Rise, Fall and Circulation of Maximizing Methods in Population Genetics

This paper mentions the pioneering work of our very own Joe Felsenstein who is sometimes referred to as Mastermind of Evolutionary Biology.

This paper is of interest to me because I’m interested in highlighting whether population genetics is a help or is actually damaging to the case of universal common ancestry (UCD) or if the field is so conflicted as to not be a viable tool in the question of UCD at all.

I merely posting it as a conversation since at the present time I have no specialization in this topic.

Describing the theoretical population geneticists of the 1960s, Joseph Felsenstein reminisced: “our central obsession was finding out what function evolution would try to maximize. Population geneticists used to think, following Sewall Wright, that mean relative fitness, W, would be maximized by natural selection” (Felsenstein 2000). The present paper describes the genesis, diffusion and fall of this “obsession”, by giving a biography of the mean fitness function in population genetics. This modeling method devised by Sewall Wright in the 1930s found its heyday in the late 1950s and early 1960s, in the wake of Motoo Kimura’s and Richard Lewontin’s works. It seemed a reliable guide in the mathematical study of deterministic effects (the study of natural selection in populations of infinite size, with no drift), leading to powerful generalizations presenting law-like properties. Progress in population genetics theory, it then seemed, would come from the application of this method to the study of systems with several genes. This ambition came to a halt in the context of the influential objections made by the Australian mathematician Patrick Moran in 1963. These objections triggered a controversy between mathematically- and biologically-inclined geneticists, with affected both the formal standards and the aims of population genetics as a science. Over the course of the 1960s, the mean fitness method withered with the ambition of developing the deterministic theory. The mathematical theory became increasingly complex. Kimura re-focused his modeling work on the theory of random processes; as a result of his computer simulations, Lewontin became the staunchest critic of maximizing principles in evolutionary biology. The mean fitness method then migrated to other research areas, being refashioned and used in evolutionary quantitative genetics and behavioral ecology.

The paper is accessible from research gate:


EDIT: corrected “Master of Evolution” to “Mastermind of Evolutionary Biology”

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Now I want to change @Joe_Felsenstein’s title to “master of evolution”.


The correct phrase is “Mastermind of Evolutionary Biology”

Joe Mentions it here on his website:


  • Well, I suppose that being called (along with a lot of other people) a “mastermind of evolutionary biology” is cool. Artist Günter Bachelier has used some sort of genetic algorithm to modify an image of me, 1000 times.

Best quote from the paper by Lewontin:

‘‘Unfortunately, these maximization
principles turn out not to apply generally; and the only way to
know when they do is to solve the kinetic equations that we were trying
to avoid in the first place (…) we are still not free to ignore the material
particularities that underlie phenomena. When all is said and done,
‘God is in the details’’’ (Lewontin, 1982, pp. 113–114. See also
Lewontin, 1979). For

“God is in the details.” Amen.

Who refers to him that way?

What does this paper have to do with common ancestry?

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I feel certain that Sal intends some kind of point or perhaps lesson, but as usual he fails to say what it is. Any guesses?


Looks like a complex question fallacy to me, along with a failure to understand what the paper is about.

I suggest that you ask @Eddie for help. He’s read so much more than anyone else here, at least according to him…

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Gunter Bachelier. I provided a link to Joe’s own website where Joe himself said so.

I just learned that @Joe_Felsenstein is a Mastermind of evolutionary biology!!! How is that not a worthwhile discovery!

Apparently what it means is that my face is covered with all those triangles.


Merry Christmas and Gut Yontif, Joe and everyone else.

@Joe_Felsenstein, the paper is interesting nonetheless. Thanks @stcordova for posting it.

