Defending the validity and significance of the new theorem “Fundamental Theorem of Natural Selection With Mutations, Part I: Fisher’s Impact

– Bill Basener and John Sanford

Joe Felsenstein and Michael Lynch (JF and ML) wrote a blog post, “Does Basener and Sanford’s model of mutation vs selection show that deleterious mutations are unstoppable?”  Their post is thoughtful and we are glad to continue the dialogue. This is the first part of a response to their post, focusing on the impact of R. A. Fisher’s work.  Our paper can be found at: https://link.springer.com/article/10.1007/s00285-017-1190-x

First, a short background on our paper:

The primary thesis of our paper is that Fisher was wrong, in a fundamental way, in his belief that his theorem (“The Fundamental Theorem of Natural Selection”), implied the certainty of ongoing fitness increase. His claim was that mutations continually provide variance, and selection turns the variance into fitness increase.  Central to his logic was that collectively; mutations have a net zero effect on fitness.  While Fisher assumed mutations are collectively fitness-neutral, it is now known that the vast majority of mutations are deleterious. So mutations can potentially push fitness down – even in the presence of selection.

Additionally, we provided a new mathematical model for the process of mutation and selection over time, which comes in an infinite population version and a finite population version.  The infinite population version uses a classical differential equations mutation/selection framework, with multiple reproducing subpopulations and mutations occurring between subpopulations, but incorporating a probabilistic distribution for mutation effects.  The finite version is obtained by adding the constraint that any subpopulation with less than one organism is assumed to have no members.

Our model is backed by a literature review in Section 2 of our paper (covering 9 pages with 71 citations), with Section 2.2 discussing previous infinite populations models and Section 2.3 focusing on finite ones.  Our  model is new in that it includes an arbitrary distribution of mutational effects, and we do not assume mutations are 50/50 beneficial /deleterious (as did Fisher), and we did not assume that all mutations have the same fixed effect (as with Lynch’s finite population models).

Part I: Ronald A. Fisher’s Impact – First, let’s discuss Fisher and the critique by Felsenstein and Lynch of our work on Fisher’s Theorem, and its historical importance:

In their critique, JF and ML do not dispute our logic regarding Fisher’s Theorem, but provide their perspective that Fisher’s contribution to population genetics and evolutionary theory was very limited. They say,

“One of us (JF) has argued at The Skeptical Zone that they have misread the literature on population genetics. The theory of mutation and natural selection developed during the 1920s, was relatively fully developed before Fisher’s 1930 book. Fisher’s FTNS has been difficult to understand, and subsequent work has not depended on it. But that still leaves us with the issue of whether the B and S simulations show some startling behavior…”

We respectfully disagree with their perspective that Fisher’s book and Theorem had only a minor impact. The book they refer to is “Genetical Theory of Natural Selection” (GTNS), which is where he published his FTNS Theorem.  To begin with, Google Scholar lists that Fisher’s book, GTNS, has been cited 20,254 times – this is not insignificant.

Below are some quotes from standard sources and leaders in the field that are consistent with our view that Fisher’s work, that his book GTNS contributed significantly to establishing the field of Population Genetics and his theorem FTNS was central to establishing Neo-Darwinian Theory.

From the book Philosophy of Biology, (Section on Fisher written by Robert A. Skipper, Jr., 2007, p.44):

“The Genetical Theory of Natural Selection is a point of departure in contemporaneous evolutionary thought, responsible in part for the origination of theoretical population genetics and what is commonly called the “modern synthetic theory of evolution.”

this continues,

“To be sure, Fisher’s work in statistics was revolutionary at the field’s conceptual foundation.  Moreover, Fisher’s work in genetics, highlighted mainly by his 1930 The Genetical Theory of Natural Selection, would, with good company in Haldane and Wright, revolutionize biology.”

In his textbook Population Genetics, M. Hamilton writes:

“Fisher’s 1930 book The Genetical Theory of Natural Selection established a rigorous mathematical framework that coupled Mendelian inheritance and Darwin’s quantitative model of natural selection.” (p. 204)

And then calls Fisher’s book,

“the first comprehensive treatment of natural selection that came out of the modern synthesis” (p. 206)

In the book The Logic of Chance: The Nature and Origin of Biological Evolution, author Eugene V. Koonin (who has authored over 600 articles, is Senior Investigator at NIH, and editor-in-Chief of the journal Biology Direct) writes:

“The foundations for the critically important synthesis of Darwinism and genetics were set in the late 1920s and early 1930s by the trio of outstanding theoretical geneticists: Ronald Fisher, Sewall Wright, and J. B. S. Haldane. They applied rigorous mathematics and statistics to develop an idealized description of the evolution of biological populations. The great statistician Fisher apparently was the first to see that, far from damning Darwinism, genetics provided a natural, solid foundation for Darwinian evolution. Fisher summarized his conclusions in the seminal 1930 book The Genetical Theory of Natural Selection (Fisher, 1930), a tome second perhaps only to Darwin’s Origin in its importance for evolutionary biology.5 This was the beginning of a spectacular revival of Darwinism that later became known as Modern Synthesis (a term mostly used in the United States) or neo-Darwinism (in the British and European traditions).”

