolution are taken as evidence "for" punctuated equilibria. And still
other examples in the origin of life, where evidence against the
'protein-first' scenario is used as evidence "for" an alternate
'RNA-first' scenario -- and vice versa! And evidence against both of
them is used as evidence "for" a wildly implausible and unsubstantiated
'crystalline-clay-first' scenario. Then evolutionary leaders (such as
Francis Crick) use all that evidence 'against' the earthly origin of
life as evidence "for" directed-panspermia from a distant solar system.
Then they all unanimously say, "Evolution is a FACT, we are just
debating the details!"
******
Kimura argued (correctly) that neutral evolution (the neutral
substitution rate) is faster than selective evolution. But this is no
help in explaining biological adaptations -- Neutral substitutions offer
no biological benefit.
But what of neutral substitutions? Shouldn't their rate and number be
of central interest? Shouldn't evolutionists be interested in
*quantifying* their theory with numbers and real examples? Well they
haven't. But my book does. Using straightforward data and theory
supplied by Motoo Kimura himself, my book shows that in ten million
years a human-like population could, at best, substitute 25,000
*expressed* neutral mutations. That amounts to 0.0007 percent of the
genome, and is not remotely enough to solve Haldane's Dilemma or explain
human evolution. Let me repeat. My argument relies only on theory and
data supplied by evolutionists themselves. The argument is
straightforward and not difficult. Yet evolutionary genetics textbooks
contain nothing like it. The entire issue has been ignored, though it
is a central issue of their field. It could have -- and should have --
been discussed decades ago. This is yet another scandal. (And it is
made worse by the fact that I have been informing evolutionists of it on
various Internet forums for over four years already, yet they still
ignore it.)
Error catastrophe and the cost of harmful mutation are yet additional
examples. These issues are interesting, highly relevant, and of central
concern to evolutionary genetics. Yet they too are roundly ignored in
the textbooks. On the few occasions when they are discussed, it is done
in a manner that conceals, rather than reveals, the severity of the
problem. (Such as through the terminology of "mutational load".) My
book uses data and genetic theory supplied by evolutionists themselves
to show that a human-like population is within, or very near to, error
catastrophe -- even if the ENTIRE reproduction of the species is devoted
to fending it off. (This leaves no reproduction for paying the other
costs of evolutionary scenarios, such as the costs of substitution,
heterosis, random death, etc.) And for extra measure the calculation
assumes a full 97% of the human genome is COMPLETELY INERT and
unavailable to suffer harmful mutation. The allows that the harmful
mutation rate per individual is a minuscule fraction of what it
otherwise would be. Yet the harmful mutations are still abundant enough
to cause a serious theoretical problem -- error catastrophe.
Let me describe this calculation and the advantages it gives
evolutionists. Start out with the human genome and throw away HALF of
it (one haploid compliment) as a useless repeat. This gets us down to a
genome the size of an UN-fertilized human egg (that is, approximately,
without the information content brought by the sperm). We are throwing
out some functional genetic information there, and doing so is therefore
somewhat unrealistic, but the assumption nonetheless operates
*completely in favor* of evolutionists in this argument. Next throw out
a full 97% of the remaining genome as totally useless junk. Again this
operates in favor of evolutionists here. We have now greatly reduced
the operative portion of the genome, and it is only this small remaining
portion that the calculation will allow to experience harmful mutation
-- all mutation to the excluded genetic material will be considered
inert and ignored. Next obtain the mutation rate (per nucleotide) as
measured, reported, and routinely discussed by evolutionists. Then
apply the standard model of evolutionary genetics, the one model
prominent in all evolution books. That allows us to calculate the
reproduction necessary to fend off error catastrophe. The result is
that human females, on average, would have to conceive 16.3 children,
and all of that reproduction would be required solely to keep the
species from the endless genetic deterioration of error catastrophe.
Interesting? ... Yes.
Relevant? Absolutely!
The calculation is tractable. It is reasonably straightforward and
easy. The issue is of central importance. Yet I can find no
evolutionist who has published any such discussion or argument. The
entire issue is virtually absent from textbooks. This is a scandal.
And once again I have been publicly informing evolutionists of it for
over four years.