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Interesting. But not relevant, actually. I showed in my reply to Basener and Sanford’s paper in early 2018 at The Skeptical Zone that Basener and Sanford were completely wrong when they argued that the basic mathematics of natural selection versus mutation depended on Fisher’s Fundamental Theorem. I showed that the literature on mutation-versus-selection developed between 1903 and the late 1920s in a series of papers, and was well-established in the scientific literature by 1929. Fisher’s FTNS was in his 1930 book. The literature that Sal Cordova is reading is interesting in clarifying what the FTNS does and doesn’t mean, but it is very irrelevant to the issues of Basener and Sanford’s paper.


I didn’t interpret their statements that way because Bill specifically referenced George Price’s 1972 paper as the foundation of particular statement of Fisher’s theorem. Bill drew very heavily from the paper, and I think it’s unreasonable to think he missed this from Price (1972):

It has long been a mystery how Fisher (1930, 1941, 1958) derived his famous ‘fundamental
theorem of Natural Selection’ and exactly what he meant by it. He stated the theorem in these words (1930, p. 35; 1958, p. 37): ‘The rate of increase in fitness of any organism at any time is equal to its genetic variance in ftness at that time.’ And also in these words (1930, p. 46; 1958, p. 50): ‘The rate of increase of fitness of any species is equal to the genetic variance in fitness.’ He compared this result to the second law of thermodynamics, and described it as holding ‘the supreme position among the biological sciences’. Also, he 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 & 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 thetheorem holds only under very special conditions, while only a few (eg. Edwards, 1967) have thought that Fisher may have been correct – if only we could understand what he meant!

And in August 2016 , before they even began work in ernest on their paper, I alerted them to your gracious response to one my questions in December 11, 2015:

Absolute Fitness in Theoretical Evolutionary Genetics | The Skeptical Zone

Sal, this is a Fisher-like formula, a simplified version of one originally due to Sewall Wright.

I did not discuss the not-so-fundamental Fundamental Theorem of Natural Selection in the book, but I should put in a mention and citation. It turns out to be very hard to find a theorem that comes close to the FNTS and is also provable. There has been a big literature on this, with the most useful recent work by Anthony Edwards and Warren Ewens. You have to make a rather weird theorem to get one that is rigorously true.

The discussion that you found in Chapter II is the place in the book where I cover selection and mean fitness in haploids. See also section II.8 where I cover it for diploids.

So to the extent my colleagues’ (Bill and John’s) choice of words may have given the impression in your’s and Dr. Lynch’s minds that they believed FTNS was mathematically foundational to pop-gen theory, I don’t think that was their intended meaning, nor would it be consistent with the papers they themselves built their 2017 case on.

That said, now that I’m actually trying to read Price’s 1972 paper, I’m seeing the things a little more clearly…

Well, I think that this was their intended meaning. Anyway do go ahead cogitating on the FTNS and what it does and doesn’t mean. Knock yourself out. It will be irrelevant to the Basener-Sanford conclusions about mutation versus selection.

My interpretation of the paper cited in the OP is that in a population described by multi-loci, multi alleles per-loci – that in such a population, mean fitness doesn’t necessarily ever maximize. What seemed trivially obvious for single loci systems cannot be generalized to multi-loci systems.

Is that right? If we define

\text{adaptedness} \equiv \text{mean fitness } \bar{w}

then adaptendess may never head toward a maximum. Does that imply then there is no guarantee a population will become better adapted to its environment by natural selection?? :open_mouth:

The paper cited in the OP reference Joe Felsensteins work frequently, along with many other great masterminds of population genetics. A work that stood out was:

Mathematics Vs. Evolution
Felsenstein, Joe
Science; Nov 17, 1989; 246, 4932; ProQuest
pg. 941

many evolutionists will fail to find the clear and simple messages that population genetics theory once seemed to promise

Is the inevitability of adaptedness one of the promises that failed to be demonstrated mathematically?

It seems the only thing that might be maximized in real population with uncertain mutations in uncertain environments is uncertainty. Colloquially we can call increase in uncertainty as increase in entropy.

Thanks for reading, and thanks in advance for responses.

You don’t have to be perfectly adapted in order to be adapted.