Group selection for a polygenic behavioral trait: a differential proliferation model.

Conditions for natural selection to increase a polygenic behavioral trait are derived for a model in which the population is divided into a very large number of partially isolated groups of variable and varying size. Specifically, we consider an altruistic trait that is deleterious to the individual but raises the mean fitness of the group. We assume, for each generation, that all groups have the same proportion of males, k, at the time of migration and that each group contributes Mf females and Mm males to a pool of migrants, from which Mf females and Mm males are randomly parceled out to each group. This assumption ensures that at equilibrium between random drift and a low level of migration and neglecting the small per locus effect of selection, each group has the same expected value of Wright's fixation index, FST = F. AT equilibrium, this is approximately 1/(1 + 4Me), where Me = 2kMf + 2(1 - k)Mm. The trait will increase when (b - c)/c greater than (1-F)/2F=2Me, where b is the expected benefit to the group and c is the expected cost of a unit change in the mean value of the altruistic trait. In particular, the group selection analogue of Hamilton's inequality, c/b less than r, where r is the coefficient of relationship, is obtained. The effect of isolation is enhanced if migration is mainly between adjacent groups and if group splitting is along family lines, as data on population structure of primates seem to indicate.