******
> I can't quite grasp the concept that neutral evolution should be able to
> substitute alleles at a much greater rate than selection, when in an individual
> case obviously selection will fix a beneficial mutation much faster than drift
> will fix a neutral one.
Johnson homed in on a reasonable and commonplace question -- Why is
neutral evolution faster? That question baffled many people (including
me for a long time). So I address it in my book. Kimura and the
traditional commentators said it is because neutral substitutions have
"no cost". But that is incorrect, they do have a cost of substitution
(in fact a high one). The secret to their speed is in the higher
reproductive excess available to pay for them (specifically it is a
stochastic reproductive excess), and especially in special substitution
mechanisms that are available to neutral, but not beneficial,
substitutions. I specifically identify what those are, and make
coherent and consistent the Haldane-style cost-payment theory.
David L. Rosen
DJohn1117 wrote:
>
> My vanished message also said something about rates of phenotypic
> evolution--how does the rate of evolution for a particular trait vary if other
> traits are also being selected? I assume the quantitative geneticists and
> plant and animal breeders care about that one. Are there realistic
> mathematical models that try to answer that question?
>
Some traites are easily separable. Genes act by producing proteins
that are parts of enzymes that produce trains of biochemical sequences.
These sequences often branch, producing pleiotropy. Many genes can affect the
same traite, and one gene can affect many traites. However, if a gene affects an
enzyme that appears near the end of a sequence, then often the gene really will
affect one or only a few traites. If a phenotypic traite isn't so simple,
I don't think one could define it as a inherited traite. So I think that
Mendelian heredity should be considered only a simplifying assumption that
strictly applies to only a few traites over a short period of time.
For more long range evolution, development must be considered more
carefully.
wjre...@mmm.com
The centerpiece of Haldane's Dilemma is the cost of substitution, and I
have repeatedly said fitness has virtually NOTHING to do with the
problem. I stated it many times and explained it from several angles.
Joe Felsenstein has not even attempted to refute the point. Yet he
could not have missed me saying it. No reader here could have.
Well, Felsenstein's latest post attempts to summarize my viewpoint --
except he *completely leaves out* the cost of substitution, and he
focuses *exclusively* on fitness. Then he says, "That is what I think
ReMine is saying." !!!
I do not see how any awake reader could honestly make that mistake.
Felsenstein could not more fundamentally misrepresent me. Felsenstein's
post caused me to wonder: Is he asleep? Is he bored? Is he becoming
obfuscational? Is he serious? Is he exhausted? Is he dis-engaging? I
do not know. I only know his post is far beneath Felsenstein's
considerable capabilities.
After he misrepresents me and sets up a straw-man, he assaults it
through false arguments I have refuted several times already. But he
doesn't address my refutations, he just posts his same identical
mistakes over again.
What follows are the gory details. Casual readers should bail out here,
as it's all been said several times before.
******
Here Felsenstein sets up a straw-man. Notice the cost of substitution
appears nowhere, he focuses exclusively on "fitness":
> Let's concentrate on this. It relates to ReMine's central thesis
> about there being a limitation on how many mutations can have substituted,
> even advantageous ones. That's why I want to concentrate on it.
> If the population substitutes completely in one generation, the mutant
> would need a fitness (relative to the non-mutant allele) that is
> infinite (not 99,999) as the nonmutant is still there too. In other
> words if the alleles are a and A, and their haploid fitnesses were
> W1 and W2, the new frequency of the mutant (A) is
>
> W1 / (0.00001 W2 + 0.99999 W1)
>
> (which can only be 1 if W1 is infinitely greater than W2). Now whatever
> the advantageous mutation's fitness, it causes the rise in frequency and
> there is no problem for the organism.
>
> It might be thought to predict that after the substitution we will see
> an implausibly high fitness, so that even if there is no problem for the
> organism, there is a problem imagining this happening if we look and don't
> see that high fitness. That is what I think ReMine is saying.
Felsenstein completely misrepresented me. I said nothing like that.
Having set up that straw-man, he goes on to argue against it on false
terms, as follows:
> However if environmental deterioration is happening too the fitness that
> results will be lower than the prediction we would make just from that
> gene.
Notice his continued focus on fitness, which is virtually irrelevant to
Haldane's Dilemma.
