# Fisher’s proof of Darwinian evolution has been flipped?

December 27, 2017 | Posted by News under Darwinism, Intelligent Design, Mathematics |

That’s what they say. From the paper by Bill Basener and John Sanford on Fisher’s Fundamental Theorem of Natural Selection, published in The Journal of Mathematical Biology: Abstract:

The mutation–selection process is the most fundamental mechanism of evolution. In 1935, R. A. Fisher proved his fundamental theorem of natural selection, providing a model in which the rate of change of mean fitness is equal to the genetic variance of a species. Fisher did not include mutations in his model, but believed that mutations would provide a continual supply of variance resulting in perpetual increase in mean fitness, thus providing a foundation for neo-Darwinian theory. In this paper we re-examine Fisher’s Theorem, showing that because it disregards mutations, and because it is invalid beyond one instant in time, it has limited biological relevance. We build a differential equations model from Fisher’s first principles with mutations added, and prove a revised theorem showing the rate of change in mean fitness is equal to genetic variance plus a mutational effects term. We refer to our revised theorem as the fundamental theorem of natural selection with mutations. Our expanded theorem, and our associated analyses (analytic computation, numerical simulation, and visualization), provide a clearer understanding of the mutation–selection process, and allow application of biologically realistic parameters such as mutational effects. The expanded theorem has biological implications significantly different from what Fisher had envisioned. (public access) More.

From Creation-Evolution Headlines: “A new paper corrects errors in Fisher’s Theorem, a mathematical “proof” of Darwinism. Rather than supporting evolution, the corrected theorem inverts it.”

…

Remarkably, Fisher’s theorem by itself illustrates a self-limiting process – once all the bad alleles are eliminated, and once all the individuals carry only good alleles, then there is nothing left to select, and so selective progress must stop. The end result is that the population improves slightly and then becomes locked in stasis (no further change). It is astounding that Fisher’s Theorem does not explicitly address this profound problem! Newly arising mutations are not even part of Fisher’s mathematical formulation. Instead, Fisher simply added an informal corollary (which was never proven), which involved extrapolation from his simple proof. He assumed that a continuous flow of new mutations would continuously replenish the population’s genetic variability, thereby allowing continuous and unlimited fitness increase.

The authors of the new paper realized that one of Fisher’s pivotal assumptions was clearly false, and in fact was falsified many decades ago. In his informal corollary, Fisher essentially assumed that new mutations arose with a nearly normal distribution – with an equal proportion of good and bad mutations (so mutations would have a net fitness effect of zero). We now know that the vast majority of mutations in the functional genome are harmful, and that beneficial mutations are vanishingly rare. The simple fact that Fisher’s premise was wrong, falsifies Fisher’s corollary. Without Fisher’s corollary – Fisher’s Theorem proves only that selection improves a population’s fitness until selection exhausts the initial genetic variation, at which point selective progress ceases. Apart from his corollary, Fisher’s Theorem only shows that within an initial population with variant genetic alleles, there is limited selective progress followed by terminal stasis. More.

*See also:* Gambler’s ruin is Darwin’s ruin

### 19 Responses to *Fisher’s proof of Darwinian evolution has been flipped?*

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A word to the wise: “Mutation Driven Evolution” (Nei, 2013) is what is now in vogue. “Selectionism” is out. So, of coursse, they will “discover” a NEW “fundamental theorem of natural selection” that includes a “mutation” term.

Why didn’t they notice this before? Because they weren’t looking.

Darwinians always find what they’re looking for; and, if needed, they invent it.

(Darwin looked forward to new, young biologists who had rich imaginations. Nothing much has changed.)

PaV – Actually, we we have already looked at mutation. It’s a shame Basener is either unaware of the Price equation, or couldn’t see how to apply it to this situation (and also didn’t have the google-foo to find the literature).

Yes, Bob, we have looked at mutations and from what we know there is no way mutations produced the diversity of life starting from populations of prokaryotes or archaea.

The “selection” part is actually the elimination of the less fit over time. There isn’t any actual selection going on and there is a big difference between selection and elimination.

From “What Evolution Is” page 117:

Page 118:

Bob O’H:

Price’s equation “partitions” traits through time. In the following paper, the author says that if you substitute “fitness”=’w’, for the ‘trait’=Phi, then Price’s equation gives you Fisher’s equation.

Here’s a overview of “fundamental theorems. Notice p. 346 where theorems are compared.

This is from the article cited above, and represents, IMO, the gist of the difficulty, and the reason for ‘adding’ mutations:

[N.B. Darwinians are always “surprised.”]So, Basener concludes:

Masatoshi Nei must be pleased.

I guess your argument is this: “No, Darwinians aren’t looking for something now. They’ve known about it for a long time. Just look at Price’s equation.”

I’m afraid it only serves to underline the point I made: that is, now that an emphasis is placed on the primacy of “mutations” driving “evolution”—now, and only now, and not 40 years ago when they had the chance when Price was revisiting it—are the weaknesses of Fisher’s theorem finally being laid bare.

PaV – First, evolutionary biologists were already well aware that FFT implied a reduction in genetic variance. So whilst it might be surprising to some people, they would be people who haven’t studied the subject. It’s also why several people have looked at the effects of mutation, such as in the paper I linked to. This isn’t something new – if you had looked at the link, you would see that it was published over a quarter of a century ago.

Bob O’H:

Yes, I did look at the paper, which is on the Price Equation.

Since when did Darwinists not have an interest in mutations? That’s not what’s at issue. Rather, the 1970 paper you linked to was well before Neutral Theory took over, and well before Nei’s fully developed position on evolution.

