On the evolution of patch-type dependent immigration

• We analyse the evolution of immigration into two types of patches.
• Generalists settle in any patch, specialists settle only in good patches.
• A high death rate during the dispersal season in rewarding patches favours branching.
• Evolutionary branching may lead to a stable coexistence of a generalist & specialist.

Empirical studies of dispersal indicate that decisions to immigrate are patch-type dependent; yet theoretical models usually ignore this fact. Here, we investigate the evolution of patch-type dependent immigration of a population inhabiting and dispersing in a heterogeneous landscape, which is structured by patches of low and high reward. We model the decision to immigrate in detail from a mechanistic underpinning. With the methods of adaptive dynamics, we derive both analytical and numerical results for the evolution of immigration when life-history traits are patch-type dependent. The model exhibits evolutionary branching in a wide parameter range and the subsequent coevolution can lead to a stable coexistence of a generalist, settling in patches of any type, and a specialist that only immigrates into patches of high reward. We find that individuals always settle in the patches of high reward, in which survival until maturation, relative fecundity and emigration probability are high. We investigate how the probability to immigrate into patches of low reward changes with model parameters. For example, we show that immigration into patches of low reward increases when the emigration probability in these patches increases. Further, immigration into patches of low reward decreases when the patches of high reward become less safe during the dispersal season.