Sean Pitman wrote:[snip]
> lmucd...@yahoo.com (RobinGoodfellow) wrote in message <news:email@example.com>...
>>seanpitnos...@naturalselection.0catch.com (Sean Pitman) wrote in message <news:firstname.lastname@example.org>...
> With all due respect, what is your area of professional training? ITsk, tsk... I thank you for the career advice. I'll keep it in mind,
> mean, after reading your post I dare say that you are not only weak in
> biology, but statistics as well. Certainly your numbers and
> calculations are correct, but the logic behind your assumptions is
> extraordinarily fanciful. You sure wouldn't get away with such
> assumptions in any sort of peer reviewed medical journal or other
> statistically based science journal - that's for sure. Of course, you
> may have good success as a novelist . . .
should my current stint in computer science fall through. I wouldn't go
so far as to say that Monte-Carlo methods are my specialty, but I will
say that my own research and the research of half my colleagues would be
non-existent if they worked the way you think they do.
>>I'll try to address some of the mistakes you've made below, though IExactly what views did I state, Sean? Other than that your calculations
>>doubt that I can do much to dispel your misconceptions. Much of my
>>reply will not even concern evolution in a real sense, since I wish to
>>highlight and address the mathematical errors that you are making.
> What you ended up doing is highlighting your misunderstanding of
are, to put it plainly, irrelevant. Not even wrong - just irrelevant.
Yes, the example I give below incredibly stacks the deck in my favor.
When you're done laughing, would you care to explain to me why it is
>>>>It is even worse than that. Even random walks starting at random points
>>>This depends upon just how exponentially small the number of
>>No, it does not. If you take away anything from this discussion, it
> LOL - You really don't have a clue how insane this statement is?
insane? Especially when I can construct examples (and, if you so wish,
give you examples of real-world problems) that show this statement is true?
>>The things that *would* matter are theExcept in every real example of a working Monte-Carlo procedure, where
>>distribution of beneficial states through the state space, the types
>>of steps the local search is allowed to take (and the probabilities
>>associated with each step), and the starting point.
> This distribution of states has very little if anything to do with how
the distribution and starting point have *everything* to do whether such
a procedure is successful or not.
> For*Sigh*. The problem is that the model *you* are proposing (one I think
> example, if all the beneficial states were clustered together in one
> or two areas, the average starting point, if anything, would be
> farther way than if these states were distributed more evenly
> throughout the sequence space. So, this leaves the only really
> relevant factor - the types of steps and the number of steps per unit
> of time. That is the only really important factor in searching out
> the state space - on average.
is silly) is of a random on walk on a specific frozen sequence space
with beneficial sequences as points in that space. It does not deal
with an "average" distribution, and an "average" starting point, but
with one very specific distribution of beneficial sequences and one very
specific starting point. You cannot simply assume an "average"
distribution in the absence of background information: you have to find
out precisely the kind of distribution you are dealing with. And even
if you do find that the distribution is "stacked", it does not imply
that an intelligence was involved. The stacking could occur due to the
constraints imposed by the very definition of the problem: in the case
of evolutions, by the physical constraints governing the interactions
between the molecules involved in biological systems. In fact, why
would you expect that the regular and highly predictable physical laws
governing biochemical reactions would produce a random, "average"
distribution of "beneficial sequences"?
>>For an extremeNote, I wrote, "extereme example". My point was *not* invent a
>>example, consider a space of strings consisting of length 1000, where
>>each position can be occupied by one of 10 possible characters.
distribution which makes it likely for evolutiuon to occur (this example
has about as much to do with evolution as ballet does with quantum
mechanics), but to show how inadequate your methods are.
Mind-numbingly low. 1000*.9*.1^999, to be precise. But that is not the
> Ok. This would give you a state space of 10 to the power of 1000 or
>>Suppose there are only two beneficial strings: ABC........, and
> You are good so far. But, you must ask yourself this question: What
> The time required to cross thisOn average, yes. But didn't you just say above that the distribution
> tiny gap would require a random walk of only 10,000 steps on average.
> For a decent sized population, this could be done in just one
> Don't you see the problem with this little scenario of yours?
> Certainly this is a common mistake made by evolutionists, but it is
> none-the less a fallacy of logic. What you have done is assume that
> the density of beneficial states is unimportant to the problem of
> evolution since it is possible to have the beneficial states clustered
> around your starting point. But such a close proximity of beneficial
> states is highly unlikely. On average, the beneficial states will be
> more widely distributed throughout the sequence space.
of the sequences is irrelevant? That all that matters is "ratio" of
beneficial sequences? (Incidentally, "ratio" and "density" are not
identical. The distribution I showed you has a relatively high density
of beneficial sequences, despite a low ratio.)