In the book The Mathematics of Darwin’s Legacy, P. Schuster writes,

“Ronald Fisher, the great scholar of population genetics, presented the first mathematical unification of Darwin’s theory of natural selection and Mendel’s laws of inheritance [25].”

In the abstract to the paper Fisher’s fundamental theorem of natural selection in Trends in Ecology and Evolution (Frank and Slatkin 1992):

“Fisher’s Fundamental Theorem of natural selection is one of the most widely cited theories in evolutionary biology.”

In his textbook, Theoretical Evolutionary Genetics, Joe Felsenstein writes,

“Population genetics theory had its major developments in the 1920s-1940s (at the hands of Fisher, Wright, and Haldane)” (p. xvii)

The Wikipedia article on Fisher describes his contribution:

“In genetics, his work used mathematics to combine Mendelian genetics and natural selection; this contributed to the revival of Darwinism in the early 20th century revision of the theory of evolution known as the modern synthesis.

In 1930, The Genetical Theory of Natural Selection was first published by Clarendon Press and is dedicated to Leonard Darwin. A core work of the neo-Darwinian modern evolutionary synthesis,[29] it helped define population genetics, which Fisher founded alongside Sewall Wright and J. B. S. Haldane”

The paper What was Fisher’s fundamental theorem of natural selection and what was it for? In Studies in History and Philosophy of Biological and Biomedical Sciences (Plutynski, 2006) is probably the best thoroughly researched single source on Fisher’s theorem says:

“Fisher (1918, 1922) proposed a new way of picturing populations of organisms…. Starting with this novel conception, Fisher, Haldane, and Wright developed models of the genetics of populations.”

And then,

“Moreover, this analogy allowed Fisher to vindicate Darwin’s theory of natural selection, not by empirical demonstration, but by a mathematical argument to the effect that evolution was not only possible, but also necessary” p.75.

The quotes above from Plutynski give some good perspective on Fisher’s different contributions.  His 1918,1922 papers were foundational to population genetics.  His 1930 GTNS book was an additional significant contribution to population genetics, and his FTNS was seen as vindicating Darwin’s theory, giving what was perceived as a rigorous argument that (Darwinian) evolution is necessary, given Mendelian genetics.  The Plutynski paper is an insightful read, describing Fisher’s goals as follows:

“Fisher’s book, and the theorem in particular, is best understood as a continuation of his attempt to breach the divide between biometricians and Mendelians concerning the nature of heredity and the effectiveness of Darwinian selection. His motivation in almost all his work was to explain how it was possible to resolve this conflict, and to vindicate Darwinian selection as both a plausible and necessary cause of evolutionary change.”

Alan Grafen provides the following quote from William Hamilton describing Fisher’s Genetical Theory of Natural Selection:

“This is a book which, as a student, I weighed as of equal importance to the entire rest of my undergraduate BA course and, through the time I spent on it, I think it notched down my degree. Most chapters took me weeks, some months; … And little modified by molecular genetics, Fisher’s logic and ideas still underpin most of the ever broadening paths by which Darwinism continues its invasion of human thought. For a book that I rate only second in importance in evolution theory to Darwin’s ‘‘Origin’’ (this as joined with its supplement, ‘‘of Man’’), and also rate as undoubtedly one of the greatest books of the present century, the appearance of a variorum version is a major event. … By the time of my ultimate graduation, will I have understood all that is true in this book and will I get a First? I doubt it. In some ways some of us have overtaken Fisher; in many, however, this brilliant, daring man is still far in front.’” (Hamilton; dust-jacket of Fisher, 1930b).

Richard Dawkins ranks Fisher the greatest biologist since Darwin:

“Who is the greatest biologist since Darwin? That’s far less obvious, and no doubt many good candidates will be put forward. My own nominee would be Ronald Fisher. Not only was he the most original and constructive of the architects of the neo-Darwinian synthesis. Fisher also was the father of modern statistics and experimental design. He therefore could be said to have provided researchers in biology and medicine with their most important research tools, as well as with the modern version of biology’s central theorem.”

These quotes from a variety of sources support the tenet stated in the first sentences of our paper:

“R. A. Fisher was one of the greatest scientists of the 20th century. He is considered to be the singular founder of modern statistics and simultaneously the principle founder of population genetics (followed by Haldane and Wright). Fisher was the first to establish the conceptual link between natural selection and Mendelian genetics. This paved the way for what is now called neo-Darwinian theory.” – Basener and Sanford, 2017

Central to our paper is that Fisher’s theorem, which Dawkins calls “biology’s central theorem” does not imply what Fisher thought it did (and by extension what many others thought it did).  To clarify Fisher’s error, we distinguish between Fisher’s actual theorem (what he actually proved), and “Fisher’s Corollary”, which was unproven, and was really just an informal thought experiment based on his assumption that mutations have zero net effect on fitness. This corollary has clearly been falsified, which is essential to the popular concept that mutations simply supply genetic variance and natural selection converts this variance into ongoing increased fitness.

