Non-Poissonian bursts in the arrival of phenotypic variation can strongly affect the dynamics of adaptation

Abstract

The introduction of novel phenotypic variation in a population through random mutations plays a crucial role in evolutionary dynamics. Here we show that, when the probability that a sequence has a particular phenotype in its 1-mutational neighbourhood is low, statistical fluctuations imply that in the weak-mutation or monomorphic regime, novel phenotypic variation is not introduced at a constant rate, but rather in non-Poissonian "bursts". In other words, a novel phenotype appears multiple times in quick succession, or not at all for many generations. We use the RNA secondary-structure genotype-phenotype map to explore how increasing levels of heterogeneity in mutational neighbourhoods strengthen the bursts. Similar results are obtained for the HP model for protein tertiary structure and the Biomorphs model for morphological development. Burst can profoundly affect adaptive dynamics. Most notably, they imply that differences in arrival rates of novel variation can influence fixation rates more than fitness differences do.