> And if we don't know what the environmental effects are, we can't
> make a prediction of the resulting fitness.
First, fitness and reproductive excess are different things. Second, we
do not "predict the resulting fitness". Rather, in cost arguments we
*observe and measure* the species' *reproductive excess*, and in any
case, it is finite, which is sufficient for our discussion here.
Felsenstein continues to ignore this point:
Non-zero cost of substitution
+ Finite species' reproduction
+ the logic from Felsenstein own 1971 paper
= a limitation on the beneficial substitution rate
Felsenstein already accepts every leg of the above argument and its
conclusion. Yet he (erroneously) tries to deny the conclusion to ALL
beneficial mutations no matter what their origination. Despite my
repeated prompting he does not even address this self-contradiction.
> That makes it impossible to know from the after-the-fact
> fitness what rate of gene substitutions occurred.
The cost of substitution argument does not calculate "what rate of gene
substitutions [actually] occurred". Rather it calculates the MAXIMUM
PLAUSIBLE rate. There is a difference, and yes, it can be calculated
after-the fact, just as Felsenstein does in his 1971 paper. Felsenstein
continues to contradict his own paper, and I continue to point it out.
Below is my example that Felsenstein was addressing above. Notice how
his discussion completely misrepresented mine. [Note my figure 99,999
-- which is the cost of substitution for my example. Yes, that is
correct and is the same dimensions and units as Haldane used.
Felsenstein garbled this, saying the fitness "is infinite (not
99,999)".]
>I gave two types of counter-examples to his thesis. For one, take the
>following scenario. A population of 100,000 haploid individuals where
>one has a new beneficial mutation that substitutes in one generation.
>This scenario has a cost of substitution of 99,999. The species would
>need a reproductive excess of 99,999 in order to make this scenario
>plausible. In fact, it is not plausible for any species I know of.
>Tack 100 of these substitutions end to end, and it's still implausible,
>and for the same reason as before: the species lacks the required
>reproductive excess. This simple example directly refutes Felsenstein's
>paper. The fact that the mutation is beneficial, "good" for the
>species, and increases its "fitness" does not even slightly ease the
>problem. Something else must be brought to the table if the problem is
>to be solved. The mere 'beneficiality' of a mutation is insufficient.
Felsenstein still has not addressed this. Instead he garbled it.
J Jackson
wjre...@mmm.com wrote:
: James Acker asks for "quantitative comparison" of our arguments. But
: the key issues between Joe Felsenstein and me are predominantly
: conceptual, not numerical or quantitative. Does a beneficial mutation
: have a cost of substitution, or not? Do mutations, merely by their
: beneficiality, get around the cost limitations on substitution rate?
: Are they freed from the limitations imposed by a species' finite
: reproduction? These issues are conceptual and do not require
: quantitative numbers to resolve.
Dunno about other people, but I tend to have concrete examples floating
around my head when trying to follow these 'concentual' arguments.
I'll run an example past you good people.
Consider a harem species, e.g. Red Deer, a mutated allele gets into a male
body and its action makes that male more dominant and hence the male
monopolises a good sized harem of females, and the mutated allele gets
into lots of new bodies. Some of these bodies are males and so we recurse.
Ok. Maybe I'm being thick, but where is the cost of substition in this
case.
Run through the scenario without a mutated allele and nothing
changes. There will be a some males that dominates harems, and some males
that are excluded from procreating - same as when the mutated allele
occurs.
Jim
James G. Acker
Walter Remine replied to my post, but I have yet to see it appear
on my site. Ah, the vagaries of the Internet!
I looked at his reply and attempted to address his analogy (the
costs of mortgage payments on a house), but as I later realized and he
pointed out, trying to compare analogies is too semantic and confusing.
So, very simply, one of the things I was looking for (as was
Joe Felsenstein when he asked about fitness in Walter's "implausible"
scenario) was a way of quantifying this cost argument. My original
comment to Walter was "Why don't we focus on plausible scenarios?"
Walter replied that "evolutionists" want to only consider plausible
scenarios in order to bolster the support for evolution.
