Removing Lewontin's Fallacy From Hamilton's Rule
jim_b...@hotmail.com
individual genes rather than focusing on the differences in phylogenic
correlation structure of genes, seems to be suffering from a kind of
"Lewontin's Fallacy", as described by Edwards in his paper.
The question is, how can we generalize sociobiology's equations to look
at the correlation structures so that Hamilton's equations fall out as
a special case?
Another way of asking this might be: How can we generalize the
definition of "gene", or more accurately "allele", so that what we now
think of as alleles are a degenerate correlation structure?
Here's an approach: Look at the genome as a set of (nucleotide,locus)
pairs. Find all the structures (clusters?) with a correlation of very
nearly r=1. Those are alleles in the current sense.
I don't think we can ignore the other structures just because they have
an r<1 -- particularly where we can impute them as being due to
phylogeny.
Perplexed in Peoria
<jim_b...@hotmail.com> wrote in message news:dkr50q$2545$1...@darwin.ediacara.org...
Well, thanks for calling my attention to Edwards' paper. Here is a link
http://www.goodrumj.com/Edwards.pdf
Whether Lewontin's logic constitutes a fallacy would depend upon how
he makes use of that reasoning in an argument. It seems to me, though,
that Lewontin's choice of a sample of loci for arriving at his 85%
figure is his more serious mistake. The loci that he chose are famously
those which exhibit balanced polymorphism. Using such loci will naturally
bias the case toward variance within groups rather than between
reproductively semi-isolated groups.
But regardless of the issue of whether Lewontin is confused or politically
biased, I don't understand how this is particularly relevant to
sociobiology. The only possible relevance I can see is that it makes
it seem likely that an individual will be able to reliably distinguish
distant kin from extremely distant kin by racial cues. But, as Hamilton's
logic for kin selection shows, there is almost no gain in inclusive
fitness that can be gained by recognizing distant kin and treating them
more beneficiently that extremely distant kin.
Perhaps before discussing how to capture correlation structure in the
definition of a 'gene', you should tell us how this definition might
be productive. Presumably you are suggesting something along the lines
of being nice to your prospective in-laws, but for the life of me, I
can't imagine why such a trait would be favored by NS. If there IS
such an effect, it would certainly be a significant finding.
jim_b...@hotmail.com
> logic for kin selection shows, there is almost no gain in inclusive
> fitness that can be gained by recognizing distant kin and treating them
> more beneficiently that extremely distant kin.
You obviously aren't aware of the implications of Price's equations as
explicated by W. D. Hamilton in "Innate Social Aptitudes of Man":
http://www.geocities.com/jim_bowery/isaom.html
Perplexed in Peoria
<jim_b...@hotmail.com> wrote in message news:dkt9cf$3c3$1...@darwin.ediacara.org...
writings that you seem to be aware of is this paper, the one that Trivers
called 'Fascist' and Washburn called 'racist'. As I look at the ideas
expressed in your web site and your newsgroup oeuvre, I am let to suspect
that these criticisms are what drew you to the paper.
However, Hamilton wrote many other things, some of them more recently.
You may wish to check out the introductory essay (written in the 1990s)
to his 1971 'Spite' paper, which appears in Chapter 6 of "Narrow Roads of
Geneland". In it, Hamilton clarifies that the use of the Price equations
to justify group selection doesn't really work in the real world. The
point has been made more mathematically by Queller, Grafen, Taylor,
Frank, and others.
Now, admitedly, when I stated that there would be no gain from the ability
to recognize distant kin by racial cues, I was thinking only about kin
selection and not group selection. I do tend to discount the importance
of group selection, since I have seen adequate mathematical treatment
to convince me that no 'group' which persists longer than a single
generation can be of evolutionary significance.
The idea that you seem to be promoting - the evolutionary and biological
importance of human racial groups, with populations in the millions and
histories of coherent existence for thousands of years, and with a
kind of Spenserian duty for these groups to engage in a conflict for
group survival - well, I consider these views to be better suited for
a political newsgroup than a scientific one.
jim_b...@hotmail.com
political polemics and then claim that I "seem to be promoting" "views
to be better suited for a political newsgroup than a scientific one".
I've put forth a proposal for how one can clarify the definition of
heritable "particles" which should not only provide more rigor to
definitions of "gene" such as Dawkins' provided in "The Extended
Phenotype":
'that which segregates and recombines with appreciable frequency' and
as 'any hereditary information for which there is favorable or
unfavorable selection bias equal to several or many times its rate of
endogenous change'
replacing phrases like "appreciable" and "several or many" with actual
biometrically-derived numbers -- but also provides numbers for
correlation structures beyond the allele, such as those referenced by
Edwards.
I'd appreciate some honest feedback on the idea rather than a political
characterization of the consequences of the idea.
Perplexed in Peoria
<jim_b...@hotmail.com> wrote in message news:dl027b$1cu7$1...@darwin.ediacara.org...
