Fisher’s Fundamental Theorem of Natural Selection: the death sentence for Darwinism

Without going into the deep details, we conventionally assert selection exists if there has been a reduction in diversity in a population.

As a population geneticist who works on quantitative genetics, I can confidently assert that this is rubbish. Firstly, a reduction in diversity can occur due to drift or bottlenecks. Hence, an observation of a reduction in diversity does not equate to an observation of selection. Secondly, selection can also act to increase diversity, for example if selection is disruptive.

Sal, before declaring that Fisher’s Fundamental Theorem destroys Darwinism, I suggest you find out what it actually says.

Yes, directional selection will usually have the effect of reducing additive genetic variance, but there are other forces which increase it (e.g. mutation, migration).

Thanks Sal for a great and thought provoking post!

I have some questions that I am willing to ask, but first I must state that I am no biologist nor do I have much knowledge of biology (I am actually planning to study more biology in depth after finishing college, hopefully I will have time for this), and I believe in ID more-or-less on intuitive bases rather than in-depth scientific consideration of the matter.

That said, I was thinking about your post and I am not sure if I got your point. I cannot see why the neccessary lack of natural selection in the begining of speciation invalidates the role played by it later on.
I thought of an example (not a really good one!) of a car that is moving through a path full of falling rocks. The car (and therefore its engine) has to turn off for a while to let the rock fall then moves until there is another rock, and so on.
Can we say that because the car engine had to stop many times through the walk that it actually played no role in moving the car through?

Sal -

@2: OK, but, as I have pointed out, it is not even necessary.

@5: There will be a reduction in the frequency of genotypes after selection, but then there will be mating and recombination, which (unless there is assortative mating) will regenerate these genotypes.

Do you actually know what And Fisher’s Fundamental Theorem’s states? It certainly does not say that diversity is reduced.

The mean fitness increases (i.e. like the mean interest rate increases in my example form 7.5% asymptotically to 10%) in relation to the genic variance in fitness.

That would be marked incorrect, but not totally. Firstly, “in relation to” is vague. Are you a field biologist? Secondly, it’s not genic fitness that’s important, but additive genetic fitness.

For the purpose of the discussions here you got one thing right. Nothing is said about a reduction in the variance or diversity. IOW the whole post is based on a total mis-understanding of the theorem.

As to his initial statement:

“Secondly, selection can also act to increase diversity, for example if selection is disruptive.”

Bob O’H adds this clarification:

“There will be a reduction in the frequency of genotypes after selection, but then there will be mating and recombination, which (unless there is assortative mating) will regenerate these genotypes.”

————

Thus we can see that the first statement was indeed an inaccurate description of the particular process in mind.

Notice that recombination is not a selective event. It may indeed result in diversity, but it did not result from natural selection. If what Bob is saying is that selection (by eliminating some genotype) makes way for others, then that is probably true as far as it goes (and indeed, may be so obvious as to avoid the need for significant discussion). However, selection does not itself produce the new “others.”

I think this is an example of ascribing powers to selection that properly should be ascribed to other events (in this case recombination).

Regardless of the nuances of Fisher’s theorem, are we actually suggesting that selection is not, by definition, a culling process? Any way you cut it, it seems difficult to sustain the idea that selection produces anything. That is certainly not how Darwin used the term, and it is not the typical understanding today.

[...] UD on fundamental theorem of NS the uncritical acceptance of natural selection as an explanatory force for all aspects of biodiversity (without any direct evidence) is not much different than invoking an intelligent designer [...]

Seems to me, since future conditions are unknown and may favor either this or that, the most fit species is the one that is most diversified. Any population culled for fitness to a particular set of circumstances (by natural selection or whatever) must therefore be less diverse and less fit to face a foreboding and indeterminate future.

A portfolio maximized for short-term gains is not likely to be a portfolio suited to weather the vicissitudes of an unknown future economy.

Is this this what you’re trying to say, Sal?

Good analogy, Gerry.

In theory, natural selection is always interested in what provides the greatest gain. However, given that natural selection only acts in the present (and only with one particular living organism at a time), it is more accurate to say that it is only interested in immediate gain. As you point out, this could well be very different from what is best in the long run (this is another example, really, of the foresight problem irreducible complexity attacks).

