Stochastic Processes Driving Directional Evolution

Abstract

Evolution is a stochastic process, resulting from a combination of deterministic and random factors. We present results from a general theory of directional evolution that reveals how random variation in fitness, heritability, and migration influence directional evolution. First, we show how random variation in fitness produces a directional trend toward phenotypes with minimal variation in fitness. Furthermore, we demonstrate that stochastic variation in population growth rate amplifies the expected change due to directional selection in small populations. Second, we show that the evolutionary impacts of migration depend on the entire distribution of migration rates such that increasing the variance in migration rates reduces the impact of migration relative to selection. This means that changing the variance in migration rates, holding the mean constant, can substantially change the potential for local adaptation. Finally, we show that covariation between stochastic selection and stochastic heritability can drive directional evolutionary change, and that this can substantially alter the outcome of evolution in variable environments.