> You start by quoting characterizations of an academic paper in
> political polemics and then claim that I "seem to be promoting" "views
> to be better suited for a political newsgroup than a scientific one".
Ok. I was unfair to drag "political agenda's" into this, as you have not.
However, in my defense, I might point out that Lewontin commited his
'fallacy' while making a political argument, which means to me that
Edwards was making a political statement by attacking it, which suggested
to me that you had a political motive in mentioning it. But, I did,
as you suggest, jump to a conclusion. I apologize.
> I've put forth a proposal for how one can clarify the definition of
> heritable "particles" which should not only provide more rigor to
> definitions of "gene" such as Dawkins' provided in "The Extended
> Phenotype":
>
> 'that which segregates and recombines with appreciable frequency' and
> as 'any hereditary information for which there is favorable or
> unfavorable selection bias equal to several or many times its rate of
> endogenous change'
>
> replacing phrases like "appreciable" and "several or many" with actual
> biometrically-derived numbers -- but also provides numbers for
> correlation structures beyond the allele, such as those referenced by
> Edwards.
>
> I'd appreciate some honest feedback on the idea rather than a political
> characterization of the consequences of the idea.
Don't take my feedback as definitive, as I am not a professional. But
here goes:
Correlation structures could conceivably arise from two known causes:
1. Linkage, which is essentially proximity on the chromosome. Most
proposals to alter our conception of a gene to something larger
simply make the gene longer as a sequence of base pairs. And there
is no particular theoretical problem with this because those long
units are frequently inherited as a unit - that is, the larger unit
usually segregates as a unit.
2. Assortive mating, which allows even unlinked small genes to remain
correlated. (Actually, selection could also do the job, if there
is sufficient hybrid dysfunction).
The trouble with extending the concept of a gene to include such entities
defined by cluster analysis is that technically, such clusters are not
sufficiently heritable to deserve the name 'genes'.
This is not to say that investigating the reasons why such non-heritable
clusters form and persist is not a scientific question. Nor is it
unscientific to worry about the consequences of such clusters. But
my first inclination is to think that calling them genes would be a
mistake. And I also doubt that they would work well with the 1964
logic of Hamilton's kin selection.
These clusters would work as 'genes' using Hamilton's 1970-76 logic
based on the Price equations, which is what you suggested. However,
be aware! Analyses based on the Price equations can be ACTIVELY
MISLEADING regarding causality. (Also, be aware that I am pretty
much alone among the sane posters to this newsgroup in mistrusting
the use of the 1970 version of Hamilton's rule so vehemently.)
jim_b...@hotmail.com
The point of a revised formulation is to parameterize the "units", what
I'm trying to recast as "particles" to be consistent with Hamilton's
term, so that linkage disequilibrium, among other things, falls out of
them on a continuum.
> Assortive mating... sufficient hybrid dysfunction
>From a "gene"'s-eye-view the important thing is not _how_ they will end
up sharing a genome but _that_ they will end up sharing a genome. A
fair meiotic lottery is the most stark example of this tendency toward
cooperation (aka "altruism") enforced by group reward/punishment, but
there can be others.
> The trouble with extending the concept of a gene to include such entities
> defined by cluster analysis is that technically, such clusters are not
> sufficiently heritable to deserve the name 'genes'.
Again, "sufficiently heritable" depends a lot on what is going on all
over the place, not just cross-over linkage. An obvious case here is
homozygousity which simplifies the environment by creating certain
base-line assumptions for the evolution at other loci.
> Analyses based on the Price equations can be ACTIVELY
> MISLEADING regarding causality.
Well, I again point to my prior point about the "gene"'s-eye-view not
caring about mechanism.
But you're correct that there are pitfalls here. A big stride may have
been made toward bringing Price's equations out of the confusing haze
by Matthijs van Veelen's "On the use of the Price equation", Journal of
Theoretical Biology, 237, (2005) 412-426.:
Abstract
This paper distinguishes two categories of questions that the Price
equation can help us answer. The two different types of questions
require two different disciplines that are related, but nonetheless
move in opposite directions. These disciplines are probability theory
on the one hand and statistical inference on the other. In the
literature on the Price equation this distinction is not made. As a
result of this, questions that require a probability model are
regularly approached with statistical tools.
In this paper, we examine the possibilities of the Price equation for
answering questions of either type. By spending extra attention on
mathematical formalities, we avoid the two disciplines to get mixed up.
After that, we look at some examples, both from kin selection and from
group selection, that show how the inappropriate use of statistical
terminology can put us on the wrong track. Statements that are
'derived' with the help of the Price equation are, therefore, in
many cases not the answers they seem to be. Going through the
derivations in reverse can, however, be helpful as a guide how to build
proper (probabilistic) models that do give answers.