> For example, say that there are 10 beneficial sequences in thisUnless, of course, it follows from the properties of the problem that
> sequence space of 1e1000. Now say one of these 10 beneficial
> sequences just happens to be one change away from your starting point
> and so the gap is only a random walk of 10,000 steps as you calculated
> above. However, on average, how long will it take to find any one of
> the other 9 beneficial states? That is the real question. You rest
> your faith in evolution on this inane notion that all of these states
> will be clustered around your starting point. If they were, that
> certainly would be a fabulous stroke of luck - like it was *designed*
> that way. But, in real life, outside of intelligent design, such
> strokes of luck are so remote as to be impossible for all practical
> purposes. On average we would expect that the other nine sequences
> would be separated from each other and our starting point by around
> 1e999 random walk steps/mutations (i.e., on average it is reasonable
> to expect there to be around 999 differences between each of the 10
> beneficial sequences). So, even if a starting sequence did happen to
> be so extraordinarily lucky to be just one positional change away from
> one of the "winning" sequences, the odds are that this luck will not
> hold up as well in the evolution of any of the other 9 "winning"
> sequences this side of a practical eternity of time.
the other 9 benefecial sequences must be close to the starting sequence.
> Real time experiments support this position rather nicely. ForI've already covered how you've completely misinterpreted Lenski's
> example, a recent and very interesting paper was published by Lenski
> et. al., entitled, "The Evolutionary Origin of Complex Features" in
> the 2003 May issue of Nature. In this particular experiment the
> researchers studied 50 different populations, or genomes, of 3,600
> individuals. Each individual began with 50 lines of code and no
> ability to perform "logic operations". Those that evolved the ability
> to perform logic operations were rewarded, and the rewards were larger
> for operations that were "more complex". After only15,873 generations,
> 23 of the genomes yielded descendants capable of carrying out the most
> complex logic operation: taking two inputs and determining if they are
> equivalent (the "EQU" function).
research in the other post. But let's run with this for a bit:
> In principle, 16 mutations (recombinations) coupled with the threeAs a minor quibble, I believe they actually started with NAND (you need
> instructions that were present in the original digital ancestor could
> have combined to produce an organism that was able to perform the
> complex equivalence operation. According to the researcher themselves,
> "Given the ancestral genome of length 50 and 26 possible instructions
> at each site, there are ~5.6 x 10e70 genotypes [sequence space]; and
> even this number underestimates the genotypic space because length
> Of course this sequence space was overcome in smaller steps. The
it for all the other functions). But I could be wrong - I've read that
paper months ago.
> The average gap between theseAnd after years of painstaking research, Sean finally invents the wheel.
> pre-defined steppingstone sequences was 2.5 steps, translating into an
> average search space between beneficial sequences of only 3,400 random
> walk steps. Of course, with a population of 3,600 individuals in a
> population, a random walk of 3,400 will be covered in short order by
> at least one member of that population. And, this is exactly what
> happened. The average number of mutations required to cross the
> 16-step gap was only 103 mutations per population.
> Now that is lightening fast evolution. Certainly if real life
> Interestingly enough, Lenski and the other scientists went on to set
> "At the other extreme, 50 populations evolved in an environment where
Yes, evolution does not pop complex systems out of thin air, but
constructs through integration and co-optation of simpler functional
components. Move along, folks, nothing to see here!
> Isn't that just fascinating? When the intermediate stepping stoneHere's a question for you. There were only 5 beneficial functions in
> functions were removed, the neutral gap that was created successfully
> blocked the evolution of the EQU function, which happened *not* to be
> right next door to their starting point. Of course, this is only to
> be expected based on statistical averages that go strongly against the
> notion that very many possible starting points would just happen to be
> very close to an EQU functional sequence in such a vast sequence
that big old sequence space of yours. They are all very standard
Boolean functions: in no way were they specifically designed by Lenski
et. al. to ease the way to into evolving the EQ functions. How come
they were all sufficiently close in sequence space to one another, when
according to you such a thing is so highly improbable?
> Now, isn't this consistent with my predictions? This experiment wasYou are not even close. Lenski et. al. didn't define which *sequences*
> successful because the intelligent designers were capable to defining
> what sequences were "beneficial" for their evolving "organisms." If
> enough sequences are defined as beneficial and they are placed in just
> the right way, with the right number of spaces between them, then
> certainly such a high ratio will result in rapid evolution - as we saw
> here. However, when neutral non-defined gaps are present, they are a
> real problem for evolution. In this case, a gap of just 16 neutral
> mutations effectively blocked the evolution of the EQU function.
were "beneficial". They didn't even design functions to serve
specifically as stepping stones in the evolutionary pathways of EQ.