Frankly, natural selection is only interested in culling the organisms that don’t make the grade today. Here. Right now. It has no foresight; creates nothing; produces nothing; generates nothing. It only culls.

Thus, natural selection, by definition, can only eliminate, not create. Yet the irony is that people often confuse the issue and think that natural selection is somehow a driving force for creating new kinds of things.

The concept of natural selection may have some (exceedingly limited, in my view) value in terms of describing the survival of the fittest, but has absolutely nothing to say about the arrival of the fittest.

I think Sal’s post is interesting because it highlights that not only is natural selection unable to create anything, but also that natural selection — the culling force that it is — often needs to be suspended in order for any real creative work to take place. I’ll have to think about Sal’s point a bit more, but I think this is a very significant additional nuance.

Greetings, Sal:

Throughout this discussion, I think it is very important to keep in mind that Darwin’s algorithm (Daniel Dennett’s term) for natural selection has three prerequisites:

1) variety (that is, substantive differences between phenotypes in populations);

2) heredity (that is, vertical inheritance of phenotypic characters); and

3) fecundity (that is, reproduction that can, but need not necessarily, exceed replacement).

Given these prerequisites, the following outcome is virtually inevitable:

4) unequal non-random survival and reproduction (i.e. proliferation of certain phenotypes relative to others).

As I have pointed out repeatedly, the key to understanding evolution is to focus on the “engines of variation”; that is, those mechanisms (there are literally hundreds, perhaps thousands) by which new phenotypic characters are produced. These characters, produced by the various mechanisms that I list at my blog:
(http://evolutionlist.blogspot.com/2007/10/rm-ns-creationist-and-id-strawman.html)

provide the raw material upon which natural selection, sexual selection, genetic drift, meiotic drive, and all other sources of linkage disequilibrium operate.

Fisher’s Fundamental Theorem, concisely stated, says that the rate of natural selection is a direct function of the amount of genetic variance in a population. That is, the greater the variation, the more raw material natural selection has to work on, and therefore the greater the degree of genetic change over time (note the emphasis on genetic change; as I have already pointed out in other threads, this is a serious limitation of Fisher’s approach, a limitation that also applies to the “modern evolutionary synthesis” as it existed in 1959).

But, according to Fisher’s mathematical models, natural selection can only result in a decrease in overall genetic variance. This is because the effect of natural selection is to remove some variants while preserving others. The variants that are removed represent a decrease in genetic variance, hence Sal’s contention is essentially correct.

While it is true that disruptive selection (also called “diversifying selection”) has the effect of producing two (or more) peaks in mean character states, rather than one (as in the case of both directional and stabilizing selection), it is not true that disruptive selection produces a net increase in genetic variation by itself. Only if the “engines of variation” produce the requisite new genetic material to allow for the shift in mean character state(s) will this happen.

Ergo, it is not natural selection that “produces” new variation at all. On the contrary, natural selection merely channels the immense variety produced by the “engines of variation” into particular adaptive zones. Those zones exist, not because of selection, but because of the tremendous capacity for producing new variations that exist in the sources of variation that I have listed on my blog.

So, in the interests of fair play, I hereby suggest to the ID supporters reading this post that opposing natural selection is a pointless exercise. Current evolutionary theory has already moved far beyond the limited theoretical models that formed the basis for the “modern evolutionary synthesis”. You are literally attacking a dead horse.

Rather, the real focus of everyone’s attention should be on the “engines of variation”. That is, on those mechanisms by which variation in phenotypic characters is produced. If I were an ID supporter (I’m not, BTW, but I have good friends who are), I would strongly recommend investigating the dynamics of the various mechanisms by which phenotypic variation is produced (it is maintained, of course, by selection and drift, but that’s not the point).

If the processes by which variation are produced can be shown convincingly to demonstrate foresight (i.e. that they produce characters that, when produced, are already necessarily adaptive), then ID may be a reasonable and useful component of any hypothesis for the origin and proliferation of adaptive characters in populations.

If, however, the processes by which variation are produced can be shown convincingly to not demonstrate foresight (i.e. that they produce characters that, when produced, are not necessarily immediately adaptive, but become so following a change in environmental conditions), then ID is unnecessary as an hypothesis for the origin and proliferation of adaptive characters in populations.