Keywords: The Price equation; Kin selection; Group selection;
Probability theory; Statistics
name_and_add...@hotmail.com
Perplexed in Peoria wrote:
> (Also, be aware that I am pretty
> much alone among the sane posters to this newsgroup in mistrusting
> the use of the 1970 version of Hamilton's rule so vehemently.)
I understand the reasons for this mistrust. I share your opinion here.
The problem is that this derivation is straight from Price's theorem,
which says everything and nothing. If we want to show that Hamilton's
rule is a general principle, this is the way we have to go. But if we
want to say anything about causality we need an explicit model, and
with that disappears our generality. So, learn to love the 1970
derivation, whilst keeping in mind exactly what it is for, and what it
is not for. It has its uses, but yes, it could also be abused.
John Edser
name_and_add...@hotmail.com wrote:-
> > Perplexed in Peoria wrote:
> > (Also, be aware that I am pretty
> > much alone among the sane posters to this newsgroup in mistrusting
> > the use of the 1970 version of Hamilton's rule so vehemently.)
JE:-
It is a classic act of tribal insanity to declare that only your own chosen
tribal group remains sane, without providing any refutable arguments as to
why this may or may not be, the case.
> I understand the reasons for this mistrust. I share your opinion here.
> The problem is that this derivation is straight from Price's theorem,
> which says everything and nothing.
JE:-
Price's theorem is not empirically based, i.e. while it is a valid
proposition of mathematics it is not a valid proposition of science.
Converting sense in mathematics into sense within the sciences is quite
simple in principle if not in practice: define within the mathematical
proposition at least one constant algebraic term which can be verified or
refuted within nature. Hamilton's Rule was and remains an invalid
proposition of science even if it is mathematically valid unless at least
one constant algebraic term is included on just one of the rule.
> If we want to show that Hamilton's
> rule is a general principle, this is the way we have to go. But if we
> want to say anything about causality we need an explicit model, and
> with that disappears our generality.
JE:-
Yes, Popper would agree with you because the most general of statements are
just epistemological perpetual motion machines, i.e. tautologies where
causality remains 100% reversible. So far, Hamilton's Rule has not been
supplied with any empirically based fitness limits which are absolutely
required to break Hamilton's fitness tautology. Like Price's mathematics, HR
does not represent a valid proposition of science.
> So, learn to love the 1970
> derivation, whilst keeping in mind exactly what it is for, and what it
> is not for.
JE:-
That is why you have to love what Hamilton appears to be attempting but
utterly hate what it has subsequently become. The errors within the rule are
and remain, gross. Hamilton et al show almost no understanding of just
evolutionary theory basics: conserving levels of selection and correctly
converting one level into another so they can be compared. Hamilton's
mathematics treats its delicate biological levels of selection as if they
are just mince meat. A famous biochemist once joked: "don't worry about the
organism concept, they all look the same under the Wareing Blender....
Three major errors exist:
1)The rule remains a 100% relative and therefore just a tautological
proposition of mathematics. Therefore none of the 4 _conditional_ WHY
propositions, i.e. why Hamilton's allele appears to spread on just a 100%
relative basis when rb>c or -rb<-c which are:
i) Altruism (positive c conditional to positive b)
ii) Selfishness (negative conditional to a negative b)
iii) Mutualism (negative c conditional to a positive b)
iv) Spite (positive c conditional to a negative b)
remain empirically valid. This is because, in every single case, the
separation of the only two empirically based independent selectees that
actually exist within HR which are:
a) The one group centric b
b) The one organism centric c
become destroyed by the wareing blender of population genetics leaving just
the one group centric selectee soup produced when c is merged with b as c
takes all fitness responsibility away from b. Unless at least two
independent selectee's remain defined (which means c cannot take any fitness
responsibility for b), the rule is not even a valid minimal proposition of
evolutionary theory. To satisfy this requirement at least two independent
selectees must be _defined_ and _remain conserved_ at all times to allow a
minimum of valid Darwinian competition.
The only two unconditional WHY propositions which alone CAN conserve
Hamilton's defined two selectees and maintain them throughout are:
v) Unconditional Selfishness(any negative c).
vii) Unconditional Altruism (any positive c).
However, because the rule remains just a tautology, it becomes impossible to
tell them apart simply because rb>c remains mathematically equivalent to
-rb<-c. This means the best the rule can offer is that while it can measure
when rb>c and can argue that one allele appears to increase relative to
another it cannot say why this is the case because it cannot tell if this is
happening via unconditional selfishness or unconditional altruism.
Note: unconditional mutualism is not even represented.
2) The deletion of n (the number of recipients)from the rule.
Because Hamilton et al VERY STRICTLY define gene centricity to be the number
of genes replicated over organism generations (organism centric gene
replications) and NOT organism group generations (organism group centric
gene replications) then the group centric b must be converted to organism
centric by dividing b by n which is then converted to gene centric by
multiplying b/n by r producing rb/n. Exactly the same process must be done
with c where it is divided by n' (the number of actors which is defined to
be 1) and then multiplied by r' which is just the relatedness of the actor
to itself, which of course is 1, so r'c/n' = 1. It is interesting to not
that if you expand the number of actors to n'> 1 that this logic becomes
much more immediate.