What they have done is to name some functions of intermediate complexity
that might be beneficial to the organism. They certainly did not tell
their program how to reach these functions, or what the systems
performing these functions might look like, but simply indicated that
there are functions at varying levels of complexity that might be useful
to an organism in its environment. Thus, they have demonstrated exactly
what they set out to: that in evolution, complex functional features are
acquired through co-optation and modification of simpler ones.
talk.origins feedback pages, or Fox News. :)
>> Thus, a randomYes, Sean, because your statistical argument is so-oooo sophisticated
>>walk that restarts each time after the first step (or alternatively, a
>>random walk performed by a large population of sequences, each
>>starting at state ABC...) is expected to explore, on average, 10000
>>states before finding the next beneficial sequence.
> Yes, but you are failing to consider the likelihood that your "winning
>>Now, below, we
> Oh, I can hardly wait!
>>>It also depends
>>OK. Let's take my example, instead, and apply your calculations.
> Ok, I'm glad that you at least realize the size of the state space.
that we simple folk can't keep up...
But, Sean, I don't understand! You were telling me just above that the
>>Since the ratio of beneficial sequences to
> Yes, that is the real question and the answer is very simple - You
distribution doesn't matter at all! I am applying your very rigorous,
unquestionably correct method for computing the average number of states
examined (that should work regardless of distribution and starting
point), and it tells me I should be examining 10^1000/2 states on
average. So why on earth am I examining only 10,000? Is it just
remotely possible that the distribution, and *not* the ratio, might be
what is playing the deciding role?
Once you say "yes", then you and I can talk what an average distribution
>>The answer is simple - the ratio of beneficial states does NOT matter!And have I done so? Though, now that you mention it, it may very well
> Yes it does. You are ignoring the highly unlikely nature of your
be likely, and in fact even necessary, depending on the nature of the
problem we are examining. (And again, please remember that my toy
example has absolutely nothing to do with biological evolution - I am
just pointing out the general inadequacy of your methodology.)
> The ratio of beneficial to non-beneficial in yourI am glad that I possess so much mystique in your mind's eye. :) But,
> hypothetical scenario is absolutely miniscule and yet you still have
> this amazing faith that the starting point will most likely be close
> to the only other "winning" sequence in an absolutely enormous
> sequence space?! Your logic here is truly mysterious and your faith
> is most impressive. I'm sorry, but I just can't get into that boat
> with you. You are simply beyond me.
again, the purpose of my example was to blow a hole in your probability
calculations, rather than to present a workable scenario of evolution.
All I was trying to argue with this example is that your math needs a
lot of work.
>> All that matters is their distribution, and how well a particularAgain, I can present you with examples of real world problems where
>>random walk is suited to explore this distribution.
> Again, you must consider the odds that your "distribution" will be so
these distributions just happen to be this fortuitious. If they
weren't, then Monte-Carlo methods would be useless in solving them.
Remember, these distributions don't arise at random, they follow
necessarily from the properties of the problem. So your arguments about
"averages" don't apply here.
> It basically has to be a set up forYes, but your caclulations are based on the equally unfounded assumption
> success. The deck must be stacked in an extraordinary way in your
> favor in order for your position to be tenable. If such a stacked
> deck happened at your table in Las Vegas you would be asked to leave
> the casino in short order or be arrested for "cheating" by intelligent
> design since such deck stacking only happens via intelligent design.
> Mindless processes cannot stack the deck like this. It is
> statistically impossible - for all practical purposes.
>>(Again, it is a
> Come now Robin - who is trying to stack the deck artificially in their
that the deck is not stacked in any way, shape, or form. (That is, if
the sequences were really distributed evenly in your frozen sequence
space, then your probability calculation would still be off, but not by
too much.) What makes you think that the laws of physics do not stack
the deck sufficiently to make evolution possible? You may feel that
they can't: but in the meantime, you should be striving to find out what
the actual distribution is, rather than assuming it is unstacked. (Not
that this would make your model relevant, but it'll be a small step in
the right direction.)
