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.
Recent Comments