Flexible matrix models for two sexes
Sex differences in vital rates and mate availability can have important effects on population- and evolutionary dynamics. These effects and how they vary depending on mating strategies can be explored with extensions to traditional matrix models.
We look at a recent paper on continuous-time two-sex matrix models:
"Mating, births, and transitions: a flexible two-sex matrix model for evolutionary demography" (Shyu & Caswell 2018, Population Ecology)
Models of sexually-reproducing populations that consider only a single sex cannot capture the effects of sex-specific demographic differences and mate availability. We present a new framework for two-sex demographic models that implements and extends the birth-matrix mating-rule approach of Pollak. The model is a continuous-time matrix model that explicitly includes the processes of mating (which is nonlinear but homogeneous), offspring production, and demographic transitions and survival. The resulting nonlinear model converges to exponential growth with an equilibrium population composition. The model can incorporate age- or stage-structured life histories and flexible mating functions. As an example, we apply the model to analyze the effects of mating strategies (polygamy or monogamy, and mated unions composed of males and females, of variable duration) on the response to sex-biased harvesting. The combination of demographic complexity with the interaction of the sexes can have major population dynamic effects and can change the outcome of evolution on sex-related characters.