And please: in the interests of intellectual integrity, please do not quote parts of the foregoing analysis out of context. In particular, it would be grossly intellectually dishonest to characterize the foregoing as asserting only that “ID may be a reasonable and useful component of any hypothesis for the origin and proliferation of adaptive characters in populations”, without also including the second half of that assertion: that without a convincing demonstration that new variations are immediately adaptive, “ID is unnecessary as an hypothesis for the origin and proliferation of adaptive characters in populations.”

Thank you for a very stimulating discussion!

Eric @ 10 - Strictly you’re correct, for this case. But we usually think over the full life cycle, i.e. from one developmental stage to the same one in the next generation. Otherwise it gets too complicated.

Sal @ 9 -

Unless the individual groups have identical absolute growth values, I don’t see that there wil be any thing but a reduction in the variance of the growth rates. Is that correct, Bob.

No it isn’t. Think of two genotypes, with the fitter one being rarer.

Sal @ 11 -

Let the reader understand, Bob accuses me of not fundamentally understanding the theorem. I’ve laid out the case in terms of an interest rate bearing portfolio. He can at least argue that I don’t understand Fisher’s theorem in terms of the math in this context.

You totallyu mis-represented FFT in your original post - put simply, it does not say that selection reduces diversity. Either you didn’t understand the theorem, or you did, and you were being dishonest. I’d rather go for the former theory: I’m an optimist and believe most people are honest. Now if you want to argue me out of that position….

Incidentally, the statement that natural selection doesn’t create is hardly controversial. Declaring it defeats evolution is like declaring that it is impossible for a car to have been driven more than a few kilometers, because after that its petrol would have run out.

I meant eventually. For example

But FFT is only about what will happen over a short period of time. So this would be an irrelevant attempt to shift goalposts.

One thing I like about posts like these is that it does something that, frankly, the public world needs more of - showing that even among non-IDists, there’s quite a lot of discussion about the mechanisms of evolution, just how much natural selection factors into the process, etc.

Even as someone who leans more towards TE than ID, I love to read about these divisions, innovations, models, etc. It’s my view that ID will have reached a point of mainstream acceptance when it begins to provide predictive, design-based models of evolutionary development - how to promote the introduction and direction of traits in a given environment over a long period of time.

It’s a tall order, but I still think the day will come.

Good post and discussion, Sal, et al.

Everyone, please note that Allen MacNeill has a fair and relevant comment at #15. Approval for this comment would have occurred after subsequent comments were posted and it ought not be lost to readers.

Sal - regardless of what we call Fisher’s theorem, it is what it is.

As for ReMine, he’s wrong on point 1, it still holds if growth rates change, but the changing growth rates have to be accounted for. As I’ve already pointed out, FFT is a short-term theorem.

Crow doesn’t mis-handle the theorem. If you read what you quoted, you’ll see that he puts qualifiers in there. Your comment after the quote is fully accounted for by the “as long as there is additive variance for this trait” qualification. I guess you’re too busy learning new skills to have remembered you Introductory Quotemining lessons. That qualification should have been changed to an ellipsis.

You comparison of mutation and selection as forces in evolution is comparing apples and oranges. Mutation is a force that adds variation, and selection is one of the many forces that molds the variation. Both are important, but they’re important for different parts of the process.

Sal you don’t seem to be responding to what I write any more, so I’ll just point out that you’re also ignoring the possibility that a mutant increases fitness.

Sal wrote (in #24):

“…if mutants keep popping up in the population that are more reproductively successful than the existing population, growth rates will grow indefinitely till the species is practically an epidemic.”

However, both sides in this debate agree that deleterious mutations greatly outnumber beneficial ones. Hence, only those relatively rare mutations that have a positive effect on reproductive success will increase in relative frequency in populations.

“Reproductive success is not necessarily to be equated with more complex organisms. We know that some species like blind cave fish are more reproductively effective by becoming more simple”

Indeed, as Stephen J. Gould often pointed out, assuming that selection necessarily results in increased complexity is a fallacy. This argument is analogous to his argument against “progress” in evolution. As a good friend of mine (who is also a herpetologist) likes to assert, “It’s all been downhill since the Mesozoic.”

