The maintenance of polymorphism and divergence in sexually selected traits affected by frequency-dependent predation and consistent mating advantages

Questions: How does negative frequency-dependent natural selection (NFD) affect the maintenance and divergent fixation of polymorphic traits subject to directional mate preferences? What role does directional natural selection (DNS) on mate preferences play in these conditions when DNS is sex-limited versus when it is not? Negative frequency-dependent selection: NFD is characterized by a decline in the relative fitness of genotype with an increase in its relative frequency or abundance in a population. Models: We build sets of population genetic models based on the classical haploid version of the null model of sexual selection and use numerical simulations of deterministic recursions to analyse them. Conclusions: (I) Environments with NFD weaker than mate preferences of individual female types promote the fixation of sexual traits in opposite directions than environments with NFD stronger than mate preferences. (2) Strong NFD prevents the fixation of sexual traits in opposite directions despite the strong differences in mate preferences of individual female types. (3) The Fisher process interacts with NFD identically whether DNS is sex-limited or not.