While Fisher’s Theorem is mathematically correct, his Corollary is false.  The simple logical fallacy is that Fisher stated that mutations could effectively be treated as not impacting fitness, while it is now known that the vast majority of mutations are deleterious, providing a downward pressure on fitness.  Our model and our correction of Fisher’s theorem (The Fundamental Theorem of Natural Selection with Mutations), take into account the tension between the upward force of selection with the downward force of mutations.

Our correction challenges a tradition central tenet of Neo-Darwinism.  It is often viewed that the upward force of selection acts without consideration of the downward force of mutations.  See, for example, the quote from Gould still taken as :

“The core of this synthetic theory restates the two most characteristic assertions of Darwin himself: first, that evolution is a two-stage process (random variation as raw material, natural selection as a directing force); secondly, that evolutionary change is generally slow, steady, gradual, and continuous. . . Orthodox neo-Darwinians extrapolate these even and continuous changes to the most profound structural transitions in life.” (Gould 1980)

We agree (apparently) with JF and ML that Fisher’s theorem has serious flaws.  The theorem was not clearly written, and is mathematically correct but with very limited application.  One of the most respected papers on Fisher’s FTNS was written by G. Price in 1972, which we quote in our paper as follows:

“Also, he [Fisher] spoke of the “rigour” of his derivation of the theorem and of “the ease of its interpretation”. But others have variously described his derivation as “recondite” (Crow and Kimura 1970), “very difficult” (Turner 1970), or “entirely obscure” (Kempthorne 1957). And no one has ever found any other way to derive the result that Fisher seems to state. Hence, many authors (not reviewed here) have maintained that the theorem holds only under very special conditions, while only a few (e.g.. Edwards 1967) have thought that Fisher may have been correct—if only we could understand what he meant! …here that this latter view is correct. Fisher’s theorem does indeed hold with the generality that he claimed for it. The mystery and the controversy result from incomprehensibility rather than error.”

At issue is that even though the flaws in Fisher’s theorem have been knowable for a long time, it has still been used as strong support for Neo-Darwinian Theory.  In the quote from Gould above, mutations add raw material of variation, and selection turns variation into increase in fitness (evolutionary progress); selection is assumed to act as an upward force without considering the downward force of mutations.  This is strongly linked to Fisher’s Corollary.  Despite the known flaws with Fisher’s work (known at least within the population genetics community), there is still a common perception that selection acts on mutations to maximize fitness as Fisher described.  As stated in the abstract of a recent 2016 paper Natural Selection and the maximization of fitness, on expansions of Fisher’s FTNS and Darwinism, by J Birch of the University of Cambridge:

“The notion that natural selection is a process of fitness maximization gets a bad press in population genetics, yet in other areas of biology the view that organisms behave as if attempting to maximize their fitness remains widespread. “

Conclusions:

R. A. Fisher was one of the three founders of population genetics, and is considered by many to be the first and primary founder. His Fundamental Theorem of Natural Selection contributed significantly to a “revival of Darwinism” (see Koonin quote above and Wikipedia).  His theorem has been considered by many a significant and rigorous support for the Neo-Darwinian Theory (see quotes above).

Our paper shows that Fisher’s corollary is clearly false, and that he misunderstood the implications of his own theorem. He incorrectly believed that his theorem was a mathematical proof that showed that natural selection plus mutation will necessarily and always increase fitness. He also believed his theorem was on a par with a natural law (such as entropic dissipation and the second law of thermodynamics).  Because Fisher did not understand the actual fitness distribution of new mutations, his belief in the application of his “fundamental theorem of natural selection” was fundamentally and profoundly wrong – having little correspondence to biological reality. Therefore, we have reformulated Fisher’s model and have corrected his errors, thereby have established a new theorem that better describes biological reality, and allows for the specification of those key variables that will determine whether fitness will increase or decrease.

96 thoughts on “Defending the validity and significance of the new theorem “Fundamental Theorem of Natural Selection With Mutations, Part I: Fisher’s Impact”

1. Welcome to TSZ, Bill and John.

I’m pleased to see that you’re willing to interact directly with your critics here, and I look forward to following the comment thread.

2. Bill,

Thanks for visiting. You said the theorem is correct but the corollary is not. The way I understood this is to look at your visual simulations here:

https://people.rit.edu/wfbsma/evolutionary%20dynamics/EvolutionaryModel.html

Fisher’s theorem predicts “Rate of Change of Mean Fitness” should vary identically over time with “Upward Fitness Pressure: Variance in Fitness” which your simulation shows as far as I can tell. However, the corollary is shown false because simultaneously mean fitness declines.

So your simulation is consistent with the Fisher’s theorem being correct, but the corollary being false. This seems to agree with Ewens and Lessard’s views about Fisher’s theorem.

3. While Fisher assumed mutations are collectively fitness-neutral, it is now known that the vast majority of mutations are deleterious.