So, I thought about it a bit, and tried to come up with a
"plausible" scenario that I will propose for critique. It's a
drug-resistant bacteria scenario. We all know that drug-resistant
bacterial strains are an important issue in modern medicine, so it would
appear that evolution works in these cases. Herewith, a back-of-the-
envelope drug-resistant bacteria scenario.
---
We have a strain of bacteria that is susceptible to erythromicin.
Due to vagaries of the exposure application, only 75% of the non-resistant
bacteria actually die when erythromicin is applied.
We start with an original population of 100 bacteria. Of these,
1 has a new gene that makes it resistant to erythromicin. However, the
mutation slightly reduces its reproduction rate, as I'll show.
Generations ensue.
1st: 1/99 (mutant/non-mutant) 2nd: 2/198 3rd: 4/396 4th: 8/792.
However, here's where the reproductive inhibition kicks in. When the
population increases to about 1000, there are still only 8 mutated bacteria.
So the numbers are 8/992, or 0.8 % of the population.
Now apply erythromicin. 75% of the non-resistant bacteria die.
Numbers: 8/248, total population 256. Mutants are 3.1% of the population.
Generations ensue.
8/248, 16/496, 26/992 (note the reproductive inhibition again)
total = 1018, mutants are 2.6 %
Again apply erythromicin. Now, 26/248, mutants are 9.5% of the total.
Generations ensue.
26/248, 52/496, 83/992 (reproductive inhibition)
total = 1075, mutants are 8.4%
After two applications of erythromicin, the antibiotic-resistant bacteria
have gone from 0.8% of the population to 8.4% of the population.
..and so on, and so on.
---
Simple question: is this a plausible scenario for the substitution
of a gene in a population of bacteria? Why or why not? What does
this example say about gene substitution in general?
Joe Felsenstein
In article <6a00lt$tla$1...@nntp6.u.washington.edu>, <wjre...@mmm.com> wrote:
[included for threaded newsreaders]
Walter has gotten very upset at what he sees as my misrepresentations and
evasions.
I am just trying to get him to answer one question, which he has not.
The question is important because I take it to be central to his criticism
of evolution.
If we have a gene that has an advantageous mutation that raises its
fitness (let's say in a way that raises the reproductive excess), and it
substitutes, then, after the fact, does that lead to something observable?
Yes, I think ReMine and I agree it does, an increase in reproductive excess.
Can we then use the observed reproductive excess to limit the rate of
substitutions that could have occurred? If that were all that was
happening, yes. If that were all that were happening, then each
such substitution would raise the reproductive excess.
But if there are also environmental changes occurring, those could decrease
the reproductive excess. In general we don't know what environmental
changes are happening. So the fact the the reproductive excess is not
increasing without limit does not put any limit on the rate of substitution,
if environmental changes are also allowed.
ReMine's argument that observing a finite reproductive excess limits the
at which advantageous mutations substitute is thus wrong. The question is,
is this argument correct?
Let's leave aside the issue of (a) whether there is a Haldane's Dilemma,
(b) whether it is a problem for the species, (c) whether it is a problem for
evolutionists, (d) whether I tried to "solve" it in my 1971 paper, (d)
whether what I have said here recently contradicts what I said in 1971,
and (e) whether I am a terrible person. We can come back to those.
wjre...@mmm.com
James G. Acker offers a highly detailed scenario as a way to quantify the cost
of substitution argument. Unfortunately he leaves out two key pieces of
information. The main one is the final population size at which the
substitution is complete. (Note: I remind readers that this ought be a figure
that appropriately represents a continuing, on-going, long-term evolutionary
scenario. Many evolutionists offer so-called "solutions" to Haldane's Dilemma
that focus on A SINGLE HIGHLY UNUSUAL situation, and do not represent a
plausible evolutionary scenario over the long run.)
The other key piece of information is whether the new beneficial mutation is
dominant or recessive. For sake of discussion I will assume it is recessive, as
that is what evolutionists almost always assume. Why do they do that? Because
dominant substitutions are vastly less costly than recessive ones. Evolutionary
theorists want the fastest substitution rate, so they generally assume the
substitution is dominant. They rarely explain that rationale to students. They
just assume a dominant substitution, and don't say why.
Acker's scenario also offers numerous irrelevant details, more than enough to
confuse and frustrate readers. Enough to drive ya blind. This is not unusual.
