A Theory of Partial Migration

In this article we develop a game-theoretical approach to the study of evolutionarily stable partial migration, applicable to both deterministic and stochastic population models. We assume that partial migration is related to the overwintering strategies of animals: a fraction of the population overwinters locally, while another fraction migrates to other overwintering sites. We show that partial migration may arise owing to density-dependent overwintering survival and that environmental uncertainty does not need to be assumed. We also show that, when there are differences in the reproductive successes between the migratory and nonmigratory strategies, then the evolutionarily stable strategy (ESS) may be very sensitive with respect to these differences. Furthermore, when there are differences in the reproductive successes between the migratory and nonmigratory strategies, then applying the same behavior throughout life may not be an ESS (i.e., as the individual grows older, it tends to change from migration to nonmigration). On the other hand, when there are differences in the reproductive successes among ages, then this change in strategies with age is not expected. Finally, we show that uncertainty may or may not bias the ESS fraction of migratory animals depending on whether uncertainties affect the average population levels.