hpb etc.

Fisher on the Brain

Greetings from the North of England. This post has nothing really to do with the photos, but that I've had these thoughts while walking along the River Wear and gazing at the Durham Castle from my office at the IAS.

In a post from the not-too-distant past, I sketched some views about whether Fisher's 'fundamental theorem' of natural selection is 'fundamental' (in some sense to be discovered and not defined). Here are those views again, presented in a slightly different way, with the addition of Alan Grafen's (2003) view. At the end, I state what I think is the best that can be said for the theorem's biological importance. (Thanks to all the folks in the Department of Science and Technology Studies at University College London who patiently listened to my seminar on the topic --and to Joe Cain who hosted me.)

Here's the theorem as we know it today (Edwards 1994, p. 450):

The rate of increase in the mean fitness of any population at any time ascribable to natural selection acting through changes in gene frequencies is exactly equal to its additive genetic variance at that time.

Here's a litany of folks who've evaluated the theorem's significance.

Fisher ([1930] 1999, pp. 36-37)

"[T]he fundamental theorem ... bears some remarkable resemblances to the second law of thermodynamics. Both are properties of populations, or aggregates, true irrespective of the nature of the units which compose them; both are statistical laws; each requires the constant increase in a measurable quantity, in the one case the entropy of the physical system and in the other the fitness ... of a biological population ... Professor Eddington has recently remarked that 'The law that entropy always increases --the second law of thermodynamics-- holds, I think, the supreme position among the laws of nature'. It is not a little instructive that so similar a law should hold the supreme position among the biological sciences."

Price (1972, pp. 139-140)

"First of all, the generality of [Fisher's] theorem is very great since it depends only on statistical smoothing through large population size and on assumptions of absence of meiotic and gametic selection that are involved in the derivation of [the theorem]."

"We may next note that the 'fundamental theorem' is very probably the most that anyone has yet been able to say correctly about evolutionary increase in fitness under general and realistic natural conditions. Thus, the theorem is by no means a trivial, uninteresting result."

"Still one feels disappointed that it does not say more ... Much more interesting would be a theorem telling of increase in 'fitness' defined in terms of some fixed standard. Thus there is the challenge here to find a deeper definition of this elusive concept 'fitness' and to give a deeper explanation of why it increases and under what conditions."

Ewens (1989, pp. 178-179)

"Price's concluding view [of the theorem] is in the negative, and he is 'disappointed that [the theorem] does not say more' ... These views are in line with my own negative assessment of the theorem as a biological statement."

"... [T]here appears to be no justification for singling out the partial change [in mean fitness] as isolating the 'natural selection' or 'change in gene frequency' component of the total change in mean fitness ...."

... "[W]e are left with the Fundamental Theorem as an exact, although possibly incomplete, evolutionary principle."

Edwards (1994, pp. 469-471)

"First is the historical fact ... that [the theorem] led Wright to the idea of an adaptive topography in gene-frequency space which has dominated so much thinking in evolutionary biology."

"Secondly, and of more permanent value, is the fact that the theorem gives mathematical precision to the previously vague notion 'that in species in which a higher proportion of the total variance is ascribable to genetic causes, the effective selection will be more intense than in species in which the variance is to a larger extent ascribable to environmental variations'."

"The third reason why the theorem is important is that correctly interpreted is has a considerable potential for future developments in mathematical population genetics."

Grafen (2003, p. 325)

"I have come to believe that Fisher was right in his beliefs about the importance of the theorem ... In my view, Fisher thought that his fundamental theorem isolated what we might call the adaptive engine of Darwinian natural selection."

"Thus the partial nature of change is not an inability to find a stronger result [contra Price and Ewens]. Fisher believed that this partial change was the only aspect of the changes in a population's genetic constitution that was progressive, that could create design."

Plutynski (2006, p. 75)

"Why did Fisher regard his theorem as so very 'fundamental'? The answer is that the fundamental theorem was a culmination of Fisher's lifelong project to vindicate Darwinism and unify the biometrical gradualist model of evolution and Mendelism in a rigorous mathematical theorem analogous to the physical sciences."

Here's about the best I think can be said about the theorem, based on what's gone before:

Fisher, Price, and Ewens are right that the scope of the theorem is very broad, but Price and Ewens are wrong to imply that scope is irrelevant to the theorem's biological significance. If there's anything to the claim that science (whatever "science" is) aims for general law-like statements or universal laws, then scope is relevant to the theorem's being fundamental. Price and Ewens are also wrong that the theorem's "incompleteness" is a defect because....

Fisher, Edwards, and Grafen are right that Fisher's isolation of natural selection and the additive genetic variance is a biologically deep statement that sets the speed limit on adaptive evolution. That is, the partial change in mean fitness says something biologically deep about the nature of selection. And, anyway, Edwards points out that the theorem is expandable (rather than worrying about its being incomplete). Of course, Edwards and Grafen are wrong to not include scope.

(Note that I've left out Plutynski. I think she's answering the wrong question.)

I'm not sure how far I can go to endorse the above. My main concern is that "additive genetic variance" is not biologically special. That is, I think Ewens is on to something when he says that there's no justification for isolating any change in gene frequencies that calls out natural selection. But, in order to really make my concern into a criticism, I've got to work through a bunch of literature on the relationship between additive and non-additive genetic variance and natural selection. Of course, I don't think doing so will settle anything. Folks get very ... excited about additive genetic variance, narrow heritability, the breeder's equation and all that. And I'm not sure I have anything original to say. But we'll see.

References

A. W. F. Edwards (1994), "The Fundamental Theorem of Natural Selection", Biol. Rev. 69: 443-474.

W. Ewens (1989), "An Interpretation and Proof of the Fundamental Theorem of Natural Selection", Theo. Pop. Bio. 36: 167-180.

R. A. Fisher ([1930] 1999), The Genetical Theory of Natural Selection. Oxford University Press.

A. Grafen (2003), ""Fisher the Evolutionary Biologist", The Statistician 52: 319-329.

G. Price (1972), "Fisher's 'Fundamental Theorem' Made Clear", Ann. Hum. Genet., Lond. 36: 129-140.

A. Plutynski (2006), "What Was Fisher's Fundamental Theorem of Natural Selection and What Was It For?", Stud. Hist. Phil. Biol. & Biomed. Sci. 37: 59-82.

Dispatches from the Seminar: FTNS

Last Monday (29 January), my HPB seminar met to talk about Fisher's "Fundamental Theorem of Natural Selection." (Go here for the reading list.)

It's well known that Fisher's own statement of the FTNS, whether he made it in the 1930 or 1958 edition of The Genetical Theory of Natural Selection or in the 1941 paper, "Average Excess and Average Effect of a Gene Substitution", is virtually impenetrable. And so the immediate question to ask in a seminar is "What does the FTNS say?" The second question, and perhaps the more interesting one, is, "What's fundamental about the FTNS?"

The Price-Ewens interpretation is widely acknowledged to be the one that captures what Fisher wanted to say with the theorem (Ewens 1989, Price 1972). At the same time, probably the clearest statement of the theorem in words is Edwards' (1994). Edwards accepts the Price-Ewens derivation of the theorem, as he should it seems, but he words the theorem in a way that captures what Price and Ewens accomplished in more "Fisherian" terms. He says (Edwards 1994, p. 450):

The rate of increase in the mean fitness of any organism at any time ascribable to natural selection acting through changes in gene frequencies is exactly equal to its genic variance in fitness at that time.

Compare this to Fisher's 1958 (p. 37) version of the theorem:

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

Edwards (1994, pp. 450-451) explains his statement of the FTNS as follows:

This [the statement of the theorem above] is as close as I can get to Fisher's wording whilst following the interpretation of Price and Ewens. "Genic" has replaced "genetic" [to capture that Fisher means 'additive genetic variance'] and 'mean fitness' has replaced 'fitness of any organism'; these are uncontroversial rewordings. ... I have added 'ascribable to natural selection acting through changes in gene frequencies' from Fisher's own words: 'ascribable to natural selection' is from his 1941 explanation of the Theorem and '[due to all] changes in gene frequencies' is from the sentence preceding his statement of the theorem [in 1930 and 1958] modified as suggested by Price. Price and Ewens repeatedly emphasize that Fisher thought  of the immediate effect of natural selection as being only through the changes in gene frequencies. For the sake of minimizing the changes I have kept Fisher's word 'organism', though it would not now be the first choice; in fact Fisher himself replaced it by 'species' in the Summary at the end of Chapter II of The Genetical Theory. 'Population' might now be the preferred word.

So let's say, then, that the FTNS states the following:

The rate of increase in the mean fitness of any population at any time ascribable to natural selection acting through changes in gene frequencies is exactly equal to its genic variance in fitness at that time.

Let's also be clear about the theorem's assumptions: no mutation, fixed fitness values, no fertility differences, no random effects, no geographical structure, one sex only, and all the other usual assumptions except that there is no restriction on the mating structure (Ewens 1989,p. 167-168).

With all that said, Fisher's FTNS is true and exact (Edwards 1994, Ewens 1989, Price 1972). It seems to me that this is all quite uncontroversial and barely worth mentioning except for background to the more important question of the theorem's biological "fundamentality."

Out of Fisher's Genetical Theory, the papers by Edwards, Ewens, Price and a new philosophical paper by Plutynski (2006), who agrees with the Price-Ewens derivation of the theorem, our seminar listed several candidate answers to the question:

Fisher (1958, pp. 37-39)

For Fisher, the theorem makes a "deep" biological claim about the nature of selection, that is, that the partial change in mean fitness is due to single-locus gene frequency changes. Fisher also thought that the theorem's biological depth and more generally its scope afforded a comparison to the Second Law of Thermodynamics.