This is simply false. Most mutations are neutral or negligible.

Point mutations to protein coding areas of DNA have about 1/3 chance of not affecting the protein produced at all, let alone deleteriously.

It’s also trivial that if a point mutation is mildly deleterious, then the opposite of that point mutation must be mildly beneficial – so at least half of all non-fatal point mutations are not deleterious.

Thus any results dependent on the false assumption that “the vast majority of mutations are deleterious” can be immediately disregarded.

4. Roy: This is simply false. Most mutations are neutral or negligible.

That would be dependent on the population size, I think. For humans this is correct.

Roy: It’s also trivial that if a point mutation is mildly deleterious, then the opposite of that point mutation must be mildly beneficial – so at least half of all non-fatal point mutations are not deleterious.

Assuming both occur at the same frequency, which is unlikely. Because of the fitness difference the beneficial allele has a higher probability of being fixed. Now, I agree that most mutations are neutral in humans, but with respect to non-neutral mutations, the number of deleterious mutations will far outweight the advantageous ones.

5. Roy,

Hi Roy,

Here is the paragraph from our paper with citations supporting the statement. Thanks.

“The predominance of deleterious mutations over beneficial ones is well established. James Crow in (1997) stated, “Since most mutations, if they have any effect at all, are harmful, the overall impact of the mutation process must be deleterious”. Keightley and Lynch (2003) give an excellent overview of mutation accumulation experiments and conclude that “…the vast majority of mutations are deleterious. This is one of the most well-established principles of evolutionary genetics, supported by both molecular and quantitative-genetic data. This provides an explanation for many key genetic properties of natural and laboratory populations”. In (1995), Lande concluded that 90% of new mutations are deleterious and, the rest are “quasineutral” (Also see Franklin and Frankham (1998)). Gerrish and Lenski estimate the ratio of deleterious to beneficial mutations at a million to one (Gerrish and Lenski 1998b), while other estimates indicate that the number of beneficial mutations is too low to be measured statistically (Ohta 1977; Kimura 1979; Elena et al. 1998; Gerrish and Lenski 1998a). Studies across different species estimate that apart from selection, the decrease in fitness from mutations is 0.2–2% per generation, with human fitness decline estimated at 1% (See Lynch 2016; Lynch et al. 1999). Estimates suggest that the average human newborn has approximately 100 de novo mutations (Lynch 2016). Research using finite population models has been driven by the need to understand the impact of the buildup of deleterious mutations (called mutational load) in small populations of endangered species (See Lande 1995; Franklin and Frankham 1998). Of special interest is the mutational load in the human species given the relaxed selection due to social and medical advances (Kondrashov 1995; Crow 1997; Lynch 2016).”

6. Hi Keiths. Thanks. I hope to learn a lot. Diversity in views is how science progresses, though I don’t think the rate of progress is exactly equal to the variance in views.

My best friend at RIT was an evolutionary game theorist. Our families gathered every year at thanksgiving and we wrote a few papers together, though never saw Darwin in the same light. I learned a lot from him.

7. Corneel: That would be dependent on the population size, I think.

No, it would depend on the fraction of the genome that is junk. Population size has nothing to do with how frequently mutations are deleterious.

Population size has implications for the efficacy of natural selection, but not whether the mutation is deleterious or beneficial.

8. Hi Bill, welcome at TSZ.

Joe Felsenstein will have a thing or two to say about this himself, undoubtedly. But perhaps I can anticipate some of it:

Conclusions:
R. A. Fisher was one of the three founders of population genetics, and is considered by many to be the first and primary founder. His Fundamental Theorem of Natural Selection contributed significantly to a “revival of Darwinism” (see Koonin quote above and Wikipedia). His theorem has been considered by many a significant and rigorous support for the Neo-Darwinian Theory (see quotes above).

Ronald Fisher was undoubtedly a bright guy, but what I got from Joe Felsensteins criticism was that mathematical theory of recurrent mutation and genetic drift was well underway when Fisher published his fundamental theory, and these concepts have been well incorporated into evolutionary genetic theory. Hence considering the FTNS as foundational to subsequent development of the field of evolutionary biology may be somewhat exaggerated as well as your claim that biologists were oblivious of the effect of mutation pressure and that you are now radically changing the game.

9. Rumraket: No, it would depend on the fraction of the genome that is junk. Population size has nothing to do with how frequently mutations are deleterious.

Population size has implications for the efficacy of natural selection, but not whether the mutation is deleterious or beneficial.

I don’t think I agree with that: The efficacy of natural selection is exactly what determines whether a mutation is neutral or not. After all, it is quite unlikely that any mutation is truly neutral in the sense that it has no effect on fitness whatsoever. The question is whether the effect of natural selection is substantial in comparison to that of genetic drift (which depends on population size). Hence, the definition of neutrality is operational rather than functional.

I do agree that mutations are more likely to be neutral in junk DNA.

