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Evolutionary branching is analysed in a stochastic, individual-basedpopulation model under mutation and selection. In such models, the commonassumption is that individual reproduction and life career are characterised byvalues of a trait, and also by population sizes, and that mutations lead tosmall changes in trait value. Then, traditionally, the evolutionary dynamics isstudied in the limit of vanishing mutational step sizes. In the presentapproach, small but non-negligible mutational steps are considered. By means oftheoretical analysis in the limit of infinitely large populations, as well ascomputer simulations, we demonstrate how discrete mutational steps affect thepatterns of evolutionary branching. We also argue that the average time to thefirst branching depends in a sensitive way on both mutational step size andpopulation size.

Evolutionary branching in a stochastic population model with discrete mutational steps