3) The deletion of the variable e within (r^e)b (e = gene fitness epistasis)
by fixing e=1 and just forgetting all about it.
This act expands Hamilton's "allele" to be 1 haploid chromosome number.
Because HR remains just a tautology, one gene can be expanded or contacted
to anything you like because no biological exceptions can exist when
misusing a tautology as an empirically based theory of nature in its own
right. Whenever e>1 the ability of any "green beard" propositions ceases
because the costs > gains, NO EXCEPTIONS. This condemns the rule to random
mating in all cases. Because HR remains circular no escape from random
mating can ever exist. If you attempt to get around any cost benefit ratio
barrier defining say, the epistatic alleles to be very closer together and
not farther apart so they are more often inherited together then the lesser
the chances that this could happen by random mutation, so you just end up
paying THIS way. ALWAYS, a tautology provides a "what you gain on the swings
you must lose on the roundabouts" argument because you cannot get something
for nothing. Thus e > 1 prohibits all non random mating while also providing
a useful index to how hard it is to start the inclusive fitness process from
scratch. As e increases, the probability that inclusive fitness can even
start geometrically diminishes to zero.
Regards,
John Edser
Independent Researcher
name_and_add...@hotmail.com
John Edser wrote:
> name_and_add...@hotmail.com wrote:-
> > I understand the reasons for this mistrust. I share your opinion here.
> > The problem is that this derivation is straight from Price's theorem,
> > which says everything and nothing.
>
> JE:-
> Price's theorem is not empirically based, i.e. while it is a valid
> proposition of mathematics it is not a valid proposition of science.
There are two issues here. Firstly, HR is a mathematically true
statement. It doesn't need to be empirically verified because it is
true by definition. Secondly, the motivation for developing HR was to
have a predictive tool for social evolution. So there is an empirical
test we can apply, and that is to see if organisms behave as if they
were maximizing their inclusive fitness. They might not be, so this
hypothesis is falsifiable. Actually, I am more interested in a
quantitative test -- how good is the hypothesis that organisms should
behave as if maximizing their inclusive fitness at explaining our
empirical observations? Specifically, how much of the variance does
this hypothesis explain? What other hypotheses might we employ to
explain a greater proportion of the variance?
> Converting sense in mathematics into sense within the sciences is quite
> simple in principle if not in practice: define within the mathematical
> proposition at least one constant algebraic term which can be verified or
> refuted within nature.
Is this Edser's Theorem? Please provide some support for this
assertion.
> Hamilton's Rule was and remains an invalid
> proposition of science even if it is mathematically valid unless at least
> one constant algebraic term is included on just one of the rule.
>
> > If we want to show that Hamilton's
> > rule is a general principle, this is the way we have to go. But if we
> > want to say anything about causality we need an explicit model, and
> > with that disappears our generality.
>
> JE:-
> Yes, Popper would agree with you because the most general of statements are
> just epistemological perpetual motion machines, i.e. tautologies where
> causality remains 100% reversible. So far, Hamilton's Rule has not been
> supplied with any empirically based fitness limits which are absolutely
> required to break Hamilton's fitness tautology. Like Price's mathematics, HR
> does not represent a valid proposition of science.
See above.
Also, natural selection does not care about causation, only
correlation. A trait that is correlated with high fitness is favoured,
whether it caused that high fitness or not.
> > So, learn to love the 1970
> > derivation, whilst keeping in mind exactly what it is for, and what it
> > is not for.
>
> JE:-
> That is why you have to love what Hamilton appears to be attempting but
> utterly hate what it has subsequently become. The errors within the rule are
> and remain, gross. Hamilton et al show almost no understanding of just
> evolutionary theory basics: conserving levels of selection and correctly
> converting one level into another so they can be compared. Hamilton's
> mathematics treats its delicate biological levels of selection as if they
> are just mince meat. A famous biochemist once joked: "don't worry about the
> organism concept, they all look the same under the Wareing Blender....
Do you have any evidence to back up all this nonsense? Also, don't you
understand that kin selection approaches are mathematically equivalent
to levels of selection approaches? Point to one instance where
Hamilton's logic has been flawed in terms of him making a prediction
based on kin selection theory that contrasts with the prediction from
levels of selection considerations, and where the empirical evidence
favours the levels of selection approach.
