On the opportunity for polymorphism with sex-linkage or haplodiploidy

This paper addresses the assertion that X-linked and haplodiploid genetic systems are inherently limited with respect to the potential for selectively maintained genetic polymorphisms. Using a variation of Haldane and Jayakar's (1964) parameterization of selection on an X-linked locus, analytical expressions are derived for the proportion of the total parameter space (P) in which stable diallelic polymorphism is attained. P is a function of the ratio of selection coefficients (r) associated with homozygous and hemizygous genotypes, and the intensity of selection (s). Analytical expressions for the opportunity for polymorphism at an autosomal locus (P(a)) are also derived for comparison to the X-linked case. P and P(a) are maximal and equal if the ratios of selection coefficients are -1 and selection is intense. Otherwise, P is slightly less than P(a), but the difference between autosomal and sex-linked loci is less than the range of values of P obtained over the range of r. Several arguments are presented suggesting that polymorphism arising from differential selection in the sexes (r < 0) is probabilistically and biologically feasible.