Stable partial migration under a genetic threshold model of migratory behaviour

Many species show migratory behaviour in response to seasonal changes in environmental conditions. A peculiar, yet widespread phenomenon is partial migration, when a single population consists of both migratory and non‐migratory individuals. There are still many open questions regarding the stability and evolutionary significance of such populations. For passerines the inheritance of migratory activity is best described by the threshold model of quantitative genetics. Such a model has not yet been employed in theoretical studies, in which stability of partially migratory populations is usually linked to group differences in survival or reproduction. Here we develop a parsimonious model featuring a conditional genetic threshold for passerine migratory behaviour under which stable partial migration can be observed, and we explore the resulting selection landscape. Our model results show a cline in migratory behaviour across the landscape, from fully migratory populations to fully residential populations, with a fairly wide zone of partially migratory populations, which is stable in both time and space under a wide range of parameter settings. Temporal stability of the zone is linked with the yearly variance in both migration survival and resident winter survival. In contrast to other theoretical studies, we show that density dependence in winter survival is not essential for observing partially migratory populations. In addition, we observe that selection on the genetic threshold value occurs mainly at the borders of the zone of partial migration. This result suggests that fully migratory and fully residential populations in areas far from the zone of partial migration can harbour genetic diversity that allows the appearance of the alternative phenotype under (a wide range of) different conditions.