Evolution of sex-ratio: Brief review with mathematical study of some simple novel models.

Besides reviewing the unusual case of sex-ratio in the lemming and presenting alternative analyses of general models in which the shift in the usual sex-ratio 1:1 is determined by autosomal or sex-linked mutant alleles, three novel models are presented, in which the shift on the progeny sex-ratio depends on the number of copies of a mutant allele present in the parental pair. The analysis of these models with additive effects shows that: 1) autosomal mutations that alter the usual sex-ratio are eliminated from the population; 2) mutations occurring on the X chromosome lead to an evolutionary stable 1:1 sex-ratio only if the mutation favors the production of males; when the mutant allele favors the production of females, however, females will prevail in the population, with a frequency dependent impact on δ (the deviation from the usual 0.5 proportion) ; for most of the range of possible values of δ the stable but extraordinary sex-ratio will vary from 1 male : 1 female to 1 male : 3 females or 1 male : 2 females approximately depending whether the mutant allele is randomly inactivated or not.