Price (1972, pp. 139-140)

Price thinks the main importance of the theorem for biology is its scope (it requires only statistical smoothing through large N and on assumptions of no meiotic and gametic selection). Price also thinks that the theorem is the best anyone had said (at least by 1972) about natural selection. At the same time, Price thinks the theorem isn't as important, biologically, as Fisher thought, due to what he (and others) consider(s) to be the defect of treating non-additive gene effects as "environment." He further thinks that the theorem is defective because it appears to treat mean population fitness as always increasing but generally close to zero.

Ewens (1989, p. 179)

Ewens agrees with Price's assessment of the biological importance of the theorem. He's a bit clearer, however: Ewens doesn't see any justification for singling out the partial change in mean fitness Fisher does as isolating natural selection from the total change in mean fitness. After all, all of the terms of the FTNS, mean fitness, average excess, and average effect all depend on gene frequency and all change with changes in gene frequency.

Edwards (1994, p. 469-470)

Edwards says "Fisher's Fundamental Theorem of Natural Selection is important for three reasons. (p. 469)" First, the theorem directly influenced Wright's construction of the adaptive topography. Second, he agrees, mostly, with Fisher's assessment of the theorem and thinks we can't have expected more out Fisher than he gave (contra Price and Ewens). Third, it's extendable.

Plutynski (2006, p. 75)

According to Plutynski, Fisher regarded his theorem as "so very fundamental" because it was "a culmination of Fisher's lifelong project to vindicate Darwinism and unify the biometrical gradualist model of evolution and Mendelism in a rigorous mathematical theorem analogous to the physical sciences."

My own view about these five candidate answers to the "fundamentality" question is this: Price and Ewens are right. And I think we've all known this for a long time. Their assessment just follows from the math (see especially Ewens 1989, p. 171). If Fisher had captured what he thought he did with the theorem, then I think the FTNS would be fundamental in evolutionary genetics in the same way that the Hardy-Weinberg Equilibrium Principle is --you can't do population genetics without it.

Fisher is incorrect about the "depth" of the theorem for precisely the reasons Price and Ewens give about the lack of justification for singling out the partial change in mean fitness as isolating natural selection from the total change in mean fitness. This means that Edward's third reason for the importance of the theorem is mistaken. I'm certain Edwards' first reason is wrong, that is, that Wright didn't get the idea of the adaptive topography from Fisher. This is easy to see just by reading Provine's (1986) biography. And I'm not terribly confident about the substance of Edwards' third reason, although it's more a question that will be answered by history (but see Frank and Slatkin 1992 and Lessard and Castilloux 1995 for extensions of the theorem to clutch size and to fertility selection respectively).

I admit I'm not sure I understand Plutynski's claim. (Neither did the seminar participants.) Actually, I think there are lots of problems with the paper. But focusing just on Plutynski's claim about the importance of the theorem, one wonders what she means when she asks, "Why did Fisher regard his theorem as so very 'fundamental'?" (2006, p. 75). Actually, I don't know if any answer to that question is much more than historical/philosophical speculation about what was going on in Fisher's head at the time. Anyway, it's not the right "fundamentality" question to ask. But I can't see in the paper where Plutynski clearly answers the question about the theorem's biological "fundamentality." She does agree with the Price-Ewens derivation of the theorem, but it's not clear she agrees with their assessment of its importance.

Ultimately, there's not much new historically or philosophically to say about Fisher's FTNS specifically. The more interesting question concerns the place of the theorem in Fisher's larger argument for neo-Darwinism. And, actually, this is where Plutynski's paper is quite relevant. I don't think focusing on the theorem as she does, though, is the right way to answer it. But what Plutynski does say about the structure of Fisher's argument strikes me as backwards. She gets it right when she says that the theorem culminates Fisher's neo-Darwinian argument, but that's small beer --the theorem came pretty much last in the effort, so of course it does. It's the details of Fisher's argument Plutynski gets wrong. This is a major research topic of mine at the moment, and you'll see some of it on this blog in due time. For now, see here and here; there are glimmers.

References

Edwards, A. W. F. (1994), "The Fundamental Theorem of Natural Selection", Biological Reviews of the Cambridge Philosophical Society 69: 443-474.

Ewens, W. (1989), "An Interpretation and Proof of the Fundamental Theorem of Natural Selection", Theoretical Population Biology 36: 167-180.

Fisher, R. A. (1930, 1958, 1999), The Genetical Theory of Natural Selection. Oxford: Oxford University Press.

Fisher, R. A. (1941), "Average Excess and Average Effect of a Gene Substitution", Annals of Eugenics 11: 53-63.

Frank, S. and M. Slatkin (1992), "Fisher's Fundamental Theorem of Natural Selection", TREE 7: 92-95.

Lessard, S. and A.-M. Castilloux (1995), "The Fundamental Theorem of Natural Selection in Ewens' Sense: Case of Fertility Selection. Genetics 141: 733-742.

Plutynski, A. (2006), "What was Fisher's Fundamental Theorem of Natural Selection and What was it For?", Studies in History and Philosophy of Biological and Biomedical Science 37: 59-82.

Price, G. (1972), "Fisher 'Fundamental Theorem' Made Clear", Annals of Human Genetics 36: 129-140.

Provine, W. (1986), Sewall Wright and Evolutionary Biology. Chicago: University of Chicago Press.

My HPB Seminar

My history and philosophy of biology seminar had its first meeting on Monday (8 January). I mentioned a post or so ago that I would post the reading list; you'll find it below, sans some of the citation information. Here's the syllabus. (Anyone who wants cites can email me.)

The seminar follows the arc of Mike Dietrich's, "From Mendel to Molecules" paper in Fox and Wolf's Evolutionary Genetics: Concepts and Case Studies. Incidentally, that anthology is just excellent. I don't think there's a paper not worth reading in the bunch. (If only philosophers of biology would pick it up!) Razib, over at Gene Expression, has been working through the book.

At any rate, as I say, my seminar follows the arc of Dietrich's paper. Dietrich's brief history of evolutionary genetics is of its core controversies, starting with early critiques of Darwin's pangenesis all the way to controversies over the molecular clock. My course structures the history in the same way, but I don't cover as much ground. Actually, I can't cover that much ground in what for me will be an abbreviated quarter --only 8 meetings. (And I doubt I could do much better in 10.)

We started out yesterday with Dietrich's paper as background and I gave an overview of the topics we're going to focus on. There's a general theme of the rise and fall (?) of panselectionism. But there are more specific issues in the conceptual foundations of evolutionary genetics and the nature of scientific controversy. Our next meeting, a sort of two-in-one since we won't meet on MLK Day, covers the origins of population genetics and a sketch of the evolutionary synthesis --or at least the synthesis of Mendelian genetics and Darwinian natural selection. We'll have read:

• Provine 2001, The Origins of Theoretical Population Genetics
• Fisher 1922, "On the Dominance Ratio"
• Fisher 1930a, "The Distribution of Gene Ratios for Rare Mutations"
• Wright 1931, "Evolution in Mendelian Populations"
• Haldane 1932, The Causes of Evolution, Appendix
• Provine 1986, Sewall Wright and Evolutionary Biology, chapter 8 (on Wright, Fisher, and evolution)
• Hodge 1992, "A Study of Fisher and Wright"
• Gould 1983, "The Hardening of the Modern Synthesis"

I realize that's a huge amount of reading, including an entire book. But, in fact, I edited the list down. And, again, it's a two-in-one meeting.

Once we get the back story down, we'll launch into portions of the controversy between Fisher and Wright (see my own views here, here, and here), starting out with Fisher's Fundamental Theorem of Natural Selection:

• Fisher 1930b, The Genetical Theory of Natural Selection, chapter 2 (on the theorem)
• Price 1972, "Fisher's 'Fundamental Theorem' Made Clear"
• Ewens 1989, "An Interpretation and Proof of the Fundamental Theorem...."
• Edwards 1994, "The Fundamental Theorem of Natural Selection"
• Plutynski 2006, "What was Fisher's Fundamental Theorem...?"

I think I have a new way of reconstructing Fisher's construction of his theorem. So I'll no doubt have a lot to say about Plutynski's historical and philosophical view, and perhaps Price's, Ewens', and Edwards' views as well. After the FTNS, we look at Wright's adaptive landscape:

• Wright 1932, "The Roles of Mutation...."
• Provine 1986, Sewall Wright and Evolutionary Biology, chapter 9 (Wright's SBT)
• Wright 1988, "Surfaces of Selective Value Revisited"
• Ruse 1996, "Are Pictures Really Necessary?"
• Skipper 2004a "The Heuristic Role of … the Adaptive Landscape"
• Pigliucci and Kaplan 2006, Making Sense of Evolution, chapter 8 (on adaptive landscapes)

In addition to looking at Fisher's and Wright's disagreements with regard to their general theories, we'll also look at the problems endemic to each view and, on the landscape stuff, we'll worry a little about the role of diagrams in producing scientific knowledge.

Of course, this is really the tip of the iceberg in a discussion of Fisher's and Wright's theoretical disagreements. But time is a problem. And so we'll proceed to look at two key empirical debates, over the Panaxia dominula and Cepaea nemoralis:

• Provine 1986, Sewall Wright and Evolutionary Biology, chapter 12 (1940-1955)
• Turner 1987, "Random Genetic Drift...."
• Skipper forthcoming, "Revisiting the R. A. Fisher-Sewall Wright Controversy"
• Beatty 1987a, "Dobzhansky and Drift...."
• Millstein forthcoming, "Concepts of Drift and Selection...."

I'm not just interested in the debates over the roles of selection and drift in these cases, but also in the concepts of drift in particular and changes in methodology between the moth work and the snail work.

Finally, we get to the debates between Coyne, Barton, and Turelli and Wade and Goodnight over Wright's SBT, capping off our long if not truncated study of the Fisher-Wright Controversy.

• Coyne, Barton, and Turelli 1997, "A Critique of Sewall Wright's SBT"
• Wade and Goodnight 1998, "Evolution in Metapopulations...."
• Skipper 2002, "The Persistence of the R. A. Fisher-Sewall Wright Controversy"
• Skipper 2004b, "Calibration of Laboratory Models in Population Genetics"
• Plutynski 2005, "Parsimony in the Fisher-Wright Debate"

Of course we'll focus on the specific issues that occupied Coyne and Wade. But I also want to look at the role of parsimony in these specific disagreements. I've talked about this before, here. I haven't changed my mind.