Evolutionist commentators seem content to leave the issue just that way.
Haldane's Dilemma is largely an exercise in removing the many confusion factors
that evolutionists bring into the subject. I'm not picking on Acker here, no
doubt he is doing his best. I'm just saying that, in general, evolutionists
seem rather content to let confusion reign on this issue. In Haldane's Dilemma
they lack the gusto that they so capably display in other areas. As a group
they are capable of far better.
Acker's scenario focuses way too much on the individuals with the old trait, the
ones that will eventually be eliminated. He gives gobs of irrelevant figures on
them. So let me emphasize: Forget 'em! They're goners. They're outta here!
They're history. Don't focus on them or you'll just get confused. Focus on the
new trait, the one being substituted. The central issues are 'time' and the
growth of the new trait.
First let's clean up the 'time' issue. His scenario covers just seven
generations, where the new trait goes from one to 83 in number. Then his
scenario stops prematurely. The substitution is far from complete by the end of
seven generations. The complete substitution will require many, many more
generations. We cannot calculate the cost of substitution for his example,
because it does not cover a complete substitution. But there is enough
information for calculating the cost *for a few given generations*. (The cost
of substitution is merely the sum total of the costs for each generation of the
substitution.)
Let's next clean up the other key issue -- the growth of the new trait. The
above figures require an average reproductive excess per generation of 0.88 (or
88 percent). In other words, the new trait must nearly double its numbers each
generation. (In five of the seven generations, Acker has them exactly doubling
and in the other two it is somewhat less. So, by simple inspection you see the
above figure is in the ballpark.) That is the cost per generation -- 0.88. If
the species cannot supply this level of reproductive excess each generation
(applied with perfect efficiency toward substitution), then the scenario is not
plausible. If it can, then it is plausible.
Let us suppose, since Acker's example was for bacteria, that the species'
population size is on the order of 10^12 (or roughly one hundred for every human
being). If the species can supply for substitutions a reproductive excess of
0.88, then it can pay for substitutions in 43.77 generations. And the cost of
substitution is 43.77 * 0.88 = 38.51 Haldane estimated that the average cost
of substitution (for higher mammals) is 30.
wjre...@mmm.com
Joe Felsenstein's latest post advances something remarkable for resolving our
discussion:
> Can we then use the observed reproductive excess to limit
> the rate of [advantageous] substitutions that could have
> occurred? If that were all that was happening, yes.
[moderator's plea: Bill, I know this is very very exciting and all,
but could you restrain yourself in your usual fashion and wrap your
posts at about 70 columns or so, like this comment, for example?
It makes for much improved readability. And this is a point which
is relevant to all our posters, folkaroo. - JAH]
A big YES! We now agree on a central point. Felsenstein says the observed
reproductive excess puts a limit on the beneficial substitution rate -- so long as
the environment is not changing. Well his 1971 paper, and his previous posts here,
make the very same conclusion when the environment *is* changing. In other words,
it doesn't matter whether or not the environment is changing, the same conclusion
is reached -- the observed reproductive excess limits the beneficial substitution
rate. That is precisely what I have been saying from the start.
******
Felsenstein embedded his above admission within a wider argument, which we should
also discuss. Let me boil it down to its simplest terms.
1) He assumes beneficial substitution increases reproductive excess.
2) He assumes environmental change decreases reproductive excess (by some unknown
and unknowable amount).
3) He says the combination of the two makes it impossible to observe the *specific
increases* brought by beneficial substitution.
4) He concludes that since we cannot observe the necessary data, there therefore
is no observation which can identify the limit to the beneficial substitution rate
-- thus, there is a limit, we just cannot identify what it is. (If I have
misinterpreted Felsenstein, I do hope he will clear it up.)
His major error occurs at step 4. Cost of substitution arguments do not require us
to observe the specific "increases" brought by beneficial substitution and separate
them from the specific 'decreases' brought by other sources such as the
environment. We need only observe the species' reproductive excess. Yes, it is
observable, and it's not especially difficult. We need not sort out each
individual increase from each simultaneously occuring decrease, the net
reproductive excess is sufficient. In fact, we only need the AVERAGE reproductive
excess over the period of interest to us.
