Sunday, November 23, 2008

R. A. Fisher on Inclusive Fitness (again)   posted by DavidB @ 11/23/2008 04:12:00 PM

I recently posted a note on an anticipation of Hamilton's concept of inclusive fitness by R. A. Fisher in the Genetical Theory of Natural Selection.

As I pointed out, in that passage Fisher did not quantify the effect of what he called 'indirect effects of natural selection', so he did not state what we now call 'Hamilton's Rule' (though later in GTNS he came close to it in his discussion of distasteful insects).

However, I have noticed the following passage in a letter from Fisher to Leonard Darwin dated 27 June 1929, which states Hamilton's Rule for the special case of parental care:

The reproductive value at different ages must determine the extent to which parental care pays. If all ages were of equal reproductive value, a species would tend to benefit its offspring up to the point at which the offspring gains double the advantage which the parent loses, but no further. Of course immature offspring are usually worth much less, and so should be cared for only at a cheaper rate still. But if crocodiles were able to recognise their mature offspring, I suppose they would co-operate with them not only on terms of mutual advantage, but on terms of joint advantage so long as the loss of either did not exceed half the gain of the other. Hence society starts with the family. - Natural Selection, Heredity and Eugenics: Including selected correspondence of R. A. Fisher with Leonard Darwin and others, edited by J. H. Bennett (1983), p.104-5

The important qualification about the maturity of the offspring is probably also in Hamilton somewhere, but I can't immediately find it. Dawkins makes a similar point in his '12 Misunderstandings of Kin Selection'.

Added: I had another skim through Hamilton's papers, but I still couldn't find a discussion of the maturity point. However, I imagine Hamilton would have said that differences of maturity should be taken into account in quantifying the 'benefit' to an offspring of a given amount of parental care. So, for example, in a species with very high infant mortality, the benefit of a given amount of resources to an immature offspring, measured by the expected number of its own future offspring, would be less (other things being equal) than to an offspring who has already reached sexual maturity. Against this, 'other things' are seldom equal, and the benefit of a given amount of resources (e.g. food) to a newborn may be much greater than to an older offspring which can already fend for itself.

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