Then we leave Fisher and Wright and move forward to the Classical-Balance Controversy and the "Electrophoretic Revolution":

• Muller 1950, "Our Load of Mutations"
• Dobzhansky 1955, "A Review of Some Fundamental Concepts...."
• Beatty 1987b, "Weighing the Risks...."
• Lewontin 1974, The Genetic Basis of Evolutionary Change, chapter 5 (paradox of variation)
• Gillespie 1991, The Causes of Molecular Evolution, chapter 1 (protein evolution)
• Skipper forthcoming, "Stochastic Evolutionary Dynamics: Drift vs. Draft"

In this part of the course I'm really looking at the nature of selection and explanations of genetic variation. So, the emphasis will largely be on Lewontin's discussion of the Classical and Balance positions and Maynard Smith and Haigh's hitchhiking response and then later Gillespie's new approach in the guise of genetic draft. Lots and lots of selection here folks.

In our last meeting, we'll look at the neutral theory and its role not only in Lewontin's discussion but its place in evolutionary genetics more broadly.

• Dietrich 1994, "Origins of the Neutral Theory"
• Kimura 1968, "Evolutionary Rate at the Molecular Level"
• King and Jukes 1969, "Non-Darwinian Evolution"
• Dietrich 1998, "Paradox and Persuasion"
• Dietrich and Skipper forthcoming, "Manipulating Underdetermination...."

The cornerstone piece is really Dietrich's "Origins of the Neutral Theory." I say just go get it and read it. In addition to exploring the neutral theory's origins, we'll look at the controversy between Takahata and Gillespie over the nature of the molecular clock. More selection, obviously, but also biological theory assessment in situations of underdetermination.

I know I've left a huge amount off my reading list. In part, I did that because I want my students to discover some things on their own. (This is supposed to be a learning experience after all.) But I also had to consider how much heavy reading I could expect a group of mostly philosophy of science students could take in a single week. And I'm sure I'm asking too much. (I always ask too much, so don't suggest I stop, because I won't.)

I'm excited about the seminar. Not only is it the sort of seminar I've wanted to run since I got this job at UC (sorry, Razib), but the timing is terrific: I'm working on Fisher during the spring, and I think a book reflecting the topics of the seminar is falling into place.

We meet next on 22 January. If something interesting happens or if I just have something worth blogging about, I'll do so.

Does (Population) Size Matter (in Evolution)?

In the 28 April issue of Science, Eric Bazin, Sylvain Glémin, and Nicolas Galtier report that population size matters for nuclear DNA diversity, but not for mitochondrial DNA diversity. The paper was forwarded to me by one of my favorite philosophers of biology because of the explanation Bazin et al. offer for explaining the disconnection between mtDNA diversity and population size: genetic draft. Here's the story.

A basic tenet of population genetics theory is that population size and extent of genetic diversity are intimately connected. Large populations, in fact, should be genetically more diverse than small ones. Why? Neutral genetic variation is modulated by drift and mutation. Drift removes genetic variation while mutation adds it. In small populations, drift removes variation faster than mutation can add it. But as populations get larger and larger, drift is less and less effective at removing genetic variation.

This basic tenet of population genetics was challenged by allozyme polymorphism studies of genetic diversity in the 1960s. What the data suggested was that if this tenet were correct, the population sizes of the represented species should be roughly equal (see Lewontin 1974 for discussion). But of course population sizes are not equal.

By the 1980s, biologists learned that the situation suggested by the allozyme data was not nearly so bad (see Gillespie 1991 for discussion). Yet, the puzzle of the connection between population size and genetic diversity persists. In fact, the nature of genetic variation has long been something of a mystery from the point of view of population genetics.

John Maynard Smith and John Haigh (1974) offered genetic hitchhiking, or linked selection, as a solution to the apparent population size paradox suggested in Richard Lewontin's (1974) review. The idea is that when an advantageous mutant is swept to fixation by selection, genetic variation at loci that are linked to the mutant is reduced. Genetic homogeneity in large populations could be due to such a process. Maynard Smith and Haigh's hitchhiking explanation languished in large part because it depends on populations having high linkage disequilibrium.

Allozyme polymorphism studies of population diversity have been replaced by DNA-based marker studies, especially mitochondrial DNA (mtDNA) marker studies. In their Science paper, Bazin et al. analyzed diversity data for nuclear DNA from 417 species, mitochondrial DNA from 1,683 species, as well as allozyme data for 912 species. The team tested the connection between population size and genetic diversity against several ecological and phylogenetic factors. Every comparison of nuclear DNA data was congenial with the idea that population size and levels of genetic variation are connected. But not so for the mitochondrial DNA data. mtDNA variation across species, according to Bazin et al., is independent of population size.

By the end of the 1980s, some data became available that showed that genetic variation is reduced in regions of low recombination in Drosophila (see Gillespie 2001). For this reason, among others, John Gillespie revisited the hitchhiking hypothesis (2000a, 2000b, 2001). But rather than following Maynard Smith and Haigh's deterministic model, Gillespie developed a stochastic model of a process he calls genetic draft. The essential difference between genetic draft and genetic hitchhiking is that, for draft, random variables are used for the timing of a hitchhiking event and the probability that the neutral allele is linked to a selectively advantageous mutation. Gillespie was able to disconnect population size and levels of genetic variation.

Bazin et al. suggest that the homogeneity of genetic variation across species for the mtDNA data can be explained by genetic draft. Why draft? There were only very low levels of recombination in mtDNA relative to nuclear DNA. They thus think that mtDNA is ripe for hitchhiking events of the sort Gillespie describes (including his assumptions about the rate of substitution).

Of course, low levels of recombination in mtDNA relative to nuclear DNA is not enough to establish the conclusion that genetic draft explains the independence of genetic variation from population size for mtDNA. Bazin et al. also need evidence of selective substitutions --the triggers for hitchhiking events. For that, they appeal to the neutrality index as a measurement of selection. A neutrality index that is <1 is taken to show that selective amino acid substitutions have occurred. The median values of the neutrality index for both vertebrates and invertebrates is <1. Indeed, Bazin et al. argue that 58% of amino acid substitutions are selectively advantageous in invertebrate mtDNA and 12% in vertebrate mtDNA.

Other explanations for the mtDNA genetic diversity data include variations in mitochondrial mutation rate, population bottlenecks, and background selection. Bazin et al. consider each of these alternatives, but argue for various reasons that they are less likely than the genetic draft explanation. They claim, for instance, that variation in mitochondrial mutation rate is an unlikely explanation because they think it's unlikely that that mutation rate is inversely related to population size throughout the animal taxa represented in the data. They think bottlenecks are unlikely because they would have to affect the nuclear genome as well, but that was not observed. Background selection is unlikely because there is still an expectation that genetic variation increases as population size increases, which was not observed for the mtDNA data. By elimination, then, Bazin et al. end with genetic draft as the best explanation of the data.

Note: For those of you into human evolution, the summary article by Adam Eyre-Walker preceding Bazin et al.'s paper  points out that humans appear to be an exception to their observed pattern. Eyre-Walker says, "[i]f the authors are correct, then the effective population size estimated from the mitochondrial DNA should be lower than that estimated from autosomal DNA. This is not what we see in humans; the effective population sizes estimated from autosomal DNA, Y-chromosome DNA, and mitochondrial DNA are all approximatley 10,000" (p. 538). Eyre-Walker doesn't conclude that Bazin et al.'s observations are wrong. Just that "humans have such small effective population sizes that adaptive evolution in the mitochondrial genome is very rare...." (p.538).

References

Bazin, E., Glémin, S., and Galtier, N. (2006), "Population Size Does Not Influence Mitochondrial Genetic Diversity in Animals", Science 312: 570-572.

Eyre-Walker, A. (2006), "Size Does Not Matter for Mitochondrial DNA", Science 312: 537-538.

Gillespie, J. H. (1991), The Causes of Molecular Evolution. New York: Oxford University Press.

Gillespie, J. H. (2000a), "Genetic Drift in an Infinite Population: The Pseudohitchhiking Model", Genetics 155: 909-919.

Gillespie, J. H. (2000b), "The Neutral Theory in an Infinite Population", Gene 261: 11-18.

Gillespie, J. H. (2001), "Is the Population Size of a Species Relevant to its Evolution?", Evolution 55: 2161-2169.

Gillespie, J. H. (2004), Population Genetics: A Concise Guide. Baltimore, MD: Johns Hopkins University Press.

Lewontin, R. C. (1974), The Genetic Basis of Evolutionary Change. New York: Columbia University Press.

Maynard Smith, J. & J. Haigh (1974), “The Hitch-hiking Effect of a Favourable Gene”, Genetical Research 23: 23-25.

First-Rate Posts Around the Blogosphere

Sometimes, the blogosphere offers up some first-rate consumables. What ties together my three recent favorites below is that each involves philosophy of biology in one way or another (and usually not favorably).

RPM of Evolgen argues that evo-devo "doesn't really explain much." Many philosophers of biology, in my view at least, are currently bordering on an obsession with evo-devo as the new "sliced bread" of evolutionary biology. I liked RPM's brief argument. (See here, too, one of the best comments I've ever seen on my own blog, by Rasmus Winther, about my "assertion" that evo-devo won't make population genetics go away.)

John Hawks, who is too smart for his own good, wrote up a remarkable post on Massimo Pigliucci's recent paper in Biology and Philosophy (see, philosophy, even though Pigliucci is a biologist) critiquing the use of the genetic variance-covariance matrix in evolutionary genetics. The post is more than thorough and very much worth the read.

