The fundamental problems with Fisher's not-so-fundamental Fundamental Theorem of Natural Selection

Agreed, but I don’t think you need me to reflect what you say since I think you articulate your case well, especially this:

Any model has assumptions and idealizations/abstractions that limit its domain of applicability. For example, it would be wrong to try to draw conclusions about maximum fitness with a model where the role of the niche is purposely ignored.

Drawing conclusion the wrong way happens a lot, even by professionals like Richard Dawkins who claimed Fisher’s theorem was biology’s central theorem. I doubt Dawkins even understood theorem because it’s rather apparent hardly any one even knew what Fisher meant in the first place!

I was using Fisher’s theorem to illustrate the state of affairs of how wrong conclusions are arrived at because of unwitting equivocation.

it would be wrong to try to draw conclusions about maximum fitness with a model where the role of the niche is purposely ignored.

This can be simply remedied by saying “growth capacity” rather than saying “fitness”! Or “mean of the growth capacity of alleles” instead of “adaptedness.” Giving the right label goes a long way in clearing up the mess, because terms can be stated without so many qualifications and caveats that will usually be ignored anyway.

A central theorom is still an idealization and abstraction that is not expected to accurately model reality 100%. As another example, the ideal gas laws don’t accurately describe any gas. It is an approximation. You will find many physicists who think Newton’s work was some of the most important in the history of physics, but they will happily replace Newton’s equations with Einstein’s in certain situations. Having great respect for the work of Fisher in no way indicates that his models are 100% accurate or 100% applicable in modern biology.

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I don’t believe Fisher’s theorem is that central! Even Joe Felsenstein said it’s “not so fundamental”! It’s an interesting relation, but as far as utility and its consequences for biology, it’s mostly a nothing burger. And Ewens and Lessard echoed the same sentiments in 2015.

The laws and principles you cited in physics are actually used to solve problems in engineering and analysis of physical systems. The same cannot be said of Fisher’s theorem.

I don’t have any candidates for what would qualify as the central axiom of biology except maybe Virchow, which was quoted in Alberts essential cell biology book:

“Where a cell arises, there must be a previous cell, just as animals can only arise from animals and plants from plants.”

Alberts, Bruce. Essential Cell Biology (Fifth Edition) (p. 609). W. W. Norton & Company. Kindle Edition.

Now there’s a nice creationist sounding axiom! Well done Virchow!

This is Sal’s pedestrian way of stating Virchow’s principle:

It takes life to make life. It takes an animal to make an animal, a plant to make a plant.

Fisher’s theorem is mostly forgotten, and not really used except as a myth. Virchow’s principle holds on many levels to this day.

Not that I’m endorsing the view point of Queller 2017, but he attributed the central theorem of evolution to an equation stated by the Creationist Price:

fundamental_theorems_colored

from:

https://openscholarship.wustl.edu/cgi/viewcontent.cgi?article=1131&context=bio_facpubs

Since when was George Price a creationist?

The “Fundamental Theorem of Adaptation” shown in the diagram you copy from Queller says that it is “Fisher’s fundamental theorem”. But it isn’t quite – it’s a discrete-generations version. See that \bar{w} in the denominator? Not there in the FTNS. See that \Delta \bar{w}? That is change in a discrete generation, rather than the \frac{d\bar{w}}{dt} you’d get if it were a continuous time model such as Fisher uses.

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Populations do not need new mutations to evolve. Selection also acts on existing variation, which is about a million-fold more prevalent than new mutations.

@Jordan, here’s another example of how this false assumption pervades ID creationism. @stcordova is assuming that populations are composed of genetically identical individuals.

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After his conversion to Christianity, and before his suicide.

Unfortunately there is another George Price, George Macready Price, consider the founder of modern YEC before Whitcomb and Morris.

The Price in question is George R. Price, friend of WD Hamilton and John Maynard Smith.

This is one account that doesn’t mention Price’s creationism, but his conversion to Christianity and Suicide.

