Models of Polygenic Sex Determination and Sex Ratio Control

Abstract

Mathematical models are presented for sex ratio evolution in random mating populations where the sex ratio is polygenic, i.e., controlled by many genes with small effects. The models address various examples of sex determining mechanisms, female heterogamety, haplo-diploidy, environmental and polygenic sex determination and consider the evolution of sex ratio mean and variance. At equilibrium, the mean sex ratio predicted is usually the same as predicted from single locus theory (e.g., 1/2 in the simplest case). When not at equilibrium, the sex ratio, P, evolves towards it at a per-generation rate proportional to the heritability times (1/2-P)/P(1-P) or a comparable factor when fitnesses must be considered. The evolution of the sex ratio variance depends upon fitness differences within a sex. If fitness within a sex is constant, the variance increases as the sex ratio moves toward equilibrium, but does not change when the sex ratio is at equilibrium (except for mutation and changes in linkage disequilibrium). There is a negative correlation (-.64) between males and females at equilibrium, which partly obscures the total additive genetic variance. If instead fitness as a male (female) correlates with an environmental parameter among zygotes, at the sex ratio equilibrium the additive genetic variance decreases if (and only if) males are overproduced in the parts of the environment relatively beneficial to males, and similarly for females. Environmental sex determination (a system in which males develop in 1 set of environmental circumstances, females in others, but adults mix) is evolutionarily stable only if the correlation between fitness and the environmental variable of sex determination differs for males and females. These results are discussed particularly in reference to reptiles in which sex is determined by the incubation temperature of the egg.