Exact versus heuristic models of kin selection

This paper examines the conditions under which the classical inclusive fitness formulation of Hamilton (1964) provides an adequate approximation to the dynamics of gene frequency change and to conditions for genetic equilibrium, in the "additive" model of altruism between sibs of Uyenoyama and Feldman (1981). It is concluded that the classical formulation is adequate, provided that either the effect of the gene on the probability of behaving altruistically is low or the costs and benefits of altruism are small, unless the benefit/cost ratio k is very close to 2, the value that must be exceeded for altruism to be favoured. In addition, the gene for altruism must be underdominant, recessive or partially recessive in its effect on the probability of behaving altruistically, for the inclusive fitness predictions to break down significantly.