“I do not think it can be demonstrated that natural selection naturally leads to the emergence of complexity. I cited the Fundamental Theorem to suggest that Natural Selection might actually have to be disengaged for evolution to move forward.

This is an absolutely crucial insight. Indeed, if Fisher’s Fundamental Theorem has any bearing on reality (and I believe it does), then really rapid variation in populations can only happen when selection is indeed relaxed. Under what conditions does this happen? There are two that I can think of:

1) Domestication, in which breeders deliberately keep alive (and help with the reproduction of) individuals that would be less “fit” under natural conditions. Darwin pointed out repeated examples (among pigeons and other domesticated animals and plants) in which domestication resulted in dramatically increased variation, including variants that could not possibly survive under natural conditions (this is why variation is typically much less under natural conditions than under domestication).

2) Adaptive radiation following mass (or at least multiple) extinctions. The removal from a biotic community of a relatively large number of closely adapted species frees the survivors to radiate into the “empty niches” vacated by the newly extinct species. This is because the survivors have much less competition. In other words, they are in the same position as domesticated organisms; increased relative fitness as the result of decreased selection against variants.

“How can we statistically say how much or how little natural selection occurs. Kimura and others suggest a bean count — namely they state that X Percent of the genome was subject to selection.”

Here, once again, we have a problem. This formulation of “fitness” is focused on the genome, rather than on differential survival and reproduction of individuals with particular phenotypes. This excessive focus on gene- and genome-level selection is precisely the problem with the “modern evolutionary synthesis” and is the reason that new theories of variation and selection (such as those described by Jablonka and Lamb (in Evolution in Four Dimensions) and Margulis and Sagan (in Acquiring Genomes) are currently on the cutting edge of evolutionary theory. That is, they focus on phenotypic changes at the level of individuals (and groups), rather than at genotypic changes at the level of genes (i.e. what Dawkins called “selfish genes”).

“This bean count was based on the work of Haldane on the amount of population resources that would be needed to evolve each independent trait. The surprising conclusion was tha 99% or more of the genome could not be policed by natural selection. There are simply not enough population resources.”

Which is precisely why the new focus on phenotypes has revolutionized evolutionary theory. This new focus is relatively immune to both Haldane’s dilemma and to Kimura and Ohta’s theories of neutral and nearly neutral molecular evolution. In other words, focusing on phenotypes recognizes what Waddington recognized almost a half century ago: that changes in genotypes are only weakly correlated with changes in phenotypes.

“It seems to me the main driving force of evolution (assuming one is not a creationist), would have to be mutation 99% of the time. Selection can only influence 1% of evolution. Sanford’s chapter on Interference Selection seemed quite convincing to me.”

I would agree with you if you changed the word “mutation” to “variation”. As I have repeatedly pointed out, the term “mutation” captures only a tiny fraction of the full range of variation produced by the “engines of variation” listed at my blog:

http://evolutionlist.blogspot......awman.html

The vast majority of these mechanisms of variation are not “mutations” in the classical genetic sense, but do indeed produce tremendous heritable variation between phenotypes in populations. Also, most of these mechanisms of variation are not “random” in the classical genetic sense, but rather are “canalized” (to use Waddington’s term in a different context). They are, in other words, “guided” into particular adaptive zones as the result of a combination of environmental determinism and historical contingency.

Sal you don’t seem to be responding to what I write any more

Which I thought was very gracious of Sal, given #25.

DaveScot (31):

Evidently you think the principle of parsimony in scientific explanations is sound. I wish everyone here would agree to that.

I think I can hear Sir Occam sharpening his razor even now.

“Occam’s Razor” is a metaphor for the assumption, widely accepted by scientists, that simpler explanations are preferable to more complicated ones. Allen’s list of empirically observed sources of variation is not an explanation, and Occam’s Razor is not applicable.

Allen– That is, they focus on phenotypic changes at the level of individuals (and groups), rather than at genotypic changes at the level of genes (i.e. what Dawkins called “selfish genes”).

Can something have wings if it has not been coded for them in the genome?