10. Fisher has calculated (1930) that new alleles with even 1% selective advantage will routinely be lost in natural populations. According to these calculations the likelihood of losing a new allele with 1% advantage or no advantage is more than 90% in the next 31 generations (Fisher, 1930/1958; Dobzhansky, 1951; Schmidt, 1985; see also ReMine, 1993; Futuyma, 1998; Maynard Smith, 1998).

Considering genetic drift, Griffith and colleagues state in agreement with these authors:

”Even a new mutation that is slightly favorable will usually be lost in the first few generations after it appears in the population, a victim of genetic drift. If a new mutation has a selective advantage of S in the heterozygote in which it appears, then the chance is only 2S that the mutation will ever succeed in taking over the population. So a mutation that is 1 percent better in fitness than the standard allele in the population will be lost 98 percent of the time by genetic drift.”

11. In total numbers, since every mutation that isn’t lethal is in principle reversible, the number of possible beneficial mutations must exactly equal the number of deleterious ones. There is no way out of this, it must necessarily be so. For every substitution there is the reverse, for every insertion/duplication there is a deletion, and so on.

However, deleterious mutations could still be more likely to happen and that is why it would look like they are greater in number, and we could think about why that is.

One way that immediately springs to mind is that deletion of a gene that is beneficial, if no other copies exist of it, would make it extremely very unlikely for a spontaneous insertion, or what you might call a de novo “elongation” of some sort, to just so happen to fully re-create a specific lost gene. So while the mutational loss of a gene is in principle reversible, it is very unlikely.

Another reason is that many protein coding genes are, while not perfect or “optimal” (it is known for example that the rate of catalysis of many natural enzymes could be improved with very stringent selection generally not possible in the wild), still quite well adapted already, so because a large proportion of beneficial changes to the ancestral forms of these proteins have already happened and been fixed, it has become more and more unlikely for new mutations to be measurably beneficial.
Using ancestral sequence reconstruction is has been shown that many primordial enzymes, for example, were quite promiscous in their substrate preferences, and that extant descendants of these enzymes have evolved by duplication and diversification, and subsequent selection to improve the substrate specificity and isolated regulation of the different duplicates. If any such specialized enzymes should today undergo a reversal to a more promiscous state, this would be likely to be deleterious as it is likely to come with a reduction in rate of catalysis.

These same principles apply also to transcription factors and other regulatory elements that bind DNA. Once binding and regulation has been honed by selection, a change away from that state is more likely to have become deleterious with time as they have become useful or critical adaptations to the carrying organism.

This same principle would generally apply to the functional proportion of the genome as a whole, which itself would have evolved incrementally by adapting novel portions (such as duplications of already existin genes, or of expanding intergenic regions that might also be junk) of it to function well, while the already evolved remainder has in large part been under purifying selection to “keep working”.

12. Corneel: I don’t think I agree with that: The efficacy of natural selection is exactly what determines whether a mutation is neutral or not.

Are you sure you’re not thinking about the probability of fixation, rather than the mean effect on reproductive success of carriers?

IIRC the ability of natural selection to fix the mutation very much depends on population size. But the allele has (at least theoretically) some effect, s, on mean reproductive success W, whether the population has 10^2, 10^4, or 10^12 memebers. It just means that, on average, carriers of that allele have W(1+s) reproductive success. If s is a positive number, the allele is beneficial.

I don’t see how changing the population size is going to change s. Rather it will change the probability of fixation.

After all, it is quite unlikely that any mutation is truly neutral in the sense that it has no effect on fitness whatsoever. The question is whether the effect of natural selection is substantial in comparison to that of genetic drift (which depends on population size). Hence, the definition of neutrality is operational rather than functional.

Okay, we were speaking past each other then.

13. J-Mac: So a mutation that is 1 percent better in fitness than the standard allele in the population will be lost 98 percent of the time by genetic drift.

And fixed 2% of the time.

If it is the single copy, for a population of some particular size. If the population is bigger, it has higher chance of fixation, if the population is smaller, it has lower chance of fixation. If it exists in more than one individual, it has a higher chance of fixation.

Thank you for this case of non-news J-mac.

14. Rumraket: And fixed 2% of the time.

If it is the single copy, for a population of some particular size. If the population is bigger, it has higher chance of fixation, if the population is smaller, it has lower chance of fixation. If it exists in more than one individual, it has a higher chance of fixation.

Thank you for this case of non-news J-mac.

Well, the problem is that beneficial mutations are just as rare as a sensible comment from you…

15. ETA: A real flaw is some organisms just don’t reproduce in sufficient numbers for a slightly beneficial change to be “selected.”
Everything looks good in the population genetics speculative calculations though…but not in real life…

16. As I understand it, this first post is meant to be about “How important is Fisher?”, which is a debate in the “History of Science” realm, and not in any way relevant to the question “Under what conditions is mutational meltdown inevitable?”.
You are skipping ahead to the “Is Basener and Sanford’s math correct?” discussion.
Personally, I am happy to stipulate that, regarding the first question: “I do not care.”
I eagerly look forward to engaging the authors on the second question…

17. Corneel:
Hi Bill, welcome at TSZ.

Joe Felsenstein will have a thing or two to say about this himself, undoubtedly. But perhaps I can anticipate some of it:

Ronald Fisher was undoubtedly a bright guy, but what I got from Joe Felsensteins criticism was that mathematical theory of recurrent mutation and genetic drift was well underway when Fisher published his fundamental theory, and these concepts have been well incorporated into evolutionary genetic theory. Hence considering the FTNS as foundational to subsequent development of the field of evolutionary biology may be somewhat exaggerated as well as your claim that biologists were oblivious of the effect of mutation pressure and that you are now radically changing the game.