The true story of George Price, the scientist who discovered the equation for altruism and gave himself away

The account of his conversion to creationism, I can no longer find a direct secular source on the web, though supposedly there is a book that describes it. From the creationist website that mentions the book said:

Spinning Webs of Belief: Accounting for George Price – CEH

In Science today,1 Steven Frank (UC Irvine) published a review of Oren Harman’s new book, The Price of Altruism: George Price and the Search for the Origins of Kindness (Norton, 2010). Frank and the author no doubt appreciated the considerable contributions of Price, but Frank chose to consider his move away from atheism to creationism as a descent into a destructive mental illness.

Can you define “creationism” as you are using it here?

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Thank you. That confirms my assessment in the OP, but I wasn’t quite sure. I said in the OP:

But in my defense, Queller 2017 and Barton 2009 describe it as THE statement of the theorem. I think Ewens and Lessard give the more accurate description that this is merely a special case application of FTNS.

Ewens and Lessard 2015 said:

This leads to the correct statement of the FTNS in the discrete-generation case, in Price’s notation, as

\LARGE \partial_{NS}\bar{w} = \frac{\sigma^2_A}{\bar{w}}

As stated above, Price’s (1972) Eq. (5.14), corresponding to Eq. (13),
does not have the mean fitness w¯ in the denominator of the righthand
side, since his aim was to prove Fisher’s continuous-time
statement of the theorem.

Queller 2017 uses \Delta \bar{w} which I presume, using the various notations in this thread:

\LARGE \Delta \bar{w} = \partial{NS}\bar{w}=\bar{w}'-\bar{w}= \bar{w}(K+1)-\bar{w}(K)=\frac{\text{Var}(w,K)}{\bar{w}(K)}

Fair enough, the book describes Price writing to Henry Morris in 1971 to “congratulate him on his enterprise”, and he mentioned that with the exception of certainty about the global flood, he agreed with the other 2 tenets in the “Statement of Belief” that Morris’ society was using at the time. I don’t know exactly what those tenets were, but I think it’s fair to guess that at least one of them involved a clear acceptance of what we’d recognise today as YECism.

Both Oren Harman and the scientist who reviewed his biography of Price, Stephen Frank, discuss this as a symptom of Price’s descent into the mental illness that led to his suicide a few years later, and it’s not too hard to see why. His sudden conversion to Christianity is a red flag as well, given that it was for one of the weakest reasons I can image - he was a series of coincidences and thought someone must be controlling his life. Here’s Harman’s account of Price’s conversion:

