Evolution in Heterogeneous Environments: Between Soft and Hard Selection

Since their first formulations about half a century ago, the soft and hard selection models have become classical frameworks to study selection in subdivided populations. These models differ in the timing of density regulation and represent two extreme types of selection: density- and frequency-dependent selection (soft) and density- and frequency-independent selection (hard). Yet only few attempts have been made so far to model intermediate scenarios. Here, we design a model where migration may happen twice during the life cycle: before density regulation with probability d(J) (juvenile migration) and after density regulation with probability d(A) (adult migration). In the first step, we analyze the conditions for the coexistence of two specialists. We find that coexistence is possible under a large range of selection types, even when environmental heterogeneity is low. Then, we investigate the different possible outcomes obtained through gradual evolution. We show that polymorphism is more likely to evolve when the trade-off is weak, environmental heterogeneity is high, migration is low, and in particular when juvenile migration is low relative to adult migration, because the timing of migration affects the magnitude of frequency-dependent selection relative to gene flow. This model may provide a more general theoretical framework to experimentally study evolution in heterogeneous environments.