Hi Corneel, thanks.

Regarding, the general contribution of historical figures, there certainly can be differing legitimate views. I quoted W. Hamilton and Dawkins and others above who had a high view of Fisher’s book, and I also have respect for your views and certainly Joe’s. I’m an applied mathematician, so honestly I don’t have much authority on how the contribution of Fisher should be viewed, other than quoting those above, and you and Joe F. and John Sanford.

However, my understanding is that Fisher’s foundational work in population genetics was in 1918 and 1922, and his book in 1930 was significant (at minimum, it has been viewed as extremely significant by some very respected people). Those were significant works that have been built upon (20k citations to his book, for example.) How exactly these contributions are understood is not my main concern, and I respect opinions of others on the matter.

Regarding his theorem, I do not know of much in population genetics that depends on it. (I think Joe F misread our paper when they say we argue that the FTNS “is the basis for all subsequent theory in population genetics”. If anything in our paper seemed to say that, it was unintentional.) A critical point in our paper is how people have viewed the application of the FTNS. It has been used as a significant support for Neo-Darwinian Theory, but it does not effectively describe reality.

As an interesting side note – I encounter Fisher’s contributions to statistics in a lot of my other work. (I run a pair of software startup companies doing machine learning / signal processing, and teach graduate courses in data mining, data science, and machine learning in the Systems Engineering Dept. at the University of VA.) So much of the current machine learning, data science, and artificial intelligence boom traces back to Fisher and his likelihood maximization, LDA, etc. I could see intuition pointing toward today’s latest research while reading Fisher’s GTNS.

18. DNA_Jock: As I understand it, this first post is meant to be about “How important is Fisher?”, which is a debate in the “History of Science” realm

Joe Felesnstein and Michael Lynch downplay Fisher’s importance now, because his work, that revived the neo-Darwinism in 1930-ies and continued until recently, now is found to be false, at least his corollary…
Everything seemed fine until Basener and Sanford published their paper and exposed the flaws…

19. Bill and John,

I’ve just seen that you have an OP, and have sent Joe a note, to make sure he knows about it. (He’s on Pacific time, you know.) I haven’t read your OP yet, but will thank you immediately for engaging. “It’s a miracle!”

20. Just to back up a bit, this is what is at issue. Fisher’s theorem. The wiki version of the theorem was stated as:

“The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time.”

The graph below from Bill and John’s simulation illustrates the idea for a specific scenario. According to FTNS the two graphs should be identical.

21. The issue the is the corollary. The corollary is that fitness will also increase continually. A sufficient but not necessary condition to falsify the corollary is to show at least one counter example where fitness declines, but the above graph (relation) still holds. Indeed this is what the simulation shows, and as far as I can tell it agrees with Ewens and Lessard’s finding whom Joe Felsenstein also referenced. Here is another graph from the same simulation that provides a necessary counter example to “Fisher’s Corollary”.

At issue is how generalizable is the result of one simulation to other scenarios. It seems there is universal agreement there is at least one counter example to Fisher’s Corollary.

22. Finally, for contextual reference, I found a summary that actually states Fisher’s theorem in relation to other fundamental theorems of Evolutionary Biology using mathematical symbols. The nested hierarchy of equations doesn’t necessarily represent a chronological evolution since Price’s equation came long after Fisher’s theorem.

23. stcordova: The corollary is that fitness will also increase continually.

Fitness is a function of the environment. Selection might increase fitness. But another change in the environment might reduce it.

To say that fitness is increasing continually might only be to say that selection is continually compensating for disadvantageous changes in the environment.

24. Tom English:
Bill and John,

I’ve just seen that you have an OP,and have sent Joe a note, to make sure he knows about it. (He’s on Pacific time, you know.) I haven’t read your OP yet, but will thank you immediately for engaging. “It’s a miracle!”

Thanks, Tom. I hope to learn from the discussions here. Joe and Michael gave a thoughtful post on our paper, and I appreciate their interaction.

25. Regarding the first part of Bill Basener and John Sanford’s response to Joe Felsenstein and Michael Lynch, this is an issue of interpreting history. I think it is clear, like many arguments over the proper interpretation of history, that the opinions are diverse, and maybe there will be no resolution to this issue like we will regarding math issues.

I believe the next part of Bill’s response will deal with the matters that are mathematical.

So as far as I’m concerned, arguments over the interpretation of history of ideas will probably not find any sort of empirical resolution. I look forward to the next part of the response.

