Wednesday, September 17, 2008

R. A. Fisher on Population Size: Addendum   posted by DavidB @ 9/17/2008 05:16:00 AM

A while ago I posted two notes on R. A. Fisher's views on population size: Part 1 here and Part 2 here. I assembled some evidence from The Genetical Theory of Natural Selection suggesting that Fisher believed the population size of a species was usually between a million and a million million, with the latter figure being a realistic possibility for some species of small invertebrates.

In writing that post I could not find any more direct evidence, so I am pleased to have come across a letter from Fisher to C. Tate Regan, dated 7 February 1927, containing the following explicit statement:

The population number of 10^6 [1,000,000] parents in each generation represents a somewhat small species. I suppose most species lie between 10^6 and 10^12 [1,000,000,000,000], although some, such as some of the millipedes, certainly exceed the latter figure. The larger the population the less frequent need mutations be to maintain a given stock of segregating factors, or in other words, with the same mutation rates the larger will the variance (when equilibrium is attained) be. (Bennett, ed., p.255)

Earlier in the letter Fisher makes it clear that he is thinking about genes that are nearly neutral in their effect, so that variance is maintained by a balance between mutation and drift.

A population of a million million does seem very large, but Fisher's reference to millipedes confirms that he was thinking of small inverterbrates, where very large populations are quite possible. For example, a population of a million million would only require an average density of one per square metre over an area of about a tenth the size of the United States.

J. H. Bennett, ed., Natural Selection, Heredity and Eugenics: Including selected correspondence of R. A. Fisher with Leonard Darwin and others1983

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