Finally, Chris of Mixing Memory revisits his review of philosopher David Buller's book critizing evolutionary psychology (EP), Adapting Minds (MIT Press). According to Chris, "Buller's book has been rendered worthless." I've not read the book, because reading EP is too painful for me. But negative assessments have been in the philosophical air since it came out, and Chris mentions a newer review by philosopher Edouard Machery and Clark Barrett who are critical. Note: Chris points to one philosopher who claimed that Buller's book "demolished EP." I followed the link: There's no need to take it seriously.

There's lots of critical stuff to say about EP. One of my colleagues has a book coming out on the topic, which, when it's nearly out, I'll mention on this blog.

Whatever Happened to the Fisher-Wright Controversy? Final

This is the third and last installment in my "revisiting the Fisher-Wrigt controversy" series The first installment is here; the second is here. For a little context, I repost the introductory paragraph from the first and second posts. (This is another long post; just a warning.)

R. A. Fisher, J. B. S. Haldane, and Sewall Wright are the architects of theoretical population genetics. Between 1918 and 1932, these three theorists ushered in the field and set the stage for the period of the history of evolutionary biology usually called the "evolutionary synthesis." It's well known that from 1929 until Fisher's death in 1962 that Fisher and Wright were engaged in a sometimes heated controversy over their alternative qualitative interpretations of their quantitative models. In 1985, Will Provine published "The R. A. Fisher—Sewall Wright Controversy" in Oxford Surveys of Evolutionary Biology (Provine 1985). In that paper, Provine discusses three key disputes between Fisher and Wright: (1) evolution of dominance, (2) their general evolutionary theories, and (3) evolution of the Scarlet Tiger Moth, Panaxia dominula. Now, Provine's biography of Wright published in 1986 is a fuller treatment of the controversy (Provine 1986). However, I'm in the process of writing, basically, a new version of Provine's paper in which I revisit each of the debates of his 1985 essay. In this post, I look at Fisher's and Wright's dispute over their general evolutionary theories . I think I don't quite do justice to the debate with this post, but I do think it's a fair overview. And it does presume some familiarity with Fisher's and Wright's general evolutionary theories.

The debates between Fisher and Wright during the late 1920s and 1930s, over dominance and their general evlutionary theories, were largely theoretical. However, in 1947, Fisher, with the ecological geneticist E. B. Ford published an experimental paper aimed at discrediting Wright's Shifting Balance Theory and substantiating Fisher's natural selection theory (Fisher and Ford 1947). Fisher and Ford's paper describes and analyzes data from what was at the time a fairly novel field experimental technique, the capture and release protocol, used in populations of the moth Panaxia dominula. Fisher and Ford argued via their experimental results that even in small(ish) populations ( between 1,000 and 10,000) -Wright's assumed norm- genetic drift -Wright's most important evolutionary factor according to Fisher and Ford- was evolutionarily inefficacious. Fisher and Ford argue further that natural selection, even in smallish populations, is the driving factor of evolution.

The capture and release protocol that Fisher and Ford describe in their 1947 paper was carried out between the years 1939-1946. Moths, mainly in Cothill, Oxfordshire, England, were captured (and re-captured), marked inconspicuously with paint (or not if re-captured), scored for phenotype of interest (or as a re-capture), and released if unharmed. The purpose of Fisher and Ford's capture and release protocol was to collect data over time for fluctuations in frequency of genes of interest by scoring particular phenotypes, here wing coloration patterns. The Scarlet Tiger moth is easily identified by its wing coloration. The forewing is black with iridescent green structural coloring and a pattern of green or white spots. The hind wing is usually bright scarlet with black markings. In Fisher and Ford's Panaxia study, form dominula, f. medionigra, and the very rare f. bimacula refer to particular patterns of wing coloration that were assumed to correspond to dominant homozygous (AA), heterozygous (Aa), and recessive homozygous (aa) genotypes respectively (color plates can be found in Fisher and Ford 1947). Breeding studies had been done by E. A. Cockayne (1928), Ford (1940), and H. B. D. Kettlewell (1942) which provided the genotype-phenotype correspondence. (Note: Sorry that there is no photo here. In my experience, the Typepad blogging software is poor at handling images.)

Fisher and Ford argued  their data showed  the fluctuations in the frequencies of the f. medionigra genes were too large from year to year to be due to genetic drift. Essentially, their specific argument was that even though population size was sufficiently small for genetic drift to be effective, drift nevertheless was not a factor (because the gene frequency changes were too high to merely be due to chance). For the years the population was studied, the average population size was in the range of 3,200-4,000 moths, with approximately 11% overall being f. medionigra, and a total gene frequency change of approximately 6% (Fisher and Ford 1947: 150, 164). Fisher and Ford ultimately inferred that because changes in gene frequencies in the moth populations were not due to random genetic drift, they must be due to natural selection.

In 1948, Wright published a critique of Fisher and Ford's study (Wright 1948). Wright objected on several grounds. First, Fisher and Ford had misinterpreted the role Wright had assumed for random genetic drift. They attributed to him more of a role than he, himself, had attributed. Second, their inference that selection must be the cause of the changes in gene frequencies in the populations of the moths was not justified experimentally. Fisher and Ford provided no direct evidence that selection is the cause; they only infer it after rejecting drift. Wright's paper drew an acerbic attack from Fisher and Ford published in 1950 (Fisher and Ford 1950). Wright (1951) again responded. The substance of the disagreement, after Wright (1948), is the problem of interpreting Wright's view of the role of genetic drift in evolution. These exchanges have all been thoroughly discussed by Provine (1986). What I am about to discuss has not been discussed (at least not the work since 1962; but see Provine's 1986 brief discussion of Ford's summary of the work in the 1964 and 1975 editions of his Ecological Genetics, Ford 1964; 1975).

The experimental work on Panaxia has continued in the spirit of Fisher and Ford's pioneering study. In fact, the work on Panaxia comprises one of the longest-running ecological genetics field experiments, lasting around 60 years, in the history of the scientific field, with the most complete scientific review having been completed by L. M. Cook and David A. Jones for the years 1939-1995 (Cook and Jones 1996). Basically, the ongoing Panaxia work has been, by and large, taken as 60 years of replication of Fisher and Ford's 1947 findings. (Certainly Cook and Jones agree with this assessment.) Interestingly, the only direct observational evidence of selection (e.g., observation of a long-term environmental perturbation such as predation, see e.g., Endler's 1986, chapter 3 methods of detection) acting to change gene frequencies of the f. medionigra genes in the Panaxia work is due to P. M. Sheppard working with Cook and with Ford (Sheppard 1951; Sheppard and Cook 1962; Ford and Sheppard 1969). The selectionist interpretation of the Panaxia work has largely been based on the same eliminative inference (i.e., the inference from observed gene frequency fluctuations independent of a perturbation) Fisher and Ford made in 1947 (in spite of Wright's 1948 criticism of it).

Between 1993 and 1997, however, Cyril A. Clarke, David Goulson, and Denis F. Owen published a series of experimental and review papers criticizing the broad-ranging Panaxia work (Owen and Clarke 1993; Owen and Goulson 1994; Goulson and Owen 1997). Interestingly, the biologists started out with the intention of replicating Fisher and Ford's (1947) results. However, each of the biologists argue ultimately  there are good reasons reject the selectionist interpretation of the data: Selection is not the cause of the changes in gene frequencies. Genetic drift is not the cause either.

Owen and Clarke in 1993 reported and analyzed data from a combined reared and wild capture and release protocol with Panaxia in 1991-1992 in Cothill and two other Oxfordshire fens (viz., Dry Sandford, North Hinksey). During their protocol, they noted  f. medionigra was extremely variable. Owen and Clarke were suspicious of this variability, prompting them to change their scoring technique. Rather than scoring the moths simply for the three forms, following Fisher and Ford (1947), they complicated their technique, scoring the phenotype by more specific patternings of wing coloration (Owen and Clarke 1993: 396-397). On the standard model, moths with a small or absent spot combined with either a yellow, black, or absent hindwing spot are scored as f. medionigra. Owen and Clarke scored only moths with a small or absent forewing spot in combination with a black hindwing spot as f. medionigra; the others were scored as f. medionigra-like. Using the revised scoring model, the frequency of the apparent f. medionigra gene frequencies that Owen and Clarke reported were, they claim, some of the largest on record (Owen and Clarke 1993: 398). Depending on which phenotypes are scored as f. medionigra, with the low frequency scoring only f. medionigra and the high frequencies all-inclusive, the frequency estimates were 0.4%-49% for their 1991 reared population, 0.4-2.7% for their 1992 wild population, and a remarkable, so they claim, 2.7%-41.9% for their 1992 reared population. This last is four times as high as any population since 1939.

Owen and Clarke found the variability in their data, tied directly to the variability in the form of the moth, impossible to reconcile without looking more closely at the causes of the variability. Although they could not definitively say, they suggested  the extreme variability of wing coloration phenotypes was due to an environmental factor (this effect is well understood by developmental biologists but perhaps less so by ecologists). Temperature fluctuations, which would cause an overall darkening in the wing color pattern would make f. dominula look more like f. medionigra and f. medionigra look more like the rare f. bimacula. Owen and Clarke believed such an environmental effect would account for the exaggerated representation of f. medionigra on the standard scoring model. Owen and Clarke raised the issue that Fisher and Ford's original study, as well as the subsequent studies, may be compromised due to probable scoring errors related to temperature effects on the expression of the wing coloration phenotypes in the moths. That is, the gene frequency data may be corrupted because some phenotypes may have been scored as the wrong genotype. Such scoring errors, argued Owen and Clarke, would skew the results and their analysis significantly. Owen and Clarke noted something interesting: Kettlewell had done temperature controlled breeding experiments in the lab in 1943-1944 (Kettlewell 1943/1944). He had shown  temperature fluctuations caused differences in expression of the wing coloration phenotype. Now, Kettlewell's experiments were done before Fisher and Ford's 1947 paper. Yet, Fisher and Ford, at least according to the published record, did not mention Kettlewell's findings. (The paper of Kettlewell's that Fisher and Ford do cite is not his temperature effects paper.)