To make an analogy. Countless things affect your income. Some tick it upward,
while others may simultaneously tick it downward. But we need not sort all those
out. Your income is your income -- there is only one, and it is observable even if
all the countless other things are not. Moreover, we need only observe your
AVERAGE income to see whether a given house purchase is plausible. It is the same
with the cost of substitution. Over the long haul, you cannot get away from the
average.
Let me come at this from yet another angle. Felsenstein has now acknowledged
(finally!) that we can use the observed reproductive excess to limit the rate which
beneficial substitutions could have occurred -- so long as the environment isn't
changing. Let's take that as an agreed starting point. Now add a whole bunch of
random environmental change. Because it is random in its concern for the species,
it would tend to HARM the species and REDUCE its reproductive excess. Would this
lower the substitution rate? Yes, by Felsenstein's own logic it would. Would the
resultant reproductive excess be observable? Yes, there is no reason why it
wouldn't be.
Felsenstein invites us on a wild goose chase to identify, sort out, and "observe"
each of the infinitude of multifarious increases and decreases to reproduction that
nature has to hold. That level of detail always was irrelevant to cost of
substitution arguments.
******
Below is Felsenstein's wording, for sake of documentation:
> If we have a gene that has an advantageous mutation that
> raises its fitness (let's say in a way that raises the
> reproductive excess), and it substitutes, then, after the fact,
> does that lead to something observable? Yes, I think
> ReMine and I agree it does, an increase in reproductive
> excess. Can we then use the observed reproductive excess
> to limit the rate of substitutions that could have occurred?
> If that were all that was happening, yes. If that were all
> that were happening, then each such substitution would
> raise the reproductive excess.
>
> But if there are also environmental changes occurring,
> those could decrease the reproductive excess. In general
> we don't know what environmental changes are happening.
> So the fact the reproductive excess is not increasing
> without limit does not put any limit on the rate of
> substitution, if environmental changes are also allowed.
>
> ReMine's argument that observing a finite reproductive
> excess limits the [rate] at which advantageous mutations
> substitute is thus wrong. The question is, is this argument
> correct?
-- Walter ReMine
wjre...@mmm.com
Jim Jackson asks us to consider the cost of substitution for a special
scenario, a harem species such as Red Deer. I caution readers against pushing
special scenarios, especially until they understand the basic concepts
involved.
Special scenarios often give a sense of easing the problem, when they do not.
Many evolutionists propose special scenarios as so-called "solutions" to
Haldane's Dilemma. Most curiously they IMMEDIATELY DROP the special scenario
as soon as they are no longer discussing Haldane's Dilemma. If a given
scenario is key to "solving" Haldane's Dilemma, then no student should be able
to get through an evolutionary textbook without having that emphasized. But
that is not what you find. Most classic "solutions" to Haldane's Dilemma
scarcely appear in evolutionary textbooks, even those specializing in
genetics. This is yet another scandal. The central issues in evolutionary
genetics are seldom in the textbooks.
Check a scenario is to see whether it is suitable as a realistic long-term
solution, something that takes place repeatedly for many generations. Check
to see it is 'complete' unto itself, and does not rely on unrealistic or
skewed statistics obtained by a theorist *selecting* the special situation.
Take all the long-term averages and normal situations into account.
A classic example is as follows. Take a population of ten million bacteria.
Add penicillin and all but one dies. Then, the evolutionist says, "See, the
substitution took just ONE generation. There is no cost." That is not
realistic as a long-term picture of evolution. It takes one special
generation and falsely models all evolution on it. There is a cost, it's just
that the scenario was carefully constructed to leave it out of its scope. The
cost must be paid (as always) by the survivors, and will take many generations
for them to slowly recoup their numbers to the point were they can acquire
another beneficial mutation.
I could give many more examples of so-called "solutions" that are nothing more
than unrealistic, special circumstances.
So Jackson wants us to consider a harem species where one dominant male sires
all the progeny. Supposedly this increases its reproduction and hastens
evolution. Well, only if the dominant male contains the beneficial mutation.
If any other male contains the beneficial mutation, it goes to waste.
What about beneficial mutations that occur in females. There is a very slim
chance it will survive its first generation. First, there is but a fifty
percent chance it will get into a given egg, and hence into a given progeny.
