Tuesday, September 23, 2008

R. A. Fisher and Inclusive Fitness   posted by DavidB @ 9/23/2008 01:20:00 AM

W. D. Hamilton is rightly given the main credit for establishing the concept of inclusive fitness. He gave it its name, developed its mathematical theory, and examined a wide range of empirical evidence for it.

There had of course been occasional anticipations of inclusive fitness, going back to Darwin's treatment of neuter social insects in the Origin. Hamilton himself mentioned three such partial anticipations: by G. C. Williams, by J. B. S. Haldane, and by R. A. Fisher in his treatment of the evolution of distastefulness among insects (Hamilton, Narrow Roads of Gene Land, vol. 1, pp.49-50).

Curiously, neither Hamilton nor many other commentators seem to have noticed a more general and prominent formulation of the concept by Fisher in the Genetical Theory of Natural Selection......

In Chapter 2 of that book, on the 'Fundamental Theorem of Natural Selection', there is a section headed 'Reproductive Value', which contains the following passage (with emphasis added):

We may ask, not only about the newly born, but about persons of any chosen age, what is the present value of their future offspring; and if present value is calculated at the rate determined before [in the section on the 'Malthusian Parameter'], the question has a definite meaning - To what extent will persons of this age, on average, contribute to the ancestry of future generations? The question is one of some interest, since the direct action of Natural Selection must be proportional to this contribution. There will also, no doubt, be indirect effects in cases in which an animal favours or impedes the survival or reproduction of its relatives; as a suckling mother assists the survival of her child, as in mankind a mother past bearing may greatly promote the reproduction of her children, as a foetus and in less measure a sucking child inhibits conception, and most strikingly of all in the services of neuter insects to their queen. - The Genetical Theory of Natural Selection, Variorum Edition, ed. Henry Bennett, 1999 p.27

What Fisher here describes as 'indirect effects' may be considered a concise but very general statement of what was later defined by Hamilton as inclusive fitness. Fisher's brief remark may have been overlooked, not only because the statement is not mathematically quantified, but because Fisher immediately goes on to say that 'such indirect effects will in very many cases be unimportant compared to the effects of personal reproduction', and he does not discuss them further. He therefore treats them essentially as a complication to be mentioned but cleared out of the way. Nevertheless, he does recognise the existence of such indirect effects (both positive and negative) and mentions several examples which have later been extensively treated by Hamilton and other sociobiologists.

I dare say that someone somewhere has already noticed and mentioned this passage of Fisher, but as it does not seem to be widely known it will do no harm to mention it again.

Labels: ,