A simple mathematical model of gradual Darwinian evolution: Emergence of a Gaussian trait distribution in adaptation along a fitness gradient

TL;DR

This paper presents a mathematical model demonstrating how Gaussian trait distributions naturally emerge in populations undergoing gradual Darwinian evolution driven by competition and adaptation in a constant environment.

Contribution

It introduces an analytically solvable model showing the emergence of Gaussian trait distributions during adaptation along a fitness gradient.

Findings

Gaussian trait distribution emerges from generic initial conditions.

Exact analytical solutions are obtained for the evolution dynamics.

Model applies to asexual populations in constant environments.

Abstract

We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while far from evolutionary stable equilibrium. The model admits exact analytical solution. In particular, Gaussian distribution of the trait emerges from generic initial conditions.