Impact of spatial structure on early and long-term adaptation in rugged fitness landscapes

We investigate the exploration of rugged fitness landscapes by spatially structured populations with demes on the nodes of a graph, connected by migrations. In the rare migration regime, we find that finite structures can adapt more efficiently than very large ones, especially in high-dimensional fitness landscapes. Furthermore, we show that, in most landscapes, migration asymmetries associated with some suppression of natural selection allow the population to reach higher fitness peaks first. In this sense, suppression of selection can make early adaptation more efficient. However, the time it takes to reach the first fitness peak is then increased. We also find that suppression of selection tends to enhance finite-size effects. We extend our study to frequent migrations, suggesting that our conclusions hold in this regime. We then investigate the impact of spatial structure with rare migrations on long-term evolution by studying the steady state of the population. For this, we define an effective population size for the steady-state distribution. We find that suppression of selection is associated to reduced steady-state effective population sizes, and reduced average steady-state fitnesses.