Sex ratio selection and multi-factorial sex determination in the housefly: a dynamic model

Abstract

Sex determining (SD) mechanisms are highly variable between different taxonomic groups and appear to change relatively quickly during evolution. Sex ratio selection could be a dominant force causing such changes. We investigate theoretically the effect of sex ratio selection on the dynamics of a multi‐factorial SD system. The system considered resembles the naturally occurring three‐locus system of the housefly, which allows for male heterogamety, female heterogamety and a variety of other mechanisms. Sex ratio selection is modelled by assuming cost differences in the production of sons and daughters, a scenario leading to a strong sex ratio bias in the absence of constraints imposed by the mechanism of sex determination. We show that, despite of the presumed flexibility of the SD system considered, equilibrium sex ratios never deviate strongly from 1 : 1. Even if daughters are very costly, a male‐biased sex ratio can never evolve. If sons are more costly, sex ratio can be slightly female biased but even in case of large cost differences the bias is very small (<10% from 1 : 1). Sex ratio selection can lead to a shift in the SD mechanism, but cannot be the sole cause of complete switches from one SD system to another. In fact, more than one locus remains polymorphic at equilibrium. We discuss our results in the context of evolution of the variable SD mechanism found in natural housefly populations.

The evolution of sex ratios and sex-determining systems

“…Building on early insights by Bull [1], Kozielska and coworkers [17] addressed the evolution of multi-factor sex determination by modeling a three-locus system with each locus having two alleles, similar to the system found in the housefly Musca domestica (Box 1). Selection for biased sex ratios was assumed to act via differential costs of producing sons and daughters.…”

“…GSD and sex ratios at equilibrium Although the models described above were primarily developed to address the potential for sex ratio selection to cause evolutionary shifts in sex determination, they have also generated another important insight. In models with exclusive expression of sex-determining factors in the offspring and in models that enable dual action of parental and offspring genes, the evolutionarily stable sex ratio deviates only marginally from 50:50, even when selection favors highly biased sex ratios [1,17,22]. In other words, selection for biased sex ratios yields evolutionary shifts in sex determination but does not result in the sex ratio predicted by standard theory.…”

“…In other words, selection for biased sex ratios yields evolutionary shifts in sex determination but does not result in the sex ratio predicted by standard theory. For example, in the housefly three-locus sex-determining model (Box 1), male-biased sex ratios are impossible and the female-biased sex ratios that evolve when sons are more costly to produce are smaller than predicted under perfect maternal or offspring control [17]. The reason for this result is that mixtures between genotypes that create biased sex ratios are not evolutionarily stable.…”

“…The multi-factor sex-determining system of houseflies Musca domestica ( Figure Ia; reproduced with permission from Peter Koomen) is well established ( [17,44] and references therein). Most abundant is male heterogamety, with a dominant male determiner (M) on the Y chromosome.…”

“…Evolution of sex determination and constraints on sex ratio bias One of the most important results from recent models of sex determination is that even when selection for sex ratio bias causes changes in sex-determining mechanisms, the resulting sex ratio at equilibrium might not show the expected deviation from 50:50 [17,22]. This adds a novel perspective on the role of genetic constraints on sex ratio adjustment as it suggests that constraints evolve from a system that is free to vary, rather than a priori postulating constraints based on the 'difficulty' by which the appropriate mechanism can evolve (see also Ref.…”