In 1994, Owen and Goulson published a paper demonstrating  temperature fluctuations cause changes in the expression of wing coloration during pupal development of the moth (Owen and Goulson 1994). Genes that under mild, or normal temperatures express to look like f. dominula will under more extreme temperatures express to look like f. medionigra. To show this, Owen and Goulson had done lab breeding experiments in controlled temperature environments on Panaxia (larvae) they had brought in from Cothill and North Hinksey. The wings of moths raised in temperatures below 12°C and above 24°C darken. They then argued  there is no reliable way of tracking (in nature) changes in gene frequencies in Panaxia by observing and scoring phenotypes: Temperature fluctuations significantly affect the phenotype, belying the genotype. Ultimately, Owen and Goulson concluded  the Panaxia work is not good support for the prevailing selectionist interpretation of the Panaxia data.

There were no temperature data records in Fisher and Ford's studies; similarly for the subsequent ones. So, there is really no way to know whether temperature fluctuations really played any role in the variability of wing coloration in the moths during Fisher and Ford's or subsequent studies. Cook and Jones (1996), supporters of Fisher and Ford, claim in their review of the Panaxia work that there is nothing to worry about: They statistically analyzed weather data, independently recorded, and concluded  temperature fluctuations likely did not affect expression of the wing coloration trait (Cook and Jones 1996, 1625). So, the long-standing support for natural selection by the Panaxia work, according to Cook and Jones, goes undiminished by Owen and Goulson's 1994 temperature work.

By 1997, Goulson and Owen had done additional temperature experiments and had re-scored museum specimens of Panaxia originally scored by Fisher, Ford, their workers and subsequent workers (Goulson and Owen 1997; cf. Clarke et al. 1991). Goulson and Owen found errors in scoring had occurred in the Panaxia capture and release studies according to the Owen-Clarke revised scoring technique. Cook and Jones, in 1996, never comment on this possibility. Yet, it had been argued by Owen and Clarke (1993) that such errors were likely. Further, Goulson and Owen's newer temperature experiments further substantiate their claim  the expression of wing coloration phenotypes in Panaxia is all but controlled by fluctuations in temperature. Goulson and Owen's ultimate assessment of the Panaxia work and its contribution to the Fisher-Wright controversy is this (Goulson and Owen 1997: 616-617): Due to the severe problems with the Panaxia experimental methodologies, the results of the work must be rejected as a way of settling Fisher's and Wright's disagreement over the role of drift in evolution. As I see matters, Wright's (1948) original critique of Fisher and Ford's (1947) argument that the elimination of drift is sufficient to establish selection, ignored from the moment Wright raised it, is substantiated.

Jones, in 2000, published a paper that weakens Goulson and Owen's (1997) conclusion (Jones 2000). What Goulson and Owen lacked was a capture and release study of gene frequency fluctuations in the moth that included the relevant experimental check for temperature fluctuations. Jones (2000) published that study. Jones captured and released moths in Cothill, Oxfordshire during the years 1995-1999. Jones followed Owen and Clarke's (1993) scoring model. And, importantly, Jones monitored temperatures were monitored in precisely the locations in the Cothill Fen that the larvae of the moths pupate. For an average year-to-year population size in the range of 3,100-5,000 moths, Jones recorded gene frequency fluctuations in f. medionigra in the range 0.73% to 2.62%. Jones further found  air temperature reached lows and highs exceeding the boundaries at which Owen and Goulson (1994) reported darkening of the wings in the laboratory. Temperatures in the Cothill Fen litters ranged from 4°C to 33°C (Jones 2000: 580). However, the larvae and pupae never experienced those extremes for a prolonged period of time during any month between 1995 and 1999. The monthly mean was well within the 12°C to 24°C range for normal wing development (Jones 2000: 584).

Jones' (2000) gene frequency fluctuation data is consistent with the data collected since 1939. However, Jones never explicitly attributes the fluctuations he recorded between 1995 and 1999 to natural selection. Rather, Jones' purpose was to cast doubt on Owen and Goulson's (1994) criticism of the historical Panaxia work. My view is  Jones has done just that. But he has not managed to remove all doubt cast upon the selectionist interpretation of the historical work. Again, Wright's (1948) original criticism of Fisher and Ford's (1947) argument for selection by elimination of drift stands. The Panaxia work is not a strong case to adjudicate between the relative roles of selection and drift in evolution.

Jones' (2000) paper is, so far as I am aware, the most recent in the ongoing Panaxia work. It is hard to say whether his assessment of the work will conclude the debates. Approximately 60 years have been devoted to the Panaxia work in efforts to resolve Fisher's and Wright's original disagreement over the role of random genetic drift in evolution. The first 10 years of work were hotly debated by Fisher, Wright and their immediate associates (e.g., Ford, Sheppard). About 40 years hence have been taken up with the assumption that the continued work has successfully replicated Fisher and Ford's demonstration of the primacy of selection in (even smallish) populations of Panaxia in England. It has only been in the last 15 years that work has been done to confute the selectionist interpretation. And that work did not start with that intention; Owen and Clarke (in particular) thought they were just going to replicate the long-standing selectionist results (Owen and Clarke 1993: 393).

References

Clarke, C., F. Clarke, and D. Owen (1991), "Natural Selection and the Scarlet Tiger Moth, Panaxia dominula: Inconsistencies in the Scoring of the Heterozygote, f. medionigra", Proceedings of the Royal Society of London B 244: 203-205.

Cockayne, E. A. (1928), “Variation in Callimorpha dominula”, Entomological Record 40: 153-160.

Cook, L. M. and D. Jones (1996), “The medionigra gene in the Moth Panaxia dominula: The Case for Selection”, Philosophical Transactions of the Royal Society of London B 351: 1623-1634.

Endler, J. (1986), Natural Selection in the Wild. Princeton: Princeton University Press.

Fisher, R.A. and E. B. Ford (1947), “The Spread of a Gene in Natural Conditions in a Colony of the Moth, Panaxia dominula, L.”, Heredity 1: 143-174.

Fisher, R.A. and E. B. Ford (1950), “The Sewall Wright Effect”, Heredity 4: 117-119.

Ford, E. B. (1940), “Genetic Research in the Lepidoptera”, Annals of Eugenics 10: 227-252.

Ford, E. B. (1964), Ecological Genetics. Welwyn Garden City, UK: The Broadwater Press, Inc.

Ford, E. B. (1975), Ecological Genetics. 4th edition. London, UK: Chapman Hall.

Ford, E. B. and P. M. Sheppard (1969), “The Medionigra Polymorphism of Panaxia dominula”, Heredity 24: 561-569.

Goulson, D. and D. Owen (1997), “Long-Term Studies of the medionigra Polymorphism in the Moth Panaxia dominula: A Critique”, Oikos 80: 613-617.

Jones, D. A. (2000), "Temperatures in the Cothill Habitat of Panaxia (Callimorpha) dominula L. (The Scarlet Tiger Moth)", Heredity 84: 578-584.

Kettlewell, H. B. D. (1942), “A Survey of the Insect Panaxia (Callimorpha) dominula”, Proceedings of the South London Entomological History Society: 1-49.

Kettlewell, H. B. D. (1943/1944), “Temperature Experiments on the Pupae of (1) Heliothis peltigera Schiff., and (2) Panaxia dominula Linn.”, Proceedings of the South London Entomological Natural History Society: 69-81.

Owen, D. and C. Clarke (1993), “The medionigra Polymorphism in the, Panaxia dominula (Lepidoptera Arctiidae): A Critical Re-Assessment”, Oikos 67: 393-402.

Owen, D. and D. Goulson (1994), “Effect of Temperature on the Expression of the medionigra Phenotype of the Moth Panaxia dominula (Lepidoptera: Arctiidae)”, Oikos 71: 107-110.

Provine, W. B. (1985), “The R.A. Fisher–Sewall Wright Controversy and its Influence Upon Modern Evolutionary Biology”, in R. Dawkins and M. Ridley (ed.), Oxford Surveys in Evolutionary Biology, Vol. 2. New York: Oxford University Press: 197-219.

Provine, W. B. (1986), Sewall Wright and Evolutionary Biology. Chicago: University of Chicago Press.

Sheppard, P. M. (1951), “A Quantitative Study of Two Populations of the Moth, Panaxia dominula, L.”, Heredity 5: 349-378.

Sheppard, P. M. and L. M. Cook (1962), “The Manifold Effects of the Medionigra Gene in the moth, Panaxia dominula and the Maintenance of Polymorphism”, Heredity 17: 415-426.

Wright, S. (1948), “On the Roles of Directed and Random Changes in Gene Frequency in the Genetics of Populations”, Evolution 2: 279-294.

Wright, S. (1951), “Fisher and Ford on the “Sewall Wright Effect”“, American Scientist 39: 452-458, 479.

Whatever Happened to the Fisher-Wright Controversy? Redux

This is the second installment in my "revisiting the Fisher-Wrigt controversy." The first installment, with an addendum I just posted, is here. For a little context, I repost the introductory paragraph from the first post. (This is another long post; just a warning.) The next, and last, installment, revisits the conflict over the evolution of Panaxia dominula.

R. A. Fisher, J. B. S. Haldane, and Sewall Wright are the architects of theoretical population genetics. Between 1918 and 1932, these three theorists ushered in the field and set the stage for the period of the history of evolutionary biology usually called the "evolutionary synthesis." It's well known that from 1929 until Fisher's death in 1962 that Fisher and Wright were engaged in a sometimes heated controversy over their alternative qualitative interpretations of their quantitative models. In 1985, Will Provine published "The R. A. Fisher—Sewall Wright Controversy" in Oxford Surveys of Evolutionary Biology (Provine 1985). In that paper, Provine discusses three key disputes between Fisher and Wright: (1) evolution of dominance, (2) their general evolutionary theories, and (3) evolution of the Scarlet Tiger Moth, Panaxia dominula. Now, Provine's biography of Wright published in 1986 is a fuller treatment of the controversy (Provine 1986). However, I'm in the process of writing, basically, a new version of Provine's paper in which I revisit each of the debates of his 1985 essay. In this post, I look at Fisher's and Wright's dispute over their general evolutionary theories . I think I don't quite do justice to the debate with this post, but I do think it's a fair overview. And it does presume some familiarity with Fisher's and Wright's general evolutionary theories.

