GENETIC-ASPECTS OF KIN SELECTION - EFFECTS OF INBREEDING

Hamilton''s c/b < r rule [c = decrement to the fitness of the altruist; b = increment to the fitness of the altruist; r = measure of the degree of genetic relatedness between the altruist and the recipient], an important tool in sociobiological research, clearly functions as a positive heuristic, sensu Lakatos (1970). The theoretical underpinnings of this rule in population genetics when inbreeding is taken into account was examined. The model used is an extension of Charnov (1977) and assumes that the altruistic gene codes for a behavior between inbred individuals of a fixed genetic relationship. No consideration is given to the population or mating system processes which give rise to this relationship. In inbred populations with weak selection the right-hand side (RHS) of Hamilton''s rule depends upon gene frequency and dominance and the degree of genetic relationship between the individuals involved. Because of this dependence, stable polymorphisms in altruistic and non-altruistic alleles are possible for certain ranges of c/b ratios. Another consequence is that the more dominant the altruistic gene, the easier it is for it to invade a population, but the harder it is for it to increase to high frequencies. In the special case when the individuals involved are inbred to the same extent and gene effects are additive, the RHS of the rule is independent of gene frequency and equals bYX and rYX: Hamilton''s regression coefficient of relatedness and Wright''s correlation coefficient of relationship, respectively.