Environment heterogeneity creates fast amplifiers of natural selection in graph-structured populations.

Complex spatial structure, with partially isolated subpopulations, and environment heterogeneity, such as gradients in nutrients, oxygen, and drugs, both shape the evolution of natural populations. We investigate the impact of environment heterogeneity on mutant fixation in spatially structured populations with demes on the nodes of a graph. When migrations between demes are frequent, we find that environment heterogeneity can amplify natural selection and simultaneously accelerate mutant fixation and extinction, thereby fostering the quick fixation of beneficial mutants. We demonstrate this effect in the star graph, and more strongly in the line graph. We show that amplification requires mutants to have a stronger fitness advantage in demes with stronger migration outflow, and that this condition allows amplification in more general graphs. As a baseline, we consider circulation graphs, where migration inflow and outflow are equal in each deme. In this case, environment heterogeneity has no impact to first order, but increases the fixation probability of beneficial mutants to second order. Finally, when migrations between demes are rare, we show that environment heterogeneity can also foster amplification of selection, by allowing demes with sufficient mutant advantage to become refugia for mutants.