> In fact, there is an entire theory called theThe fact that the vast majority of mutations are neutral does not imply
> "Neutral Theory of Evolution". Of all mutations that occur in every
> generation in say, humans (around 200 to 300 per generation), the
> large majority of them are completely "neutral" and those few that are
> functional are almost always detrimental. This ratio of beneficial to
> non-beneficial is truly small and gets exponentially smaller with each
> step up the ladder of specified functional complexity. Truly,
> evolution gets into very deep weeds very quickly beyond the lowest
> levels of functional/informational complexity.
that there exists any point where there is no opportunity for a
beneficial mutation. And where such an opportunity presents itself,
evolution will eventually find it, given large enough populations and
>>>It will takeActually, your last paragraph will be approximately true only if all
>>>just over 1,000 seconds - a bit less than 20 minutes on average. But,
>>>what happens if at higher levels of functional complexity the density
>>>of beneficial functions decreases exponentially with each step up the
>>>ladder? The rate of search stays the same, but the junk sequences
>>>increase exponentially and so the time required to find the rarer and
>>>rarer beneficial states also increases exponentially.
>>The above is only true if you use the following search algorithm:
>> 1. Generate a completely random N-character sequence
> Actually the above is also true if you start with a likely starting
your "beneficial" points are uniformly spread out through your sequence
space. Even then, you probability calculation will be off by some
orders of magnitude, since you will actually need to apply combinatorial
forumlas to compute these probabilities correctly. But, I suppose,
it'll be close enough.
OK, Sean. Pause for a second. Do you really believe that evolution
>>For an alphabet of size S, where only k characters are "beneficial"
> Oh really? How do you propose that nature gets around this problem?
works by repeatedly generating random long nucleotide sequences *de
novo*? Yes or no? That is the algorithm I was describing above.
>>The above algorithm isn't even a random walkIf any. Depending on the distribution of states in sequence space, none
>>per se, since random walks make local modifications to the current
>>state, rather than generate entire states anew.
> The random walk I am talking about does indeed make local
> If a new function requires a sequenceBecause the *density* need not be infinitesimal. Locally, the density
> that does not happen to be as fortuitously close to your starting
> sequence as you like to imagine, then you might be in just a bit of a
> pickle. Please though, do explain to me how it is so easy to get from
> your current state, one random walk step at a time, to a new state
> with a new type of function when the density of beneficial sequences
> of the new type of function are extraordinarily infinitesimal?
can be quite high. Again, what exactly, is your argument against the
idea that all the beneficial sequences observed in nature would be
necessarily clustered relatively close together in sequence space, as
required by biochemicastry? Or do you have a compelling argument that
this distribution should be purely random?
>>A random walkOr it would be, if I thought the model you propose was even remotely
>>starting at a given beneficial sequence, and allowing certain
>>transitions from one sequence to another, would require a completely
>>different type of analysis. In the analyses of most such search
>>algorithms, the "ratio" of beneficial sequences would be irrelevant -
>>it is their *distribution* that would determine how well such an
>>algorithm would perform.
> The most likely distribution of beneficial sequences is determined by
realistic. But, here are a few hints for you: 1) the "sequence space"
does not have a fixed dimension; 2) the mutli-dimensional fitness
landscape changes over time, partially as the result of evolutionary
processes. If your statistics are inadequate even for your very simple
model, how can you expect them to be even remotely relevant for a
problem that is much, much more complicated?
> Against all odds the deck was stacked just right soReally, now? I would think that processes operating with predictable
> that we can still believe in evolution. Well, if this were the case
> then it would still be evolution by design. Mindless processes just
> can't stack the deck like you are proposing.
regularity might be able to. Such as, say, the laws of physics.
Remember: "mindless" != "random".
And I am saying average probabilities do not apply when you are
>>My example above demonstrates a problem
> Yes - because you stacked the deck in your favor via deliberate
concerned with determining one particular distribution. And as my
example shows, the distribution is all that matters. Find the
distribution, if you can, and then we'll talk.
>> I could alsoI didn't say all sequences are beneficial, Sean. That *would* be silly.
>>very easily construct an example where the ratio is nearly one, yet a
>>random walk starting at a given beneficial sequence would stall with a
>>very high probability.
> Oh really? You can construct a scenario where all sequences are
I did say that the ratio *approaches* one, but is not quite that.
But, here you are:
Same "sequence space" as before, but now a sequence is "beneficial" if
What does this have to do with evolution? Nothing. But everything to
>>In other words, Sean, your calculations areIf I did wish to model evolution this way, then I would gladly buy this
>>irrelevant for the kind of problem you are trying to analyze.
> Only if you want to bury your head in the sand and force yourself to
> And if you wish to model evolution as a walk between tight clusters of
property off your hands. And then sell it back to you at twice the
price, because it would still be better than the model you propose.
> Until then, this is all I have time for today.Cheers,
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