In a certain sense, this might just be a development in thought, similar to what we find in other disciplines; but, as I pointed out in my last post, the deficiencies in Fisher’s Theorem were rather obvious from the first, yet nothing was said until evolutionary biologists were ready to move on.

If you look at my first post, you will see that I was actually saying that the paper in the OP was not saying anything so surprising, that is was a shift now in how evolution is viewed.

The problem I was trying to point out, however, was that evolutionary theory is not self-correcting. It’s like a “shifting balance” theory. 🙂

Bob O’H:

As to “surprises,” the OP paper points out–as I ‘bolded’ in my penultimate post–that the surprise is on the part of those who have ‘studied’ FFT.

PaV @ 7 – the paper was from 1990, not 1970. Try again.

PaV @ 7 – they said that this may be surprising to some unspecified people. Honestly, anyone who works on evolutionary quantitative genetics would know (or see very quickly) that directional selection reduces genetic variance.

Holy cow- hold the phone! Bob and I are in agreement-

Yes it does

Sorry, ET. I’ll try not to make a habit of it.

Ok Bob, but that means you will be wrong most of the time. 😉 😛

Bob O’H:

The 1990 paper you linked to was written ‘before the Neutral Theory took over,’ and not “

wellbefore.” I stand (little) corrected. [The format of the linked paper looked a lot older than 1990. Price’s paper was from 1970]When I first looked into FFT 10 years ago, I was shocked at its formulation. It made little sense. Who could believe that genetic variance (and with it, fitness) could rise without limit?

And its reliance on differential forms of birth and death rates made it seem completely disconnected from genetics. That the FFT can, and is, used in statistical mechanics should tell you all you need to know.

But, no one, other than the author of the paper cited in the OP makes a point of the FFT’s patent contradiction. Yet, in so many minds, this remains an “icon of population genetics.” [Jonathan Wells should write a new book on this.] Why isn’t this corrected once for all? This is the reason that Wells wrote,

Zombie Science: in evolutionary biology, errors are never corrected.Since you wrote of “directional selection,” I presume you disagree with Nei’s take on evolution since in it he downplays the role of NS. But the point is that only in an atmosphere where the power of NS is called into question without push-back, does a criticism of like Basener’s dare to show its face. It’s this ‘consensus’ brand of science that taints the science of our day.

The only bright spot is that it reveals that character matters more than logical prowess. Then, maybe, universities can go back to being seminaries.

Just reading what News provides here, without any other googling, how the hell is this a refutation of evolutionary biology? If that was what News was attempting.

Well, if you thought that FFT said anything about changes in genetic variance, then no wonder you were shocked. It doesn’t: it only says something about the short-term change in the mean fitness.

That would be true if demographic rates were not affected by genetics, which would be a bold claim.

I’m sorry, I don’t get this at all. What should it tell us?

You’re over-extending. I’m sure even Nei would agree with what I wrote. I wrote nothing about whether directional selection is common or rare.

Bob O’H:

You averred:

From Wikipedia:

Bob O’H:

It is a “bold claim” to think that we know the correlation between genetics and demographics, as we see in the inability to produce a non-tautological definition of “fitness”; however, this hasn’t stopped generations of geneticists from making such bold claims.

******

As to the use of FFT in statistical mechanics, let’s remember that SM is applied to gases, and that gases are inanimate objects. I think something is wrong when your description of progressing forms of life is also applicable to gas molecules.

PaV – Sorry, I should have been clearer: FFT shows that additive genetic variance determines the rate of directional selection. But it does not say how genetic variance changes.

I see you’ve decided not to defend your suggestion that demographics is completely disconnected from genetics.

Bob O’H:

Who in their right mind would think that genetics “is completely disconnected” from demographics?

I didn’t say that the FFT “is completely disconnected;” rather, I said that his use of birth and death rates made it “seem completely disconnected.” I could have chosen to say the former, rather than the latter; but, I chose not to.

So, please, don’t put words into my mouth.

Nevertheless, you have to admit that it seems strange to tie genetics into birth and death: as my brother would joke, “Don’t eat pizza; it could kill you! I had a friend die of it. He parked across the street from his favorite pizza parlor one day, and when he crossed the street, he got hit by a car! Killed him instantly!”

Correlations can be very suspect here. Heavens, just look at “global warming” and how it’s killing off polar bears.

I think Sewell Wrights’ approach was more sensible and real. And, of course, he was a breeder, grounded in what he saw in nature; and not just a pure theorist. His starting point was better.

Studying Nei’s book, it becomes clear that the only way to write differential equations in population genetics is through the use of ‘fitness,’ even if you can’t accurately describe it. Hence, if you’re searching for such DEs, then you’re going to find some way of using “differential” births,” or something along this line.

This neither justifies the thinking, nor the equations.

Fitness tells us nothing. Who survives? The fittest. Who are the fittest? The ones who survive. Nothing predictive. Nothing grounded in a deeper reality. No distinctions; everything is lumped together under “fitness.”

Genetics, and population genetics, and paleontology are all marked by STASIS. Change is only found at the edges; and we call this “microevolution.” (Adaption is just as good a word.) And beyond this, troubles begin.

PaV – the genetics is connected to birth and death rates. Read Fisher’s book where he lays it all out. The details can get a bit tricky, but we can use path analysis to get a handle on the causal pathways.

If you want real-world examples, how about genetic diseases? For example, haemophilia. Is it so strange to say that (a) this is an inherited trait (i.e. it is genetic), and (b) people with the disorder die at a higher rate than people without it?