> Three major errors exist:
>
> 1)The rule remains a 100% relative and therefore just a tautological
> proposition of mathematics. Therefore none of the 4 _conditional_ WHY
> propositions, i.e. why Hamilton's allele appears to spread on just a 100%
> relative basis when rb>c or -rb<-c which are:
>
> i) Altruism (positive c conditional to positive b)
> ii) Selfishness (negative conditional to a negative b)
> iii) Mutualism (negative c conditional to a positive b)
> iv) Spite (positive c conditional to a negative b)
>
> remain empirically valid. This is because, in every single case, the
> separation of the only two empirically based independent selectees that
> actually exist within HR which are:
>
> a) The one group centric b
>
> b) The one organism centric c
>
> become destroyed by the wareing blender of population genetics leaving just
> the one group centric selectee soup produced when c is merged with b as c
> takes all fitness responsibility away from b. Unless at least two
> independent selectee's remain defined (which means c cannot take any fitness
> responsibility for b), the rule is not even a valid minimal proposition of
> evolutionary theory. To satisfy this requirement at least two independent
> selectees must be _defined_ and _remain conserved_ at all times to allow a
> minimum of valid Darwinian competition.
Demonstrate that this 'blending' leads to incorrect, i.e. empirically
indefensible, predictions.
> The only two unconditional WHY propositions which alone CAN conserve
> Hamilton's defined two selectees and maintain them throughout are:
>
> v) Unconditional Selfishness(any negative c).
> vii) Unconditional Altruism (any positive c).
>
> However, because the rule remains just a tautology, it becomes impossible to
> tell them apart simply because rb>c remains mathematically equivalent to
> -rb<-c. This means the best the rule can offer is that while it can measure
> when rb>c and can argue that one allele appears to increase relative to
> another it cannot say why this is the case because it cannot tell if this is
> happening via unconditional selfishness or unconditional altruism.
> Note: unconditional mutualism is not even represented.
I'm not going to argue any more about this reflected rule nonsense. All
you have managed to demonstrate is your unfamiliarity with the concept
of negative numbers. You have no support on this newsgroup nor anywhere
else for your babblings about the reflected HR and its interpretation.
> 2) The deletion of n (the number of recipients)from the rule.
>
> Because Hamilton et al VERY STRICTLY define gene centricity to be the number
> of genes replicated over organism generations (organism centric gene
> replications)
I would define "gene centricity" in terms of "the approach whereby we
focus on the gene as the unit of selection", rather than it being some
count of number of genes . . . and I believe Hamilton, who was a native
English speaker, would have followed me in this definition.
> and NOT organism group generations (organism group centric
> gene replications) then the group centric b must be converted to organism
> centric by dividing b by n which is then converted to gene centric by
> multiplying b/n by r producing rb/n.
Not sure why you are doing this. So, taking an average, you have
suggested that each of the n recipients gets a benefit b/n, and we
multiply by their relatedness (assuming all are equally related, r) to
get rb/n as the inclusive fitness benefit accrued from each recipient.
But note, there are n of these recipients, so the total inclusive
fitness benefit is n * rb/n = rb.
> Exactly the same process must be done
> with c where it is divided by n' (the number of actors which is defined to
> be 1) and then multiplied by r' which is just the relatedness of the actor
> to itself, which of course is 1, so r'c/n' = 1.
if n' = 1 and r' = 1 then r'c/n' = c. This is only equal to 1 when c =
1.
> It is interesting to not
> that if you expand the number of actors to n'> 1 that this logic becomes
> much more immediate.
We are calculating the inclusive fitness for an individual, with that
individual defined to be the actor. There is only ever one actor in any
inclusive fitness calculation.
> 3) The deletion of the variable e within (r^e)b (e = gene fitness epistasis)
> by fixing e=1 and just forgetting all about it.
Out of interest, I have never seen a derivation of this HR with
epistasis. Please define e, and properly -- simply calling it gene
fitness epistasis is not helpful. And then show me how you move from
that definition to a HR where e appears as an exponent of r.
> This act expands Hamilton's "allele" to be 1 haploid chromosome number.
> Because HR remains just a tautology, one gene can be expanded or contacted
> to anything you like because no biological exceptions can exist when
> misusing a tautology as an empirically based theory of nature in its own
> right. Whenever e>1 the ability of any "green beard" propositions ceases
> because the costs > gains, NO EXCEPTIONS. This condemns the rule to random
> mating in all cases. Because HR remains circular no escape from random
> mating can ever exist. If you attempt to get around any cost benefit ratio
> barrier defining say, the epistatic alleles to be very closer together and
> not farther apart so they are more often inherited together then the lesser
> the chances that this could happen by random mutation, so you just end up
> paying THIS way. ALWAYS, a tautology provides a "what you gain on the swings
> you must lose on the roundabouts" argument because you cannot get something
> for nothing. Thus e > 1 prohibits all non random mating while also providing
> a useful index to how hard it is to start the inclusive fitness process from
> scratch. As e increases, the probability that inclusive fitness can even
> start geometrically diminishes to zero.
Gibberish, at least until you define e, and provide the derivation I
asked for.
Perplexed in Peoria
<name_and_add...@hotmail.com> wrote in message news:dl9b88$2kv7$1...@darwin.ediacara.org...