26. Tom English:
Bill and John,

I’ve just seen that you have an OP,and have sent Joe a note, to make sure he knows about it. (He’s on Pacific time, you know.) I haven’t read your OP yet, but will thank you immediately for engaging. “It’s a miracle!”

Yes, we should compliment Dr Basener for venturing into the lion’s den. And thanks to Sal for being the lightning conductor.

27. Neil Rickert: itness is a function of the environment. Selection might increase fitness. But another change in the environment might reduce it.

To say that fitness is increasing continually might only be to say that selection is continually compensating for disadvantageous changes in the environment.

Which means fitness is relative…This also means that fitness can decrease or continue to decrease, if the environment persists… which means that the organism can’t adapt which means it can’t evolve…which is another way of saying Fisher was wrong…

Wonderful! Tell us more Mr. Science…

28. Neil Rickert: Fitness is a function of the environment. Selection might increase fitness. But another change in the environment might reduce it.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Exactly!!!

29. stcordova: I believe the next part of Bill’s response will deal with the matters that are mathematical.

Hi stcordova. Yes our part 2 will be focusing on the math. I am certainly more comfortable with math than history.

30. Alan Fox: J-Mac: if the environment persists…

There’s your error right there! The environment is not static.

You mean like during the ice-age?

31. DNA_Jock: As I understand it, this first post is meant to be about “How important is Fisher?”, which is a debate in the “History of Science” realm, and not in any way relevant to the question “Under what conditions is mutational meltdown inevitable?”.

I agree. In fact I consider the whole “How important is Fisher?” question to be rhetorical, rather than actually scientifically substantive. If it can be made to seem as if all our knowledge (and the reality) of evolution rests critically on Fisher’s theorem, then all the more impressive it can be made to appear if you can tear it down. That is of course it’s purpose.

You are skipping ahead to the “Is Basener and Sanford’s math correct?” discussion.

Well, not so much the math as the assumptions leading into it.

I think it means a great deal whether an organism has moved into a novel environment, for example, to the average effect of mutations. And I think it means a great deal how skewed towards deleterious a ratio in terms of fitness effects, both in frequency and their proportion, you think an average mutation has.

But I haven’t even commented on that, at least not directly except to say that it logically cannot be the case that the absolute number of deleterious mutations must outnumber the beneficial ones (and in the same way it can’t logically be the case that deleterious mutations on average are more deleterious in degree, than the beneficial are beneficial). A mutation that halves reproductive success, is in princple reversible and thus will double reproductive success. It cannot be otherwise.

Rather, insofar as fitness is declining despite selection, then at least in part, it must be because for various reasons beneficial mutations are less likely to happen than deleterious ones. And I think they generally are, but even here there is a question of proportion.

Do deleterious mutations really happen a million times more often than beneficial ones? You can certainly cherrypick literature where such ratios are suggested. On the other hand, you can also cherrypick literature that put the ratio at roughly 7:1, or 100:1. Basener and Sanford went for the million-to-one. I don’t wonder why.

32. Which one? But yes, that would be an example of a change in the environment.

I’m talking about the persistence of the same environment for a long period of time affecting thousands of generations…Why would which period of time mean anything?

33. Rumraket: Do deleterious mutations really happen a million times more often than beneficial ones? You can certainly cherrypick literature where such ratios are suggested. On the other hand, you can also cherrypick literature that put the ratio at roughly 7:1, or 100:1. Basener and Sanford went for the million-to-one. I don’t wonder why.

Cherry-picking works both ways and you are the master of it …

34. J-Mac: Which means fitness is relative…This also means that fitness can decrease or continue to decrease, if the environment persists

Thanks for that penetrating insight. Fitness can decrease. How truly novel.

… which means that the organism can’t adapt

Yes, when a species can’t adapt then it can’t adapt.

which means it can’t evolve…which is another way of saying Fisher was wrong…

If Fishwer was wrong then Fisher was wrong, and then we need a better theory of mutation and natural selection that better describe reality. Including the reality that, often times, organisms adapt and fitness increases.

35. J-Mac: I’m talking about the persistence of the same environment for a long period of time affecting thousands of generations…Why would which period of time mean anything?

Would 20.000 generations be enough for fitness to start declining, do you think?

36. J-Mac: I’m talking about the persistence of the same environment for a long period of time affecting thousands of generations

OK. The deep sea off the Comoro Islands?

…Why would which period of time mean anything?

My question was which Ice Age were you referring to.

ETA correct spelling

37. J-Mac: This also means that fitness can decrease or continue to decrease, if the environment persists… which means that the organism can’t adapt which means it can’t evolve…which is another way of saying Fisher was wrong…

The environment is changing all the time. It’s not just climate. A new food source, or the loss of a food source. A new predator, or a former predator goes extinct. All of the affect the environment and fitness.

38. J-Mac: Which means fitness is relative…

Oh crap! That changes everything! Surely nobody knew that fitness is relative to the environment. It’s not as if natural selection referred to the environment at all …. wait!