I would like to emphasize Allen’s comment #15 where he said…

“If I were an ID supporter…I would strongly recommend investigating the dynamics of the various mechanisms by which phenotypic variation is produced (it is maintained, of course, by selection and drift, but that’s not the point).

If the processes by which variation are produced can be shown convincingly to demonstrate foresight (i.e. that they produce characters that, when produced, are already necessarily adaptive), then ID may be a reasonable and useful component of any hypothesis for the origin and proliferation of adaptive characters in populations.”

While I am a critic of the ID Movement, I support the potential outside-the-box-thinking ID Science offers. Which is one of the reasons I put together my own ID Hypothesis (involves interconnected quantum effects).

What clearly fell out of my effort was that supporting evidence would be of a nature similar to Front Loading and/or a demonstration foresight.

Looking for demonstrations of foresight would seem to be a natural for people truly interested to promoting the scientific potential of ID.

I would like to thank everybody who is participating in this discussion :).

Allen_MacNeill

In other words, focusing on phenotypes recognizes what Waddington recognized almost a half century ago: that changes in genotypes are only weakly correlated with changes in phenotypes.

This is interesting, and makes me willing to ask this:
if changes in genotypes are only weakly correlated with changes in phenotypes, how are phenotypes produced in the first place?
This implies that there are other sources of information, sources that we do not know of, or at least do not understand to a satisfactory degree that produce the phenotype. If this is true it leads to another question, if we do not know how the organism is put together, how can we say anything about its origin and evolution?

Sal @ 30 -

so I’ll just point out that you’re also ignoring the possibility that a mutant increases fitness.

I did not ignore it. I wrote in #24:
I had missed that, but then you wrote this in post 26:

“as long as there is additive variance for this trait”

One could of course increase variance in fitness by putting in underperformers, but that wouldn’t cause indefinite increase in fitness, except via creative redifinitions of what it means to be constantly improving.
Which appears to ignore it too.

Aagh! There’s a blockquote missing: The “One could…” paragraph should be in blockquotes, and the final sentence is mine.

“[Francis] Crick challenged me with the statement that nothing can be said about evolution until we understand how organisms are put together.” (Geneticist Gabriel Dover)

Quote from: http://www.uncommondescent.com.....5B1%5D.pdf

Looks like Francis Crick agrees with me :D.

I hope that Prof. MacNeill will help me in this question.

Indeed, if Fisher’s Fundamental Theorem has any bearing on reality (and I believe it does), then really rapid variation in populations can only happen when selection is indeed relaxed.

No. A change in the environment can change the adaptive landscape, so that traits which were previously under only weak selection can become more strongly correlated with fitness, and hence change rapidly.

Which is precisely why the new focus on phenotypes has revolutionized evolutionary theory. This new focus is relatively immune to both Haldane’s dilemma and to Kimura and Ohta’s theories of neutral and nearly neutral molecular evolution.

I guess you haven’t heard Nunney talk about Haldane’s dilemma recently, have you? He showed that, in fact, you do get the same “problem”. He compared a model of phenotypic evolution in a changing environment (it might even have been one of Mike Lynch’s!) with his model of Haldane’s dilemma from the Extinction Thresholds meeting (it appeared in Annales Zoologici Fennici later. ReMine knows the reference. :-)), and found they were giving similar predictions.

As for the neutral theory, we have to deal with that in evolutionary quantitative genetics as well (i.e. the area of evolutionary biology where FFT fits in, and which concentrates on phenotypic changes and their response to evolution). I’ve been having to deal with the neutral theory when looking at population divergence, because populations drift, and so too do their phenotypes.

H’mm:

For what it’s worth, lurker X again:

__________________

Salvador: “If we presume that all life descended from a single species and diversified, how can we logically argue that diversification happens through a process of removing diversification! Some may invoke things like allopatric (geographic) speciation or sympatric speciation where mutant forms are isolated somehow from the parent population, but is this not essentially a means of protecting new species from the culling effects of natural selection? It’s surprising the illogic of Darwinian claims has not been readily apparent!”

X: But the illogic of Darwinian claims has been readily apparent — and all the way back to 1859! One of the chief criticisms of the original formulation of “Darwinism” is that “natural selection” destroys, but does not create, diversity; or, at best (i.e. with optimistic assumptions), relatively preserves some status quo.