> > > rule is a general principle, this is the way we have to go. But if we
> > > want to say anything about causality we need an explicit model, and
> > > with that disappears our generality.
> >
> > JE:-
> > Yes, Popper would agree with you because the most general of statements are
> > just epistemological perpetual motion machines, i.e. tautologies where
> > causality remains 100% reversible. So far, Hamilton's Rule has not been
> > supplied with any empirically based fitness limits which are absolutely
> > required to break Hamilton's fitness tautology. Like Price's mathematics, HR
> > does not represent a valid proposition of science.
John, you seem to limit 'proposition of science' to things that I would
call 'laws of nature'. Hamilton's law - at least the 1970 tautological
version - is not a law of nature. It is a theorem of mathematics. But
that doesn't mean that it is useless to scientists. Science makes use
of a variety of propositions with no inherent physical content -
Liouvilles's theorem, Bayes's theorem, Wigner's CPT theorem, etc.
> NAS:-
> See above.
>
> Also, natural selection does not care about causation, only
> correlation. A trait that is correlated with high fitness is favoured,
> whether it caused that high fitness or not.
That depends on whether you wish to view 'natural selection' as a
biological process (in which case formulas describing it ARE in some
weak sense 'laws of nature') or whether you only wish to view 'natural
selection' as a technique for organizing data about past populations.
If you want to view it as a biological process, which continues in the
present day, then you need to attach some kind of causality to those
correlations, if only so that you can project the observed motions of
the past into the future.
Jim McGinn
Perplexed in Peoria wrote:
> Hamilton's law - at least the 1970 tautological
> version - is not a law of nature. It is a theorem of mathematics.
You're claiming (or proposing?) Hamilton's Rule to be, "a theorem of
mathematics?" What do you mean by this?
> But that doesn't mean that it is useless to scientists. Science makes use
> of a variety of propositions with no inherent physical content -
> Liouvilles's theorem, Bayes's theorem, Wigner's CPT theorem, etc.
I think you need to be extremely explicit with respect to explaining
what you
mean by the phrase, "Science makes use of a variety of propositions
with no
inherent physical content." This phrase leaves you vulnerable to the
accusation
that you are proposing solutions that are spiritualistic.
Jim
name_and_add...@hotmail.com
Perplexed in Peoria wrote:
> <name_and_add...@hotmail.com> wrote in message news:dl9b88$2kv7$1...@darwin.ediacara.org...
> >
> > correlation. A trait that is correlated with high fitness is favoured,
> > whether it caused that high fitness or not.
>
> That depends on whether you wish to view 'natural selection' as a
> biological process (in which case formulas describing it ARE in some
> weak sense 'laws of nature') or whether you only wish to view 'natural
> selection' as a technique for organizing data about past populations.
>
> If you want to view it as a biological process, which continues in the
> present day, then you need to attach some kind of causality to those
> correlations, if only so that you can project the observed motions of
> the past into the future.
Ah, I was talking about how natural selection doesn't care about
causation, only correlation. We, on the other hand, might care about
causation, for instance if we wanted to predict the evolution of a
particular trait.
In addition to the two questions and associated approaches you mention
above, there is a third question -- and that is: Why is natural
selection interested in trait X. The answer is: Trait X is correlated
with fitness. This is the general principle at play in all the models
that you could construct to answer your question: How will trait X
change over time under the influence of natural selection?
John Edser
"Perplexed in Peoria" jimme...@sbcglobal.net wrote:-
> > > name_and_add...@hotmail.com wrote:-
> > > > If we want to show that Hamilton's
> > > > rule is a general principle, this is the way we have to go. But if
> we
> > > > want to say anything about causality we need an explicit model, and
> > > > with that disappears our generality.
> > > JE:-
> > > Yes, Popper would agree with you because the most general of
> statements are
> > > just epistemological perpetual motion machines, i.e. tautologies where
> > > causality remains 100% reversible. So far, Hamilton's Rule has not
> been
> > > supplied with any empirically based fitness limits which are
> absolutely
> > > required to break Hamilton's fitness tautology. Like Price's
> mathematics, HR
> > > does not represent a valid proposition of science.
> John, you seem to limit 'proposition of science' to things that I would
> call 'laws of nature'.
JE:-
Jim, I limit propositions of science to conjectures (theories) that can be
verified or refuted within nature.
> Hamilton's law - at least the 1970 tautological
> version - is not a law of nature. It is a theorem of mathematics. But
> that doesn't mean that it is useless to scientists. Science makes use
> of a variety of propositions with no inherent physical content -
> Liouvilles's theorem, Bayes's theorem, Wigner's CPT theorem, etc.