Fisher's and Wright's debates over dominance between 1928 and 1934 revealed underlying differences between their general evolutionary theories. But it was the publication of their major works between 1930 and 1932 that crystallized for them their apparently alternative understandings of the balance of evolutionary causes that explained cumulative evolution (Fisher 1930; Wright 1931; 1932). Interestingly, Fisher and Wright agreed on the quantitative details of mathematical population genetics (Provine 1985: 198). They disagreed about how to interpret those details. Fisher advocated natural selection as the primary explanation of  cumulative evolution (Fisher 1930). Wright, however, thought that natural selection alone was not able to solve what he took to be the key problem of evolution, viz., the problem of peak shifts (Wright 1932). Instead, a shifting balance of evolutionary factors was required, including genetic drift.

According to Provine (1985: 210), the conflict over Fisher's and Wright's understandings of evolution in Mendelian populations concerned Fisher's panselectionism and Wright's apparent emphasis on the role of genetic drift. He further suggests that the conflict was driven primarily by the failure of each to appreciate the full sophistication of the other's view. Provine is surely right that Fisher and Wright misunderstood the core, qualitative claims of each other's evolutionary theories. Nevertheless, there is more to their conflict during the 1930s than mutual confusion. Indeed, I think the locus of the conflict is Fisher's and Wright's disagreement over Wright's view that the central problem of evolutionary theory was his problem of peak shifts, i.e., the problem of traversing a surface of selective value replete with adaptive hills and valleys toward the highest adaptive peak.

Fisher argued in correspondence with Wright and in print that Wright's problem of peak shifts was confused. Yet, Wright never bent to criticism. In fact, Wright's view of the centrality of the problem of peak shifts is what underwrote his claim that his Shifting Balance Theory (SBT) described the principal processes of evolution in nature (Wright 1978: 1415). The problem of peak shifts arises for Wright because of his emphasis on epistatic interactions between genes. As Wright understood the field of gene frequencies that comprises a population, epistatic gene interaction means that genes that are adaptive in one combination will be maladaptive in another. Given Wright's view of the epistatic gene interaction and the vastness of the field of gene frequencies, the surface of selective value, i.e., Wright's adaptive landscape, will be replete with adaptive peaks and valleys. The problem of peak shifts follows: In order for a population to reach the highest adaptive peak, a way of moving from one adaptive peak, through a valley, and toward the highest adaptive peak is required. As we have seen, Wright's SBT solves the problem of peak shifts.

But according to Fisher, Wright's understanding of the adaptive landscape in multiple dimensions is flawed because, as the dimensionality of the field of gene frequencies increases the number of stable peaks on the surface of the landscape decreases (Fisher correspondence to Wright May 31, 1931 in Provine 1986: 274). Thus, claims Fisher, representation of the adaptive value of populations in multiple dimensions is not a hilly landscape. Because the peaks on the landscape become unstable as the number of parameters of the landscape increases, the adaptive landscape is actually a single peak with ridges along it; there are no valleys. Evolution on the adaptive landscape does not require the complex of evolutionary factors of Wright's SBT; natural selection alone can carry a population to the apex of the peak.

Fisher's criticism of Wright's problem of peak shifts, which was in the 1930s mostly verbal and not mathematical, has persisted. Indeed, there is a long line of criticism of the problem of peak shifts based on criticism of Wright's adaptive landscape. Provine himself thought Wright's adaptive landscape was mathematically incoherent (Provine 1988; cf. Skipper 2004). And during the 1960s and 1970s, theoretical biologists such as P. A. P. Moran (1964) and A. W. F. Edwards (1971) developed their own critiques of Wright's problem of peak shifts along the line of Fisher's. Most recently, Jerry A. Coyne, Nicholas H. Barton, and Michael Turelli (1997) raised this problem for Wright's problem of peak shifts. Indeed, Coyne and his colleagues developed a thorough critique of Wright's Shifting Balance Theory, of which one line of attack was directed at the problem of peak shifts. Coyne, Barton, and Turelli further argued, on both theoretical and empirical grounds, that the individual phases of the SBT are theoretically and empirically problematic, and that the SBT as a whole describes a complicated evolutionary process that is, on its face, unlikely to occur in nature and that, anyway, lacks empirical support, particularly relative to Fisher's natural selection theory (Coyne et al. 1997: 643).

With their critique, Coyne, Barton, and Turelli rekindled the controversy over Fisher's and Wright's general evolutionary theories: Between 1997 and 2000, in the pages of the journal Evolution, the team of Coyne, Barton and Turelli and the team of Michael Wade and Charles J. Goodnight debated the theoretical foundations of and the empirical evidence for Fisher's and Wright's general evolutionary theories (Coyne et al. 1997; 2000; Wade and Goodnight 1998; Goodnight and Wade 2000). There has been no resolution to the debates led by Coyne and Wade. However, in my own analysis of their debates, argued in support of Wade and Goodnight's (1998) conclusion that it is premature to dismiss either Fisher's or Wright's general evolutionary theories (Skipper 2002; cf. Plutynski 2005; see my post here on the differences between mine and Plutynski's views).

Coyne and his colleagues take their criticism of Wright's problem of peak shifts further than Fisher and others had (Coyne et al. 1997: 646-653). A key flaw, say Coyne, Barton, and Turelli, is that Wright's adaptive landscape is based on the assumption that the mean fitness of the population will not change, meaning that, e.g., the environment of the population is held constant. Such an assumption is highly unrealistic (as Fisher 1930 demonstrated). Environmental changes, e.g., are common, and they may plausibly change the mean fitness of the population. If that happens, the population may be brought off of an adaptive peak into an adaptive valley. In other words, say Coyne and his colleagues, peak shifts may occur in ways alternative to those Wright envisioned. In particular, genetic drift may not be required to move a population from an adaptive peak into an adaptive valley. Other factors may change the mean fitness of the population, such as frequency-dependent selection, according to which the fitness of a particular gene combination changes because of its frequency relative to others in a population. The change in fitness may shift the peaks on the landscape. Coyne, Barton, and Turelli's conclusion is that Wright's problem of peak shifts is confused.

The second set of challenges Coyne and his colleagues raise are directed at the first and third phases of the SBT individually and the three phases conjoined. They argue that phases I and III are improbable (phase II is just natural selection). For instance, phase I, genetic drift acting to decrease the fitness of small populations, is unlikely because chances are greater that the small population will go extinct rather than survive to move onto the phase II. And we have already seen their critique of the transition from phase I to phase II. Coyne, Barton, and Turelli argue that phase III, interdemic selection, is unlikely to occur in nature because it relies on the subpopulations having an unlikely, low level of gene flow between them. Empirically, Coyne and his colleagues think that there is little support for the claim that phases I and III occur in nature. And they think that there is very little empirical support for all three phases working together, i.e., for the SBT. Ultimately, Coyne, Barton, and Turelli are convinced that the SBT is too complex and delicate to occur often in nature.  (Coyne et al. 1997: 664-665). Indeed, their view is that "there are few empirical observations explained better by Wright's three-phase mechanism than by simple mass selection" so that "it seems unreasonable to consider the shifting balance process as an important explanation for evolution of adaptations" (Coyne et al. 1997: 643). With that recognition, Coyne and his colleagues opt, by appeal to parsimony, for Fisher's natural selection theory (Coyne et al. 2000: 314). For Coyne, Barton, and Turelli, if cumulative evolution can be explained adequately via a theory that postulates a small economy of entities and processes, then there is no need to invoke a theory with a larger economy of entities and processes.

Wade and Goodnight (1998) question Coyne, Barton, and Turelli's parsimony reasoning, and rightly so in my view (Skipper 2002; see also Goodnight and Wade 2000). Indeed, consider what Wade and Goodnight (1998) say about Coyne and his colleagues' appeal to parsimony as a way of rejecting Wright's SBT:

Coyne et al. …, echoing the early group selection literature, advocated Occam's razor … as grounds for dismissing the SBT. They argued … that  "there are few empirical observations explained better by Wright's three-phase mechanism than by simple mass selection" and that "it seems unreasonable to consider the shifting balance process as an important explanation for evolution of adaptations" (Wade and Goodnight 1998: 1537).

But how does parsimony figure into generality of scope of applicability of a theory? In particular, how does parsimony figure into Coyne, Barton, and Turelli's argument?

According to the biologist Richard Levins (1968: 7), it is not possible to maximize at the same time generality, realism, and precision of a model (or theory, as a cluster of models) during model building in population biology. For instance, generality might be sacrificed for realism and precision. In such an instance, a model builder might construct a model that includes as many of the real features of the system being modeled in a way that precisely captures the system's dynamics. A fruitful way of reading Wade and Goodnight (1998) it seems to me is by reading them as arguing that Coyne and his colleagues are sacrificing realism for generality and, allegedly, precision. One can make such a sacrifice by simplifying the model, i.e., by constructing a model that captures the apparently essential aspects of the system under scrutiny while removing those aspects that are apparently distracting, or those that introduce only small changes to modeling results, and by introducing patently false assumptions that facilitate study (Levins 1968: 6-7).