When Mendel’s work was “rediscovered” in 1900, the criticism of “Darwinism” again pointed out this problem. But Darwin’s Disciples, even to this day, as with the Master Himself, ignore telling criticisms … and then later “refute” them by pointing that they are old criticisms.

And, more recently . . . [the matter, e.g on Chromosome 2] involves the recognition that ‘modern evolutionary theorists’ can’t naturalistically get the proto-human species (with the human-like 2n=46 karyotype) from the hypothetical-parent species (with the ape-like 2n=48 karyotype) — for there is no naturalistic “means of protecting [the] new [proto-]species from the culling effects of natural selection.”

Salvador: “But competition is at the heart of natural selection. Thus I’ve demonstrated that in order for natural selection work, we have to prevent natural selection from working!”

X: Exactly! This is why ‘modern evolutionary theory’ has *always* had to rely upon the Just-So Story. This is why ‘modern evolutionary theorists’ always place great stock in plausibility (i.e. if one first assumes ‘modern evolutionary theory,’ then of course the Just-So Stories become plausible!) This is why ‘modern evolutionary theorists’ so often try to denigrate criticism as mere “argument from incredulity,” as though that were an effective refutation of the criticism. (Because, of course, credulity is the preferred intellectual posture of all serious and critical thinkers!)
__________________

What do you think gentlefolks?

GEM of TKI

There is the central issue lacking here of “backwards extrapolation” in the proper understanding of the dichotomy between the two theories (ID/DE).

Darwinian evolution does indeed extrapolate backwards. After all, what more can anyone do? History is inextricable from origins science. ID however always gets falsely criticized for “calculating probabilities backwards” as if it is illegal or something- but that is all that Darwinism ever does with its mechanisms- that is it makes speculative statements about history- after the fact- and ones that usually cant even be verified. Michael Behe says you cant have a mouse trap without all of its parts. They then take the liberty to “make up” a “highly improbable” and “totally backward speculative” explanation that barely even works and may not even work all — and so probably never even happened. Then, ID theorists say “wait a minute here, do you have any idea how unlikely that explanation of yours really is?” Then the DE’s scream (in the so called name of good science) “You cant calculate probabilities backwards!” Why not?

The only goal of this, obviously, is to try and construct an illogical and rigged view of science (and history) that gives their theory not only a 100% monopoly on “all of history” but makes methodological materialism “the only possible explanation by default” a priori. Yet, all the while they know that their entire explanation is nothing but a backwards historical extrapolation based theory of the gaps itself, built off of an illogical and unjustified philosophical precommitment to the methadological materialistic scienfific and philosopgical platform. Obviously, hypocrisy is not a concern for their theory. They aren’t mad about calculating probability backwards because it’s actually somehow unsceintific. No, they’re mad because its just plain unfair.

Obviously the probabilistic TRUTH about history is unfair and to be ignored because it doesn’t accord with their theory is nonsense. No one ever said that hisotry is fair. All theories are not equal.

Despite their theory consisting of stories that “they make up” (and even after the fact), they still cant (should say won’t) allow people to calculate the likelihood of their stories and explanations being true. Why, because nothing they can even “fictionally invent” can justify and constitute rationality and reason. Yet it is to be accepted and held beyond mathematical reproach.

The theory of neo-Darwinian evolution is therefore obviously irrational and unreasonable.

Math has revealed itself as materialistic evolution’s great enemy and for good reason too, because math is logical and when correctly constructed useing good historical data- refuses the lie for a broken theory.

“Well, I guess I’ll agree with you that Allen’s 47 ways by which heritable phenotypic modification can occur is not an explanation. It’s a laundry list. I’d make the list 48 items long by adding intelligent agency to the list of mechanisms and then with the addition of that start applying Occam’s Razor to the other 47, trimming away those which are made unnecessary by the mechanism of intelligent agency.” — DaveScot

Exactly. And that’s what almost all ordinary people do, intuitively, and in a matter of seconds, with this whole issue. “Looky yonder, Jeb. D’ya think that there just a-happened, all by hisself?” “Uh, lemme chaw on that a bit Roy. Nope.” Only a truly edjikated man can so easily deny the obvious.