Trait evolution in two-sex populations

TL;DR

This paper develops a mathematical model for trait evolution in two-sex populations, deriving differential equations from individual interactions, and analyzes conditions for population persistence or extinction.

Contribution

It introduces a novel individual-based model incorporating semi-random mating and derives a macroscopic system of equations for trait evolution in two-sex populations.

Findings

Criteria for population persistence or extinction

Conditions for asymptotic stability of trait distributions

Application to specific trait inheritance examples

Abstract

We present an individual-based model of phenotypic trait evolution in two-sex populations, which includes semi-random mating of individuals of the opposite sex, natural death and intra-specific competition. By passing the number of individuals to infinity, we derive the macroscopic system of nonlinear differential equations describing the evolution of trait distributions in male and female subpopulations. We study solutions, give criteria for persistence or extinction, and state theorem on asymptotic stability, which we apply later to particular examples of trait inheritance.