JE:-
The issue here concerns the proper or improper use of heuristics within the
empirically based sciences. Hamilton's Rule was and remains an empty
tautology of mathematics incorrectly proffered as valid theory of nature in
its own right. Please take another look at the premises that Felsenstein
used to derive HR and confirm or deny to readers that the premises he used
were tautological. I have requested all sbe posters of integrity to make
this basic test on a number of different occasions where I have stated will
not do this for anybody here. I find it inconceivable that anybody of
integrity would simply refuse to make this test.
HR is derived from a major oversimplification of Darwinism where TDF for the
actor was and remains, deleted. This has allowed cause and effect to become
reversed within a 100% relative proposition providing the empirically false
gene centric argument that "genes use organisms to replicate genes" which is
permeating consciousness like Herbert Spencer's tautology "survival of the
fittest" did with disastrous results. The testable scientific truth is the
contrary proposition: organisms use genes to reproduce organisms. It is just
history repeating itself because we flatly refuse to correct the errors of
the past. HR also allowed two critical simplifications: the deletion of all
epistasis e within relatedness r^e by just artificially fixing e to 1 and
the deletion of the number of recipients n which was and remains, absolutely
required to CORRECTLY convert Hamilton's ONE group centric b selectee into a
heuristic gene centric measure so that it could be compared to a gene
centric version of the ONE organism centric c with which it competes for x
reproductive resources. HR remains uncorrected for one oversimplification
and two simplifications yet it has been allowed to contest and win against
the empirically based theory it was oversimplified from which constitutes an
utter misuse of Hamilton's model, i.e. just an absurdity.
> > NAS:-
> > See above.
> >
> > Also, natural selection does not care about causation, only
> > correlation. A trait that is correlated with high fitness is favoured,
> > whether it caused that high fitness or not.
> That depends on whether you wish to view 'natural selection' as a
> biological process (in which case formulas describing it ARE in some
> weak sense 'laws of nature') or whether you only wish to view 'natural
> selection' as a technique for organizing data about past populations.
JE:-
Darwin's description of the non random process of natural selection which he
employed within a very specific theory of evolution which was then and
remains today empirically based, did allow that theory to be verified or
refuted within nature so it is NOT based on just "correlations" it is based
on very specific predictions of nature.
> If you want to view it as a biological process, which continues in the
> present day, then you need to attach some kind of causality to those
> correlations, if only so that you can project the observed motions of
> the past into the future.
JE
The "causality to those correlations" is non random natural selection
operating within refutable Darwinian theory providing predictions of non
random gene freq. changes within one population a just an effect and NOT as
a cause. That "cause" is TDF which represents a Darwinian maximand fitness.
This means that TDF cannot be selected to be reduced as Hamilton et al
continue argue that it can be within however, just a misused heuristic
exercise. I argue that TDF represents the only EMPIRICALLY refutable
maximand that actually exists within evolutionary theory where I have
outlined a test to refutation for this conjecture. NAS argues that inclusive
fitness is such a maximand. I have pointed out to him that a relative
fitness cannot constitute a maximand simply because you cannot differentiate
it from a minimand within a 100% relative proposition where a minimand
represents a contrary proposition to a maximand so it cannot be both.
Perplexed in Peoria
"Jim McGinn" <jimm...@yahoo.com> wrote in message news:dlft90$2frt$1...@darwin.ediacara.org...
>
> Perplexed in Peoria wrote:
>
> > Hamilton's law - at least the 1970 tautological
> > version - is not a law of nature. It is a theorem of mathematics.
>
> You're claiming (or proposing?) Hamilton's Rule to be, "a theorem of
> mathematics?" What do you mean by this?
Claiming.
I mean just what I say. For a sketch proof of this theorem, see NAS's
posting of a few months ago which he made to call your $10,000 prize
bluff. I notice that you never responded.
Or, see Hamilton's 1970 paper and follow the reference therein to the
Price paper. Those will provide a more detailed proof.
I refer to these results as mathematics, rather than biology, because
there are no biological laws or assumptions embedded in the derivation.
(Well, I suppose there is a kind of assumption of discrete generations.)
> > But that doesn't mean that it is useless to scientists. Science makes use
> > of a variety of propositions with no inherent physical content -
> > Liouvilles's theorem, Bayes's theorem, Wigner's CPT theorem, etc.
>
> I think you need to be extremely explicit with respect to explaining
> what you mean by the phrase, "Science makes use of a variety of
> propositions with no inherent physical content." This phrase leaves
> you vulnerable to the accusation
> that you are proposing solutions that are spiritualistic.
Well, I would have thought that my examples would quash that line of
thought. What exactly do you see as 'spiritualistic' about Liouville's
theorem? Or the CPT theorem? There is a kind of Liebnizian metaphysics
attached to some applications of Bayes's theorem, but I would never call
it 'spiritualistic'.
Perplexed in Peoria
"John Edser" <ed...@tpg.com.au> wrote in message news:dlft90$2fsj$1...@darwin.ediacara.org...
Proffered by whom. Please be specific.
> Please take another look at the premises that Felsenstein
> used to derive HR and confirm or deny to readers that the premises he used
> were tautological.