Later he would write that the “coincidences” that forced him to convert were on the order of 1/1030, odds so fleetingly miniscule that he simply had no choice but to “give in and admit that God existed.”3 “About the beginning of June,” he wrote to his brother, Edison, in the fall, trying to explain,
I happened to notice one surprising coincidence in my life, and this started me searching back through my calendar books and letters and other material, and noticing a long succession of other improbabilities, until the improbability level
became astronomical. I listed a long series of independent events having improbabilities of the order of 1/100 or 1/1000, that fitted together into a meaningful pattern, and when I multiplied these together the product was something like i over i followed by twenty or thirty zeros.4
What had been the initial “surprising coincidence”? It was bizarre and absurd, maniacal and eerie. But it had George entirely transfixed.
Back at Christmas, Bob and Margarite Sheffield, old Price family friends from New York City, had been visiting London with their two daughters, Anne and Sally. Almost immediately, though she was barely eighteen, George took a liking to Anne. Bob wasn’t particularly happy about it, and hinted to George to back off. But Anne was continuing with a friend on a trip through Europe, and after visiting Finland, Sweden, and Germany, wrote to George innocently that she was scheduled to return to London on May 15, this time alone. “Since your visit played a critical role in this,” he wrote to her later, explaining his conversion, “I know that you will be interested in hearing how this came about. Prepare yourself to hear some surprising things, for there are more things in heaven and earth than you, I presume, imagine.”5
This is how it happened: When George first saw Anne over Christmas, he noticed her uncanny similarities to another Anne, the old girlfriend from the Midwest who had come to New York to see him just before his meeting with Emanuel Piore, director of research, on the twenty-third floor of the IBM Building in New York, on July 16, 1957. It was at that fateful meeting that George turned down Piore’s offer to join IBM as a senior researcher, based on the draft of his Design Machine published a few months earlier in Fortune magazine. And it had been on the previous day, the fifteenth, that he met Anne and instead of offering to marry her, told her he’d think about things. When he had wanted to marry her around the time he had contracted polio, Anne had broken off their relationship for another man. Now, still jealous, he figured he could take his time.
Clearly, he came to believe, this had led to his downfall. For had he asked Anne, who was a Roman Catholic, to marry him that day, he would have been focused first and foremost on nailing down a stable job. And had he accepted Piore’s offer, he would never have found himself in the drug-infested predicament in the Village, selling himself short on technical manuals for GE and Sperry-Marine, and trying and failing to write No Easy Way. In fact, had he taken Piore’s offer, he would never have joined IBM on a lower rung, and might never have contracted thyroid cancer. If he hadn’t been sick, he’d never have come under “butcher” Ferguson’s knife, and his life might not have descended into misery.6
July 15, 1957, had been a fateful day, all right, of this he was certain. And so, meeting Anne Sheffield now, thirteen years later, couldn’t just be a “coincidence.” She not only looked just like the earlier Anne, she had the very same name, the very same inflections. It didn’t seem to matter that he was forty-seven and she was eighteen and the daughter of close family friends. He wanted her, he wrote to her, “so very very much.” On everything important to him—choosing to become a chemist, choosing to marry Julia, choosing to go to Ferguson, choosing not to marry the first Anne—he had always7taken the wrong path. This time he was determined not to make another mistake.
Innocent and spooked, Anne left London for home at the end of the week. Convinced that there must be more than just the hand of chance involved, alone again and lovestruck, George remembered a poem by Henry Constable that an old Harvard friend had once sent him. “To live in Hell, and Heaven to behold / To welcome life, and die a living death /…If this be love, if love in this be grounded…” He couldn’t quite remember the rest, and started searching for the poem in his papers. When he couldn’t find it, he ran over to the British Museum Library. Fingering through the index cards, he came upon another Henry Constable, not the sixteenth century poet but a twentieth century theologian and believer in conditional immortality whose titles—Hades: or the Intermediate State of Man; Restitution of All Things; The Duration and the Nature of Future Punishment—sent shivers down his spine. Once again—an identical name and a message!8
Walking back to his flat on Little Titchfield beneath the spire, George contemplated his phone number. It was 580-2399, the last four digits signaling a minute before midnight. Of course 2359 was technically correct, but to him 2399 was meaningful, and that’s what really mattered. Was this another message? Could someone be signaling to him that the clock of doom was about to strike, that only a moment remained to make the right choice in life, finally, once and for all?9
As he looked through his diaries and letters, he saw more and more “coincidences.” Names, numbers, dates—they aligned in such ways that a pattern couldn’t honestly be ruled out. Someone was speaking to him, of this he was sure. “It wasn’t that I wanted to believe,” he later wrote to Anne, “but there wasn’t any alternative.” Finally, forty-seven years old and a lifelong fanatical atheist, he gave in and bowed to the spire. On June 14, George Price walked out of his flat up the stairs and through the warm, honey-colored circular portico of All Souls Church.

The books goes into more detail about Price’s spiral into more and more fanatical beliefs, and his final months, but let’s just say I think we should consider Price, particularly in the latter years of his life, a highly variable source of insights. Citing Price’s work on evolutionary biology and claiming him as a creationist is rather like a megavitamin therapist discussing Linus Pauling’s work in chemistry then snidely remarking that Pauling too believed that massive doses of vitamins could cure anything.

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Thank you so much for finding this.

I was unaware and never read the other details you generously provided here. Though I never met him, reading about him, I always hoped he had become a true Christian before he passed away. Yes, he spiraled downward mentally, but I was hoping somewhere his soul was saved.

