Tuesday, April 03, 2007

A note on '2s'   posted by p-ter @ 4/03/2007 03:39:00 PM

On this site, given our interest in the research by Hawks and Cochran, most people are familiar with Haldane's result that the fixation probability for an advantageous allele is about 2s. According to the paramaterization of most modern population genetics texts, this is somewhat confusing-- normally, the fitnesses of different genotypes (call then AA, Aa, and aa) are noted as 1, 1+sh and 1+s. s is then the advantage to one homozygote and h is a parameter that takes into account dominance. Simple acceptance of Haldane's result would lead one to think that the most important parameter in determining the fixation probability is s. This is counterintuitive, given that any new allele exists for a while almost exclusively in heterozygotes.

Indeed, as noted by Hawks and Cochran, the original derivation of Haldane's result ( note the use of generating function methods in a branching process, very similar to an epidemiological model I've outlined before) considers only a dominant allele, in which case h=1 and 1+sh = 1+s. For an allele of arbitrary dominance, however, the fate of the new allele is almost completely determined by its effect in the heterozygote, in which case the probability of fixation is better noted as about 2hs, rather than 2s.