J-Mac: This also means that fitness can decrease or continue to decrease, if the environment persists…

The other way around J-Mac.

J-Mac: which means that the organism can’t adapt which means it can’t evolve…

It’s the population J-Mac, not the organism. The population contains lots of organisms each with variable characteristics. If the environment changes, then a subpopulation might survive the changes. If so, then the surviving individuals reproduce and their fitness-related alleles thus get fixed, and recombined, in the new population. If the environment persists, then we get mostly random genetic drift after the selection period.

39. Here is the paragraph from our paper with citations supporting the statement.Thanks.

That merely confirms that you are taking the ratio of deleterious mutations to beneficial ones, and ignoring the neutral/negligible ones.

Crow refers to mutations that have an effect. Keightley and Lynch are discussing amino-acid altering mutations, not all mutations. Lande is also talking about a subset of mutations, and anyway 95) is not “the vast majority”. If I have the correct paper, Gerrish/Lenski simply do not say what you claim they do; while Ohta and Kimura actually concluded that most mutations were neutral.

Your sources simply do not support your claim.

40. (I am in communication with Mike Lynch about making a response to this post).

Anyway,

J-Mac:
Fisher has calculated (1930) that new alleles with even 1% selective advantage will routinely be lost in natural populations. According to these calculations the likelihood of losing a new allele with 1% advantage or no advantage is more than 90% in the next 31 generations (Fisher, 1930/1958; Dobzhansky, 1951; Schmidt, 1985; see also ReMine, 1993; Futuyma, 1998; Maynard Smith, 1998).

Considering genetic drift, Griffith and colleagues state in agreement with these authors:

”Even a new mutation that is slightly favorable will usually be lost in the first few generations after it appears in the population, a victim of genetic drift. If a new mutation has a selective advantage of S in the heterozygote in which it appears, then the chance is only 2S that the mutation will ever succeed in taking over the population. So a mutation that is 1 percent better in fitness than the standard allele in the population will be lost 98 percent of the time by genetic drift.”

In the meantime we may compare J-Mac’s uncharacteristically well-written comment with the statement by Wolf-Ekkehard Lönnig here, where he quotes himself saying in a podcast that

Fisher, perhaps the most important forerunner of the neo-Darwinian theory, has calculated (1930) that new alleles with even 1% selective advantage (i.e., more than is usually expected by neo-Darwinian theorists), will routinely be lost in natural populations. According to these calculations the likelihood of loosing a new allele with 1% advantage or no advantage is more than 90% in the next 31 generations (Fisher, 1930/1958; Dobzhansky, 1951; Schmidt, 1985; see also ReMine, 1993; Futuyma, 1998; Maynard Smith, 1998). Considering genetic drift, i.e. random fluctuations of gene frequencies in populations, Griffith and colleagues state in agreement with these authors (1999, p. 564):

Even a new mutation that is slightly favorable will usually be lost in the first few generations after it appears in the population, a victim of genetic drift. If a new mutation has a selective advantage of S in the heterozygote in which it appears, then the chance is only 2S that the mutation will ever succeed in taking over the population. So a mutation that is 1 percent better in fitness than the standard allele in the population will be lost 98 percent of the time by genetic drift.

Obviously great minds think alike.

41. Joe,

The one thing J-Mac can say in his defense is that no one who actually knows him would ever suspect him of writing something as coherent as that.

Still pretty sleazy not to cite his source, though.

42. Joe Felsenstein:
(I am in communication with Mike Lynch about making a response to this post).

Anyway,

In the meantime we may compare J-Mac’s uncharacteristically well-written comment with the statement by Wolf-Ekkehard Lönnig here, where he quotes himself saying in a podcast that

Obviously great minds think alike.

Are you suggesting what I think you suggesting, Joe?
BTW: You have never quoted someone whose thoughts are aligned with yours? How about Michael Lynch?

You also forgot to mention the randomness in natural selection piece… You don’t like it or it just slipped your mind?

43. J-Mac, to Joe:

Are you suggesting what I think you suggesting, Joe?

Yes, J-Mac. That’s exactly what he’s suggesting.

It couldn’t be any more obvious.

ETA: Haha. I see you’ve added the “BTW:” part to your comment.

44. The difference, of course, is that when Joe quotes someone, he has the decency to indicate that he is doing so.

45. Joe Felsenstein: (I am in communication with Mike Lynch about making a response to this post).

So, you are not doing any work? Well that just makes the two of us…but it makes you a hypocrite caught in the act…lol 😉
Nothing new, eh?

But you are free to speculate about the fitness this and fitness that and still be afraid to go out in the wild to see what the real world looks like outside of your unfounded speculations…
What do you think?

46. The theory of mutation and natural selection developed during the 1920s, was relatively fully developed before Fisher’s 1930 book. Fisher’s

Joe Felsenstein and Michael Lynch
TSZ

and

“Population genetics theory had its major developments in the 1920s-1940s (at the hands of Fisher, Wright, and Haldane)” (p. xvii)

Joe Felsenstein
Theoretical Evolutionary Genetics

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