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June 01, 2006

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jay odenbaugh

Rob,

First, kudos on what is a very interesting and rich blog. Second, you write the following:

"What the architects of population genetics achievement consisted in was, in Fisher's words, "a clearing of the ground of the debris of anti-Darwinian criticism" (Fisher [1932] 1983, pp. 289-290). That is, what Fisher, Haldane, and Wright managed to do was demonstrate how possibly, against the anti-Darwinians of the time, that natural selection alone could suffice to explain evolutionary change."

I find this view very attractive (especially more so than the unificationist line) but it raises a very general point about what the architects accomplished. Let me explain by way of example.

Anti-Darwinians largely agreed in the belief that natural selection was not a very powerful evolutionary "force". The alternatives - macromutations, orthogenesis, etc. - they were thought to be more efficacious.

Fisher for example responded by articulating a model where very small differences in fitness over generational time could take traits to fixation. So, the question "Is is possible for small differences in fitness to drive traits to fixation" is answered "yes". However, if i remember correctly, Fisher assumed the population size to be infinite (or effectively infinite). Given that idealization, why should the anti-Darwinians have been convinced by Fisher's argument? To my knowledge, this idealization was not relaxed at the time, so they could have denied that Fisher provided a how-possibly explanation.

At any rate, I may have the details wrong so it is just an open question...

jay

Robert Skipper

Jay,

Thanks heaps for reading. I enjoy the blog, even if I've not been posting much recently. The blog is especially rewarding when my colleages leave comments.... Now, you said:

However, if i remember correctly, Fisher assumed the population size to be infinite (or effectively infinite). Given that idealization, why should the anti-Darwinians have been convinced by Fisher's argument?

As I've looked more and more at Fisher, I think there's a good deal of legend surrounding his population size "assumption." The central question is why Fisher thought this assumption was reasonable. The answer in the air, and implicit in the received narratives, is that Fisher began thinking about the role of natural selection under the assumptions that populations were very large (for theoretical purposes, infinite). But I think that's incorrect.

I've begun a paper in which I treat Fisher's 1918 and 1922 papers and the 1930 book as one long argument (with some surrounding stuff). In doing so, precisely how Fisher justifies the population size assumption, among other assumptions, becomes pretty clear. It's clearest in Fisher's treatment of the Hagedoorn effect in 1922, in which he argues that the effect must be negligible since most populations (says Fisher) must be greater than 10^4 in size. The question then becomes whether we think that population size is too large for comfort --generally. And that's an empirical question.

At any rate, once Fisher lays out the parameters that depend on small population sizes, he sees then that he's able to assume, for mathematical purposes, that populations are infinitely large. No longer does size matter.

In response to your comment, the anti-Darwinians would have had to criticize Fisher's reasoning regarding mutation rates, the Hagedoorn effect, migration, and the lot before they could've gotten him for a bad assumption about population size. Fisher was much more careful than many of us have given him credit for being. And his arguments about these other parameters are pretty good. (And often too mathematically involved for his critics.)

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