Evolutionary branching in a stochastic population model with discrete mutational steps

TL;DR

This paper investigates how discrete mutational steps influence evolutionary branching in stochastic population models, revealing that mutational step size and population size critically affect branching patterns and timing.

Contribution

It introduces an analysis of evolutionary branching considering non-negligible mutational steps, extending traditional models that assume infinitesimal mutations.

Findings

Discrete mutational steps significantly alter branching patterns.

Average time to first branching depends on mutational step size and population size.

Theoretical and simulation results show sensitivity of evolutionary dynamics to mutational step size.

Abstract

Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a trait, and also by population sizes, and that mutations lead to small changes in trait value. Then, traditionally, the evolutionary dynamics is studied in the limit of vanishing mutational step sizes. In the present approach, small but non-negligible mutational steps are considered. By means of theoretical analysis in the limit of infinitely large populations, as well as computer simulations, we demonstrate how discrete mutational steps affect the patterns of evolutionary branching. We also argue that the average time to the first branching depends in a sensitive way on both mutational step size and population size.