Model of phenotypic evolution in hermaphroditic populations

TL;DR

This paper develops a mathematical model for phenotypic evolution in hermaphroditic populations, incorporating mating behaviors, and analyzes the long-term distribution of traits through nonlinear equations.

Contribution

It introduces a new individual-based model that accounts for random and assortative mating, deriving a nonlinear transport equation and analyzing its attractors.

Findings

Existence of a one-dimensional attractor is proved.

A formula for the phenotypic trait distribution in the asymptotic population is derived.

The model captures the effects of mating patterns on phenotypic evolution.

Abstract

We consider an individual based model of phenotypic evolution in hermaphroditic populations which includes random and assortative mating of individuals. By increasing the number of individuals to infinity we obtain a nonlinear transport equation, which describes the evolution of distribution of phenotypic traits. Existence of an one-dimensional attractor is proved and the formula for the density of phenotypic traits in the limiting (asymptotic) population is derived in some particular case.