Deny. There are a variety of non-tautological (i.e. 'empirical', 'refutable')
premises. Random mating, Mendelian segregation, etc.
The premises used by NAS in his derivation are more problematic. There
is far less empirical content there.
[snip remainder]
John Edser
name_and_add...@hotmail.com wrote:-
> > Perplexed in Peoria wrote:
> > If you want to view it as a biological process, which continues in the
> > present day, then you need to attach some kind of causality to those
> > correlations, if only so that you can project the observed motions of
> > the past into the future.
> Ah, I was talking about how natural selection doesn't care about
> causation, only correlation.
JE:_
Which was not correct.
> We, on the other hand, might care about
> causation, for instance if we wanted to predict the evolution of a
> particular trait.
JE:-
Darwinian theory predicts a heritable trait can change in an evolutionary
way (a way that is NOT represented as just a random pattern of change within
one population) as this one trait effects the Total Darwinian Fitness of
fertile forms in a dependent and NOT a independent way, i.e. the selection
of one trait remains 100% dependent on every other heritable trait within
each selected fertile form, no exceptions. The formal term for this is: gene
fitness epistasis which remains total per gene per genome. However, within
HR it has been deleted as a deliberate oversimplification to allow cause and
effect to become reversed within HR, i.e. allow "genes to use bodies to
maximally reproduce genes" producing organism altruism via selfish geneism
when _empirically_ the contrary proposition remains verified: "bodies use
genes to maximally reproduce bodies" predicting selfish organisms which
produce altruism at the heuristic gene level of selection. The reproduction
of fertile forms alone represents nature's empirically based maximand and
*NOT* Hamilton's inclusive and just 100% relative and heuristic replication
of genes over _organism_ generations of these genes.
> In addition to the two questions and associated approaches you mention
> above, there is a third question -- and that is: Why is natural
> selection interested in trait X. The answer is: Trait X is correlated
> with fitness. This is the general principle at play in all the models
> that you could construct to answer your question: How will trait X
> change over time under the influence of natural selection?
JE:-
The trait x is NOT just "correlated" to fitness it is _causally determined_
by fitness. The problem is the gene centric Neo Darwinists can only provide
a "hand waving" and irrefutable definition of fitness. OTOH Darwinism can
provide an objective and refutable definition of it: Total Darwinian Fitness
(TDF). Gene centric models simply oversimplify TDF and then proceed to
utterly misuse this oversimplification by allowing the tautology produced by
it to be invalidly employed as a theory of nature in its own right. Again I
request NAS and JM to revisit Felsenstein's propositions from which he
derives HR and ask them to concur of deny that they are just tautological. I
will repeat that doing this test and making their findings public is a test
of their integrity.
NAS should address the problems of HR that I have outlined which are: the
oversimplification (deletion of a constant term) discussed above and two
other critical simplifications (the deletion of two variables):
a) The error of the deletion of n within b/n is required to be
corrected to be able to convert the group centric b into an organism centric
b allowing it to be compared to the organism centric c where subsequently
Hamilton converts both to gene centric using relatedness:
rb/n > r'c/n'
where:
r = relatedness of the actor to the recipients
b = a _group_ centric organism fitness gain (an increase in b organisms
reproduced to n recipients as a whole) to just the one _organism_ centric
actor.
n = number of organism recipients.
r' = 1 the relatedness of the actor to itself.
c = the organism cost to the actor of the b extra organisms reproduced by
n recipients which is group centric and not organism centric. The variable c
represents a cost because it is the number of organisms not reproduced by
the actor, i.e. an organism centric cost to an organism actor. However, the
group centric b fitness remains entirely controlled by the independent
action of Hamilton's group of recipients made up of n Darwinian organisms
with which the actor is dealing in an attempt to inclusively reproduce just
one allele by proxy.
n' = 1 the number of actors which however can be > 1. Note: only when n'>1
does the logic as to why n cannot be deleted become obvious.
In any CORRECT transformation of b and c to just a heuristic gene centric
exercise using r, b must be divided by n just as c must be divided by n' to
be logically self consistent and mathematically correct. The only single
case where Hamilton's allele can increase, even on just a 100% relative
basis, is when the actor inclusively selects itself which is just normal
Darwinian reproduction. Eventually Hamilton's tautology moves full circle
proving it to be just an absurd Empirical proposition as are all tautologies
incorrectly proffered as valid theories of nature in their own right.
2) The deletion of e within r^e
where:
e = gene fitness epistasis where in nature (empirically) ALL genomic genes,
without any exceptions, have a _fitness_ dependency to at least one other
gene on one other chromosome within the same genome.
NAS et al should note that the deletion of n represents a fatal ERROR of
Hamilton et al whereas the deletion of TDF and e respectively, constitute a
deliberate oversimplification and simplification which remain uncorrected
and therefore misused to this day.