If the progeny is male, there is but a further slim chance it will become the
dominant male. If it is female, then the same slim odds apply for the next
generation. For most beneficial mutations (where the selective value is low)
there is about one chance in four it will survive the first generation.
(Fifty percent loss through meiosis, and another loss of slightly less than
fifty-percent because nearly half the population, all but one male, is a
genetic dead-end. Further losses occur because random death takes a bite out
of the species' reproduction each generation.)
The scenario relies (as many evolutionary scenarios do) on an unrealistic
model of a SINGLE mutation causing some new beneficial trait, and the new
trait supposedly impels its male possessor immediately into "dominance" where
it sires all the progeny. How convenient. But that is unrealistic on a
number of levels.
The scenario doesn't end there, because the twenty or so animals in the harem
are seldom a species. They are but a small part of a much larger reproductive
group, the species. For beneficial substitution to propagate throughout the
species, it must travel *out* of the harem into other groups, and that is
precisely where the reproductive isolation of the harem further SLOWS the
substitution process. Limited migration between sub-populations slows the
spread of new beneficial mutations -- it does not stop the spread, but slows
it.
There is still a cost of substitution, and it is the same as without the harem
scenario. Rather, the scenario attempts to increase the reproductive excess
allotted to beneficial substitutions, but it is questionable how much it
actually accomplishes that. The harem scenario wastes a lot of reproduction
in producing male offspring who then never procreate. Virtually half the
species' reproduction goes to waste.
In any event, the reproductive excess is still finite, so there is still a
cost limitation to the substitution rate. Those fundamental mechanics of the
problem are largely unchanged.
> Run through the scenario without a mutated allele and
> nothing changes. There will be a some males that
> dominates harems, and some males that are excluded
> from procreating - same as when the mutated allele
> occurs.
I remind Jackson that if there is no substitution, then there is no cost of
substitution -- but your scenario does not get the substitution either. If the
cost isn't paid, your scenario doesn't get the substitution.
========================================
ERRATA: In my recent post to James Acker, I mis-typed "recessive" instead of
"dominant", though this was clear from the context of the remaining
paragraph. The complete paragraph is below, with the correction in brackets.
The other key piece of information is whether the new beneficial mutation is
dominant or recessive. For sake of discussion I will assume it is [dominant],
as
that is what evolutionists almost always assume. Why do they do that?
Because
dominant substitutions are vastly less costly than recessive ones.
Evolutionary
theorists want the fastest substitution rate, so they generally assume the
substitution is dominant. They rarely explain that rationale to students.
They
just assume a dominant substitution, and don't say why.
DJohn1117
Is there some maximum rate of substitution you have in mind that would pose a
problem for evolutionists? Haldane gave a figure of 1 gene substitution per
300 generations, though I've read that under other models of selection one can
get around that limit. I don't know the details. But anyway, leaving that
aside, are you saying that Haldane's limit, if roughly accurate, would
constrain evolution so much that we wouldn't be able to explain the amount of
genetic change that should have taken place in some specific example? (Say
over the past 5 million years between people and chimps.)
Kimura thought Haldane's maximum limit for gene substitution was evidence for
his neutral theory, because nucleotides are apparently substituted at a rate
hundreds of times higher than 1 per 300 generations. I'm summarizing what he
says on page 25 of The Neutral Theory of Molecular Evolution. Rightly or
wrongly, he evidently didn't think Haldane's limiting rate posed any
fundamental problem for Darwinism as an explanation for adaptive evolution.
Donald
J Jackson
For reference I posted:
"Consider a harem species, e.g. Red Deer, a mutated allele gets into a
male body and its action makes that male more dominant and hence the male
monopolises a good sized harem of females, and the mutated allele gets
into lots of new bodies. Some of these bodies are males and so we
recurse.
Ok. Maybe I'm being thick, but where is the cost of substition in this
case.
Run through the scenario without a mutated allele and nothing
changes. There will be a some males that dominates harems, and some males
that are excluded from procreating - same as when the mutated allele
occurs."
I get as a reply a lot of hand waving (see below) about this being a
special case etc etc. Actually it is not as special as all that as it
represents an end of a continuum of cases dependant on sexual
reproduction, differing sized sex gametes and vast over production of
small gametes.
