Never speak “ill” of Fisher!

By Razib Khan | March 5, 2013 12:13 pm

In the post below I alluded to the views of R. A. Fisher. This was a moderately dangerous move on my part because many of Fisher’s views have been transmitted only through later researchers, who may have lacked a clear understanding of what Fisher himself was trying to say. Heap on top of that the reality that the debate between Fisher and Sewall Wright was often abstruse for the evolutionary biologists who nevertheless managed to take sides and transmit their understandings of the conflict, and it’s a recipe for misrepresentation. With that in mind let me enter into the record an email from a friend who has engaged in a deep reading of Fisher, and attempted to understand his reasoning (no, this is not A. W. F. Edwards!):

I’ve complained about this kind of thing to you before, so I don’t suppose I’ll make much headway now. But let me try again. 🙂  Allow me to quote Warren Ewens:

It is appropriate to comment briefly on the bearing of the above considerations on the differences between Fisher and Wright. Wright’s view of evolution focused on subdivided subpopulations and an “adaptive topography” in which populations moved so as steadily to increase mean fitness, except for rare occasions where random changes in gene frequency lead to temporary decreases in mean fitness as the population crosses a valley in the adaptive topography in moving from one peak to another. Fisher resisted this viewpoint, and unfortunately an aspect of Wright’s view which was of relatively minor significance to him, namely the effect of random genetic drift, was blown out of all proportion in the ensuing controversy and obscured the central issues.The central issues to Fisher concerned Wright’s assumption of random mating and the implied (incorrectly, in the multi-locus case) steady increase in W
 [fitness -Razib]. Thus Fisher (1958b) states: “I have never, indeed, written about W and its relationships … the existence of such a potential function [i.e. a function non-decreasing in time] … W is not a general property of natural populations, but arises only in the special and restricted cases Wright … considers.” This theme is also discussed at length in Fisher (1941): the specific assumption made by Wright and objected to by Fisher is that of random mating, under which, for a one-locus system, W does increase, as we have noted. Fisher was strongly influenced in his formulation by the argument that mating is not necessarily random, that the average excess and the average effect are not necessarily equal, that genotype frequencies are thus not necessarily in Hardy-Weinberg proportions, and that the total change in W can be negative. This was central to his viewpoint and the Fundamental Theorem was an attempt to achieve a partial result in this generally complex picture.

Two ironies arise from this. The first is that, as noted in this quotation and also in preceding sections, the Fundamental Theorem has nothing to do with changes in W, whereas in later years Wright increasingly invoked it to support his theories. Thus in his last paper Wright (1988) says: “The effects [on gene frequencies in an adaptive topography] may be calculated using Fisher’s ‘Fundamental Theorem of Natural Selection’.” It is clear that Fisher never got his interpretation of the theorem across to Wright, or almost anyone else. [My emphasis -Razib]

The second has been pointed out to me by Steven Frank (personal communication). This is, in Frank’s words, that “Wright, who was so interested in gene interactions and inbreeding, insisted on a formulation that cannot work when gene interactions are present, whereas Fisher, who is usually regarded as a single-locus panselectionist, insisted strongly on formulations that took account of inbreeding and interactions”. This is a fascinating and ironical insight, since it demonstrates a real reversal of the generally perceived positions of Fisher and Wright, and of the generally perceived central features of their evolutionary theories.

I suppose the legend of Fisher’s views, in particular for many American biologists who have received a “Wrightian” story, resembles our “understanding” Herbert Spencer’s views of “Social Darwinism” (which owes more to Richard Hofstadter’s treatment of the movement). The legend is strong enough that I keep forgetting the complexity of the truth. Not enough to make me a post-modernist, but a cautionary tale.

CATEGORIZED UNDER: Evolutionary Genetics

Comments (1)

  1. Luis Aldamiz

    I find Fisher’s theorem rather logical because fitness does not exist in a vacuum but depends on context. Hence populations and even species rely on diversity to be able to adapt quickly to changing conditions (either locally or because of migration). I hope you are not rejecting this, really.


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About Razib Khan

I have degrees in biology and biochemistry, a passion for genetics, history, and philosophy, and shrimp is my favorite food. In relation to nationality I'm a American Northwesterner, in politics I'm a reactionary, and as for religion I have none (I'm an atheist). If you want to know more, see the links at


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