Seasonal density-dependence can select for partial migrants in migratory species

Whether, and which, individuals migrate or not is rapidly changing in many populations. Exactly how and why environmental change alters migration propensity is not well understood. We constructed density-dependent structured population models to explore conditions for the coexistence of migrants and residents. Our theoretical models were motivated by empirical data identified via a systematic literature review. We find that the equilibrium density in the season with the strongest density-dependence of a strategy predicts whether the strategy will become dominant within the population. This equilibrium density represents strategy fitness in a seasonal environment and can be used to examine selection on migratory behaviour. Whether partial migration can be maintained within a population depends on where in the annual cycle density-dependence operates. Diversified bet-hedging, where parents produce a mix of migrants and residents, also maintains partial migration. Our study disentangles density-dependent and density-independent rates in a population with seasonal structure, potentially providing routes to explain the rapid change in migration strategies observed in many populations.

Methods
We investigate how different density-dependent regimes influence the coexistence of migratory and resident strategies within a population by developing a theoretical model. Our structured population model is motivated by empirical evidence from a literature review. In our model of a partially migratory population, migrants and residents share breeding grounds and overwinter apart. Based on such seasonal population structure, we constructed two monomorphic models where only migrants or residents exist in the population to calculate their strategy-specific equilibrium density for each season, and a polymorphic model with two strategies competing in the same population to calculate the proportion of each strategy at equilibrium. We can thus explore when two strategies coexist and when they cannot by modelling different scenarios.