I think I maybe need to rephrase, because Remine seems to be making this
more difficult than it is.
wjre...@mmm.com wrote:
................snip...........
:
: So Jackson wants us to consider a harem species where one dominant male sires
: all the progeny. Supposedly this increases its reproduction and hastens
: evolution. Well, only if the dominant male contains the beneficial mutation.
: If any other male contains the beneficial mutation, it goes to waste.
:
: What about beneficial mutations that occur in females. There is a very slim
: chance it will survive its first generation. First, there is but a fifty
: percent chance it will get into a given egg, and hence into a given progeny.
: If the progeny is male, there is but a further slim chance it will become the
: dominant male. If it is female, then the same slim odds apply for the next
: generation. For most beneficial mutations (where the selective value is low)
: there is about one chance in four it will survive the first generation.
: (Fifty percent loss through meiosis, and another loss of slightly less than
: fifty-percent because nearly half the population, all but one male, is a
: genetic dead-end. Further losses occur because random death takes a bite out
: of the species' reproduction each generation.)
All of which is fine hedging. But just let's take two possible outcomes,
1) The mutant allele really is beneficially, i.e. it makes it into future
generations big time. i.e. it substitutes
2) The mutant allele doesn't make it and the basic unmoutated allele
stays .i.e it doesn't substitute.
My point is that I don't see the difference. I don't see what a 'cost'
might be and where the 'cost' of substitution is. What is the difference
in the two scenarios that imposes some sort of cost on 1) as opposed to
2)? Remine has not even attempted to show me.
Perhaps he'd like a second go?
Jim
: The scenario relies (as many evolutionary scenarios do) on an unrealistic
: model of a SINGLE mutation causing some new beneficial trait, and the new
: trait supposedly impels its male possessor immediately into "dominance" where
: it sires all the progeny. How convenient. But that is unrealistic on a
: number of levels.
:
: The scenario doesn't end there, because the twenty or so animals in the harem
: are seldom a species. They are but a small part of a much larger reproductive
: group, the species. For beneficial substitution to propagate throughout the
: species, it must travel *out* of the harem into other groups, and that is
: precisely where the reproductive isolation of the harem further SLOWS the
: substitution process. Limited migration between sub-populations slows the
: spread of new beneficial mutations -- it does not stop the spread, but slows
: it.
:
: There is still a cost of substitution,
Where - please identify for the more slow among us.
: ........ and it is the same as without the harem
: scenario. Rather, the scenario attempts to increase the reproductive excess
: allotted to beneficial substitutions, but it is questionable how much it
: actually accomplishes that. The harem scenario wastes a lot of reproduction
: in producing male offspring who then never procreate. Virtually half the
: species' reproduction goes to waste.
This I find unbelievable. If I had read this without knowing my natural
history I would conclude that someone here was arguing that a harem
reproductive strategy couldn't work, it has all these faults, problems
etc. Shame about it existing, and allowing the species that do have to
survive as weel as others that do not.
: In any event, the reproductive excess is still finite, so there is still a
: cost limitation to the substitution rate. Those fundamental mechanics of the
: problem are largely unchanged.
please elaborate further with respect to the example.
: > Run through the scenario without a mutated allele and
: > nothing changes. There will be a some males that
: > dominates harems, and some males that are excluded
: > from procreating - same as when the mutated allele
: > occurs.
:
: I remind Jackson that if there is no substitution, then there is no cost of
: substitution -- but your scenario does not get the substitution either. If the
: cost isn't paid, your scenario doesn't get the substitution.
YES but just what is the cost in this scenario?
Jim
Donal Hickey
DJohn1117 wrote:
>
> Rightly or
> wrongly, he (Kimura) evidently didn't think Haldane's limiting rate posed any
> fundamental problem for Darwinism as an explanation for adaptive evolution.
>
I agree entirely. And this is the issue that Walter ReMine continues to
avoid. He is merely attacking a "paper tiger" of his own construction.
Of course, if he can show that his tiger has real teeth, then we all
should pay attention. Until, he does so, however, there is not much
point in arguing about what ReMine said Felsenstein said Haldane said.
Donal.