Fisher's natural selection theory exemplifies a fairly extreme form of the above approach to model construction in my view. Consider the following as an illustration of the point. A driving (mathematical) assumption that Fisher makes in constructing his theory is that populations are infinitely large and panmictic (randomly mating). Indeed, Fisher had argued earlier that natural populations are rarely smaller than 10,000 individuals (and that gene flow was sufficient to treat populations as if they are effectively infinite (Fisher 1922). The evolutionary consequences of the assumption that populations are large is important for assigning evolutionary importance to genetic drift, migration, epistasis, etc. In other words, by assuming that populations are infinitely large, a model builder is able to treat genetic drift, migration, epistasis, etc. as elements that introduce only small changes to the modeling results and, so, is able to treat such factors as unimportant in modeling evolution. Take genetic drift, for instance. Genetic drift is evolutionary efficacious in populations that are smallish (and certainly not infinitely large and panmictic). If a population is too small, drift will take it to extinction. But if the population is very large (e.g., infinite), then the effects of drift are negligible. So, assuming that populations are infinitely large allows a modeler to discount the evolutionary importance of random genetic drift. Indeed, Fisher used the assumption that populations are infinitely large to great effect in The Genetical Theory of Natural Selection, allowing him to set aside such things as effects of drift and migration on the evolution of populations and assign considerably little importance to any evolutionary consequences of epistasis (Fisher 1930).

As I understand Coyne, Barton, and Turelli's critique of the SBT and advocacy of Fisher's theory of natural selection, they are claiming that the simplifying assumptions endemic to Fisher's theory enable them to explain, in a way that preserves precision of modeling results (i.e., so that the results stay well within standards of error). Yet, for Wade and Goodnight, it is the paring down of the models based on such assumptions that is a matter of debate. Consider, e.g., the following comment that Wade and Goodnight make:

It is common place to reify additive effects and treat them as properties of genes, independent of genetic and ecological context. Perhaps the fault lies not so much with Fisher's LST [natural selection theory] as with the uncritical application of it to evolutionary problems it was not meant to solve, such as speciation, or to ecological and genetic contexts in which it does not hold, such as evolution in metapopulations. For the reasons discussed above [previously in Wade and Goodnight 1998], accepting the LST [natural selection theory] over the SBT on the grounds of parsimony … does not seem warranted to us (Wade and Goodnight 1998: 1549).

On Wade and Goodnight's view, there is considerable evidence that it is not always the case that when the infinitely large population size assumption is made in a model, for example, that the results are at all precise. Consequently, Coyne, Barton, and Turelli's parsimony reasoning is problematic.

Ultimately, Wade and Goodnight agree with Coyne, Barton, and Turelli that Wright's (1978b) claim that the SBT describes the principal processes of cumulative evolution is mistaken. However, they think that appealing to parsimony to reject the SBT altogether is a mistake. There are serious challenges for both the SBT and Fisher's natural selection theory. And the task at hand is to determine how, when, and where to apply the theories of Fisher and Wright to evolutionary problems (Wade and Goodnight 1998: 1537, 1548; Goodnight and Wade 2000: 317, 322). In any event, it seems clear from the preceding analysis that the theoretical issues Fisher and Wright debates in the 1930s continue to see work.

References

Edwards, A.W.F. (1971), "Review of Wright (1969)", Heredity 26: 332-338.

Fisher, R. A. (1930b), The Genetical Theory of Natural Selection. Oxford: Oxford University Press.

Fisher, R. A. (1922), "On the Dominance Ratio", Proceedings of the Royal Society of Edinburgh 42: 321-341.

Fisher, R. A. (1958), The Genetical Theory of Natural Selection. 2nd edition. New York: Dover Publications.

Fisher, R. A. (1999), The Genetical Theory of Natural Selection: A Complete Variorum Edition. J. H. Bennett (ed.). New York: Oxford University Press.

Goodnight, C. J. and Wade, M. J. (2000), "The Ongoing Synthesis: A Reply to Coyne, Barton, and Turelli", Evolution 54, 317-324.

Levins, R. (1968), Evolution in Changing Environments. Princeton: Princeton University Press.

Moran, P. A. P. (1964), "On the Non-Existence of Adaptive Topographies", Annals of Human Genetics 27: 383-393.

Plutynski, A. (2005), "Parsimony and the Fisher-Wright Debate", Biology and Philosophy 20: 697-713.

Provine, W. B. (1985), "The R.A. Fisher–Sewall Wright Controversy and its Influence Upon Modern Evolutionary Biology", in R. Dawkins and M. Ridley (ed.), Oxford Surveys in Evolutionary Biology, Vol. 2. New York: Oxford University Press: 197-219.

Provine, W. B. (1986), Sewall Wright and Evolutionary Biology. Chicago: University of Chicago Press.

Skipper, Jr., R. A., (2002), "The Persistence of the R. A. Fisher-Sewall Wright Controversy", Biology and Philosophy 17: 341-367.

Skipper, Jr., R. A. (2004), "The Heuristic Role of Sewall Wright's 1932 Adaptive Landscape Diagram", Philosophy of Science 71: 1176-1188.

Wright, S. (1931), "Evolution in Mendelian Populations", Genetics 16: 97-159. Reprinted in William B. Provine (ed.) (1986), Sewall Wright: Evolution: Selected Papers. Chicago: University of Chicago Press: 98-160.

Wright, S. (1932), "The Roles of Mutation, Inbreeding, Crossbreeding and Selection in Evolution", Proceedings of the Sixth Annual Congress of Genetics 1: 356-366. Reprinted in William B. Provine (ed.) (1986), Sewall Wright: Evolution: Selected Papers. Chicago: University of Chicago Press: 161-177.

Wright, S. (1978b), "The Relation of Livestock Breeding to Theories of Evolution", Journal of Animal Science 46: 1192-1200. Reprinted in William B. Provine (1986), Sewall Wright: Evolution: Selected Papers: Chicago: University of Chicago Press: 1-11.

Wright, S. (1988), "Surfaces of Selective Value Revisited", American Naturalist 131: 115-123.

10 Assertions About Evolution

Razib at Gene Expression has assigned us all another one of those exercises that can steal an entire day: Come up with 10 assertions --he said "assertions"-- about evolution (scroll down for his 10). I tried to avoid doing my homework. But then, just like school, I got called out (will I never learn?). So, here are my assertions --I tried to stay as specific to evolutionary biology as possible.

1. biological evolution is not merely "change in gene frequency over generational time"
2. Fisher's fundamental theorem is true, but not fundamental
3. Wright's "adaptive landscape" is not entirely incoherent
4. the gene is not the unit of selection
5. natural selection is one of several evolutionary causes
6. the Price Equation doesn't distinguish selection from drift (but there is a distinction)
7. genetic drift is not binomial sampling
8. the connection between ρ, the rate of substitution, and N, population size, which is assumed to be 4Nus, where u is the mutation rate, is mysterious
9. there's much more to species/speciation than the BCS and allopatry + natural selection
10. evo-devo will not make population genetics go away

Let the criticism begin. (Actually, please, let the criticism begin. I may learn something.) Take a look at the assertions that RPM and Aferensis came up with as well.

Vanity (with a modicum of substance)

I just picked up a review of Jerry Coyne and H. Allen Orr's (2004) Speciation by Hope Hollocher in The Quarterly Review of Biology (Hollacher 2006; you need a subscription to read the review online). The review is negative:

Speciation is a controversial topic. This controversy results from the inherent complexity that comes from studying a process rather than a single time event, and it permeates all aspects of the field. There is almost a religious fervor associated with opposing camps, and the acrimony of debate is palpable at times. However, it is this same clash of competing ideas that presents an exceptionally exciting arena for performing research. I say, “vive la différence!” and I do not think I am alone in expressing this sentiment. The recognition that there is room for pluralism in speciation studies has been gaining acceptance over the last 15 years. Research has revealed a multitude of evolutionary forces involved in divergence, and no longer does a single mechanism or mode of speciation reign supreme. Speciation by Coyne and Orr is not an ecumenical book in this regard. The authors take the stance that to include any notion of pluralism would be to admit defeat. The end result is a volume that is polemical, but not dialogic. In short, Speciation is simply dogmatic. (p. 153)

Hollocher's remarks remind me of what I said about Coyne, Nick Barton, and Michael Turelli's (1997) criticisms of Wright's Shifting Balance Theory in my 2002 paper , "The Persistence of the R. A. Fisher-Sewall Wright Controversy." I argued that CBT failed to internalize that the evolutionary domain is thoroughly heterogeneous so that there is no, one general theory of evolution that explains it (following Beatty 1995). Many theories are required. Notice that I said "internalize." CBT seem to be aware of the heterogeneity of the evolutionary domain. At the same time, the push and push at the idea that low selection pressures acting on mutations of small effect is sufficient to explain the evolutionary domain --Fisher's natural selection theory anyone? (Probably, the apparent recognition of heterogeneity is just rhetoric.)

According to Hollocher, Coyne and Orr argue similarly in Speciation:

The main take-home message of the book is that speciation is most often driven by natural selection occurring in allopatry to yield species that are reproductively isolated from each other. The tone of the volume is rather disparaging toward ideas that challenge this orthodoxy, and the burden of proof rests disproportionately on the shoulders of those researchers who deviate from this norm. Allopatry and natural selection are deemed the null expectations against which everything else is to be judged. If tests prove to be ambiguous, then allopatry and natural selection are declared the undisputed winners. In the end, Coyne and Orr would have you believe that to think speciation may occur by any other means would be absurd—e.g., “[a]llopatric speciation appears so plausible that it hardly seems worth documenting” (p 123). To perform research outside their paradigm would seem to be downright foolhardy—e.g., “[i]n sum, the evidence for sympatric speciation is still scant . . . it is hard to see how the data at hand can justify the current wave of enthusiasm for sympatric speciation” (p 178). What is particularly disturbing is that proof of strict allopatry, or even the exclusive role of natural selection, is also lacking and is not given the same critical treatment in the book because they are both considered so obvious—e.g., “[w]e have very little mathematical theory describing how indirect selection in allopatry drives speciation. . . . [S]peciation by selection in allopatry is conceptually straightforward and little mathematics is required” (p 387). If the same strict criteria were applied to these ideas, they too would reveal shortcomings of their own. The authors’ support appears to be based more on intuition and familiarity than on empirical rigor. (p. 154)

She continues:

Coyne and Orr define species by employing a relaxed version of the Biological Species Concept (BSC) that allows for some gene flow. Speciation then simply becomes the evolution of reproductive isolating barriers. The rest of the text that follows requires one to view species and speciation from this single standpoint. Many evolutionary biologists are comfortable with this approach (and I use it in my own research), but there is no getting around the fact that adopting this species concept does lead to some odd predicaments, and even contradictions, that are readily apparent in this volume. For example, in allopatry, species remain undefined by the BSC because they are not in contact. Yet, Coyne and Orr claim that most speciation occurs in allopatry. Logically, you cannot have it both ways (i.e., you cannot have the most common geographical mode of speciation lead to species groups that remain undefined within that context). Taking their definition of speciation to heart should actually encourage researchers to direct their programs more toward studying cases of sympatry and parapatry, where isolating barriers are more readily detected and the evolutionary forces driving them can be directly tested. In practice, the authors admit to resorting to genotypic, phylogenetic, and morphological criteria to define species boundaries in allopatry because of this difficulty, but, in doing so, they erode the distinctions they have made between their relaxed BSC and competing ideas. Asexual organisms or even organisms that have both sexual and asexual modes of reproduction fall outside the realm of speciation studies altogether within their framework, but can be easily  accommodated if other species concepts are applied (e.g., the cohesion species concept or genotypic clustering), making it clear that Coyne and Orr’s treatment of speciation represents only a particular subset of the entire field. (p. 154)

Again, I said similar things in my "Persistence" paper both in criticizing CBT and in suggesting next steps with respect to the assessment of Wright's SBT. Criticizing CBT, I argued that their appeals to parsimony bias their interpretation of the data (but they make it look very good). And in suggesting next steps, simply put, theoretical pluralism is the rule.

Hollacher's review is worth the short time it takes to read. Speciation is worth going back through with her thesis in mind. Now, the vanity in this post isn't the obvious comparison of my argument about CBT and Hollacher's about Speciation. Rather, it's that Hollacher cited three references, namely, Dobzhansky's 1951 (third edition) Genetics and the Origin of Species, Mayr's 1963 Animal Species and Evolution, and my own "Persistence" paper. What great company! But I know: There's nothing to read into this coincidence. Nevertheless, egos are fragile. Especially the egos of academics! (And, yes, I'm prepared to take a few jibes about my vanity.)

References

Beatty J. (1995), "The Evolutionary Contingency Thesis", in Wolters G. and Lennox J.G. (eds), Concepts, Theories, and Rationality in the Biological Sciences. University of Pittsburgh Press, Pittsburgh, PA, pp. 45–81.

Coyne, J. A., N. H. Barton, and M. Turelli (1997), “Perspective: A Critique of Sewall Wright’s Shifting Balance Theory of Evolution”, Evolution 51: 643-671.

Coyne, J. and H. A. Orr (2004), Speciation. Sunderland, MA: Sinauer and Associates.

Dobzhansky T. (1951), Genetics and the Origin of Species. Third Edition. New York: Columbia University Press.

Hollacher, H. (2006), "Evolution and Dogma", The Quarterly Review of Biology 81: 153-156.

Mayr E. (1963), Animal Species and Evolution. Cambridge (MA): Harvard University Press.

Skipper R A, Jr. (2002), "The Persistence of the R. A. Fisher-Sewall Wright Controversy", Biology & Philosophy 17(3): 341–367.

Whatever Happened to the Fisher-Wright Controversy?

I know I have two other topics in the "blog hopper," but I'm about to add a third. I'll get back to explanation (1 and 2) and theory assessment (1). I want to do a little history here.

R. A. Fisher, J. B. S. Haldane, and Sewall Wright are the architects of theoretical population genetics. Between 1918 and 1932, these three theorists ushered in the field and set the stage for the period of the history of evolutionary biology usually called the "evolutionary synthesis." It's well known that from 1929 until Fisher's death in 1962 that Fisher and Wright were engaged in a sometimes heated controversy over their alternative qualitative interpretations of their quantitative models. In 1985, Will Provine published "The R. A. Fisher—Sewall Wright Controversy" in Oxford Surveys of Evolutionary Biology (Provine 1985). In that paper, Provine discusses three key disputes between Fisher and Wright: (1) evolution of dominance, (2) their general evolutionary theories, and (3) evolution of the Scarlet Tiger Moth, Panaxia dominula. Now, Provine's biography of Wright published in 1986 is a fuller treatment of the controversy (Provine 1986). However, I'm in the process of writing, basically, a new version of Provine's paper in which I revisit each of the debates of his 1985 essay. In this post, I look at Fisher's and Wright's dispute over genetic dominance. I'm not as confident as I'd like to be in what I've got here. So comments wou;ld be helpful. I'll post on the other two controversies subsequently.

Fisher’s and Wright’s debates over dominance were the first, major public debates of the broader Fisher–Wright controversy (Provine 1985: 206). Fisher and Wright each constructed a theory of dominance firmly grounded in the core assumptions of their respective theories. Indeed, they believed that if one or the other were shown to be incorrect, disastrous consequences for the corresponding evolutionary theory were sure to follow (Provine 1986: 303). The work I critically discuss here has contributed to what seems to me as the closest thing there is to a resolution of any issue in the controversy. Fisher’s evolutionary theory of dominance has been, if not outright falsified, then shown to be obsolete. Wright’s physiological theory of dominance has been shown to be at least the foundations of the correct theory (cf. Allchin's 2002, 2005 more general discussions of puzzles about the biology of dominance). However, the apparent resolution of Fisher's and Wright's dominance debates holds no substantive consequences for either Fisher's or Wright's general evolutionary theories. Ultimately, any corroboration that the extendibility of the general theories to dominance might have afforded has been trumped by independent empirical evidence for or against the general theories.

Genetic mutations are almost always recessive to their wild-types. Fisher proposed, in 1928 and again in 1931, that this phenomenon was to be accounted for evolutionarily (1928a; 1928b; 1930a; 1930b; 1931; see also 1958; 1999). That is, Fisher claimed that the dominance of the wild-type allele is not an inherently physiological phenomenon. Rather, alleles are not dominant initially, or normally; dominance evolves. Wright criticized Fisher’s view in 1929 and, later in 1934, proposed his own account of the phenomenon of dominance (Wright 1929a; 1929b; 1934). Wright argued, in polar opposition to Fisher, that dominance is essentially physiological. Although there are a handful of alternative theories of dominance and/or its evolution (e.g., Haldane 1930; Muller 1932; Plunkett 1933), Fisher’s and Wright’s remain the main competitors in the ongoing evolutionary controversy (Charlesworth 1979; Mayo and Bürger 1997; Orr 1991).

Fisher proposes his evolutionary account of dominance as directly connected to his general theory of evolution. Indeed, it is grounded in assumptions that populations are large, that selection acting on mutation is the primary factor of evolutionary change, that selection pressures are small and accumulate over a long period of time, that the mutation rate is low, and that mutations are usually deleterious (see Provine 1971: 147-152). The more specific foundation of Fisher’s theory of dominance is his claim that heterozygotes for rare deleterious alleles are at a much higher frequency than homozygotes in a large and randomly mating population at equilibrium (1928a: 115). Fisher believed that the heterozygotes are maintained by recurrent mutation from the wild-type allele at the locus. Such maintenance he thought would be most likely to occur in large populations (Provine 1971).

Fisher’s theory of the evolution of dominance is as follows (1928a; 1930a; 1931). Mutant alleles are initially semi-dominant. Most mutations are observed to be recessive or nearly so to the wild-type due to selection for modifiers at other loci and this increases the fitness of the heterozygote. (Note that Fisher here ignores any intrinsically genetic effect of the modifiers; selection plays the crucial role in accounting for any such contextual effects.) Fisher referred mainly to genetics studies on Drosophila melanogaster led by Thomas Hunt Morgan to substantiate this claim (Fisher 1928a: 115; the study is Morgan et al. 1925). Selection to improve the fitness of the mutant homozygotes is ineffective because they are rare relative to the heterozygotes and also because the wild-type in the heterozygote makes them more susceptible to modification toward the wild-type. The level of the mutants is, over time, reduced to zero while the selection pressure remains constant. Fisher initially had no empirical evidence for his prediction of the relationship between selection and heritability when he published his evolutionary account of dominance. But soon after he was able to follow up with two cases, a case involving cotton plants and a case involving poultry, which he was certain supported his theory (Fisher 1928b). Fisher’s 1931 paper synthesizes and extends the work he did on the topic in 1928 and 1930 (1931; see also 1958; 1999).

Fisher’s theory has been consistently criticized ever since he proposed it. Wright’s criticism was immediate (1929a; see also Haldane 1930; Ewens 1967). Wright first developed what he considered to be a most charitable model of Fisher’s theory, and then proceeded to criticize it. Wright showed mathematically that because the mutant heterozygotes are so rare, selection for a gene that would modify them could only be as strong as the mutation rate for mutants at the locus undergoing modification. Dominance could, thus, not assert itself. Wright also argued that a weak selection pressure would be unlikely to overcome the effects of random drift or the selection consequences of pleiotropic effects of the dominance modifier. Fisher thought that Wright’s criticisms of his evolutionary account were weak (Fisher 1929; see Provine 1986: 243-250 for a detailed discussion).

Wright believed that the function of most gene loci is to specify enzymes, and that most mutations cause a decrease in enzymatic activity (1934a). Accordingly, Wright proposed that dominance is the outcome of the normal allele at a locus being a highly active one and producing enough gene product for normal viability. That is, evolution has nothing to do with dominance, contra Fisher; dominance is simply the result of genetic interaction. Wright predicted, in contrast to Fisher, that there would be a negative relationship between selection and the fitness of the mutant heterozygote. Fisher published a venomous attack on Wright’s 1934 theory, but it is hardly substantive (Fisher 1934). Wright defended his view against Fisher’s attack (Wright 1934b). The debate is thoroughly documented, and so I will not recapitulate it here (see especially