Frequency-Dependent Models for X-linked Loci in Kangaroos

Abstract

In kangaroos, the paternal X-chromosome is genetically inactivated, so that there is not a perfect correspondence between phenotype and genotype frequencies. Following the demonstration by Cooper in 1976 that constant fitnesses are much less likely to lead to balanced polymorphisms under this type of inheritance than under autosomal or ordinary sex-linkage, we examined the situation with regard to frequency dependency under simple exponential and arithmetic fitness function models. Except for the case of exponential fitness functions operating in females only, which results in allele frequency cycles of neutral stability, all cases examined yield single stable equilibrium points. Addition of a constant to the fitness functions converts the cyclic case to one with a single stable equilibrium point and results in a slower approach to equilibrium in the other cases.