The other thing that I seem to recall was that his colleagues (either Hamilton or Smith or someone) knew of his creationist views, but they still supported him in helping him get published. That was decent of them and commendable.

This is the discrete generation of version of Fisher’s theorem for haploids (which Joe Calls Fisher-like):

discrete_fisher

I did a numerical example here to illustrate this. With the following parameters for 3 varieties of haploid genomes, suppose:

scenario_1

then one will notice the last two columns have identical numbers, a prediction of Fisher’s Theorem!

Let us call this example, Scenario 1. I’ll post another scenario, Scenario 2, in the next comment as it shows the limitation of Fisher’s theorem.

Now consider another scenario which I call Scenario 2.

scenario_2

One should note that the first row of scenario 1 and scenario 2 are identical even though the respective individuals have different fitness profiles between the two scenarios. This emphasizes that the mean and variance don’t give enough information to describe the trajectory of the population, except for just one generation or time instance. Here is a graph of the above 2 scenarios:

fishers_theorem_graph

This graph confirms of Basener and Sandford’s claim that Fisher’s theorem is valid for one time instance, but is insufficient to determine the trajectory the population beyond that one time instance. The fact the graphs are not unique even though they share the same starting point in terms of variance and mean fitness is evidence of Basener and Sanford’s claim. And to be fair, Lessard and Ewens made the same claim before Basener and Sanford.

I’m merely providing a worked out example of this.

Hence, Fisher’s Fundamental theorem is not-so-fundamental! It’s an interesting relation, but hardly biology’s central theorem.

I’ve suggested a candidate for biology’s central theorem or principle, but it sounds to much like creationism. It is a principle that is found in textbook biochemistry and cellular biology material, namely Virchow’s principle:

Cell come only from pre-existing cells. Plant cells come from pre-existing plant cells, and animal cells come from pre-existing animal cells.

I’d say that principle is more fundamental to biology than Fisher’s Theorem!

It fails once you get back far enough in time, since all eukaryotes are related by common descent. So yes, that’s a creationist principle, and it’s wrong.

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Amazing! Well, not-so-amazing. And not-so-new. C. C. Li gave a proof in the 1970s and I think that Sewall Wright was aware of this but didn’t bother with this haploid case. In my online book Theoretical Evolutionary Genetics this is equations (II-103) to (II-108). Sal has verified, numerically, that the proof is correct. Stay tuned, and Sal will be posting a series of numerical examples to show that Pythagoras’s Theorem is actually correct.

Yes, and in addition, Basener and Sanford’s “corrected” Fundamental Theorem has the same property – to predict the long-term behavior of the case you can’t just keep using the same variance of fitness, but have to follow the gene frequencies, using the equations for mutation and selection, and keep recalculating that variance each generation. Or alternatively you can just use the equations for mutation and selection, and forget the FTNS.

Of course Basener and Sanford also regarded Fisher’s FTNS as the foundation of all subsequent work on mutation and selection. Actually, it isn’t. The basic equations for change of gene frequencies under mutation and selection were published in the 1920s, before Fisher’s 1930 book.

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Hi, Sal.

If ever you realize your dream of teaching an undergrad level course in Creation Science, will you have people on hand like the various experts who have been contributing in this thread? It seems you will need that, otherwise who will point out to your students all the amateurish mistakes you keep making?

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Of course, look at John Harshman. All I have to do is post something and he’ll weigh in with his insights. I’m happy to pass them on, but I can’t help it if my students laugh at his or your appeals to multiverses as explanations.

Your book is the finest book indeed on pop gen. Better than Hartl and Clark, and Gillespie, or Kimura and Crow…

I understand Fisher’s theorem better than Richard Dawkins thanks to you.
Dawkins is under the mistaken impression FTNS is biology’s central theorem. So I have one up on him as far as FTNS.

I can cite page 94 of your book where you point out Fisher’s Theorem is not so fundamental.