Abstract
Males of many polygynous animal species contribute nutrition, nest sites, parental care or other material benefit to their mates in addition to their gametes. Variation in female reproductive success may be caused by variation in the quantity or quality of the male contribution; in such cases a female''s mate choice affects her reproductive success. Polygenic and haploid 2 allele models are presented here for the joint evolution of a male secondary sexual trait and a female mating preference for that character. The male trait affects male survivorship, mating success and the number of offspring produced per mating. A female''s reproductive success is consequently affected by the type of male she mates. This selection on fecundity is assumed to operate in 1 of 2 ways. Under the assumption of limited male reproductive potential, the fecundity per mating is a declining function of the number of females to which a male is mated. Under the alternative assumption of unlimited male reproductive potential, the fecundity per mating is independent of the number of females mated, but does depend directly on the male''s trait. The evolutionary equilibrium under both forms of fecundity selection maximizes immediate female reproductive success. The equilibrium may or may not maximize male survivorship: when male reproductive potential is unlimited, the equilibrium for the male trait may lie far from the point that is optimal for male viability, and so average male survival can decrease under this form of sexual selection. The models also show that it is possible for the evolutionary equilibrium to become unstable, in which case the population will evolve rapidly away from the equilibrium in a maladaptive runaway process. These models address the sexy son hypothesis of Weatherhead and Robertson (1979), which contends that selection can create an equilibrium at which females on the average mate with certain attractive types of males that give them inferior material resources and therefore decrease the females'' immediate reproductive success. The logic of this argument is that the females are compensated for their fecundity deficit by the mating success of their sons, which bear their fathers'' genes and so are attractive to females. Results from the models developed here show that no such evolutionary balance is possible; the sexy son hypothesis is not supported. Female fecundity is maximized at the evolutionary equilibrium, and is not offset against the fitness of descendants.