An adaptive dynamics approach to sex ratio evolution in demographic two-sex models

Background/Question/Methods
The evolution of sex ratio, the ratio of male to female births in an individual’s offspring production strategy, is a frequency-dependent process that selects against the more frequent sex. One useful approach for studying frequency-dependent selection is adaptive dynamics, a phenotype-based framework that views evolution as a series of invasions by rare mutants. Because reproduction is shaped by the entire life cycle, studies of sex ratio may benefit from the use of an explicitly demographic two-sex model. Here, we present a demographic approach to sex ratio evolution that combines adaptive dynamics with nonlinear (frequency-dependent) matrix population models. These “matrix-based adaptive dynamics” methods allow the incorporation of any relevant population structure, including multiple sexes, into evolutionary projections.

Results/Conclusions
We have analyzed a series of two-sex, frequency-dependent matrix population models in order to characterize potential outcomes for sex ratio evolution. We find and classify multiple evolutionary scenarios, including evolutionary stable strategies resistant to invasion and branching points leading to phenotypic divergence. These matrix-based adaptive dynamics methods lend insight into alternative evolutionary outcomes in two-sex populations and can be similarly applied to other demographically-structured populations with linear or nonlinear dynamics.