The coexistence of migrant and non-migrants within a population, known as partial migration, is widespread among birds, fish, and mammals. Game theoretical models have been used to demonstrate that density dependence can maintain partial migration as an evolutionary stable strategy (ESS), however these results are difficult to apply broadly. The models use only one form of density dependence or combine multiple forms which cannot be assessed separately, and no forms of density dependence have been directly compared. Given that partially migratory taxa encompass all major vertebrate groups, as well as some invertebrates, modeling results that are more broadly applicable are important. In this study, we compare four complimentary forms of density dependence during reproduction using a simple population matrix model. We use adaptive dynamics to determine if each of the four forms allow for partial migration as an evolutionarily stable strategy and convergent stable strategy (CSS).
Results/Conclusions
By comparing forms of density dependence with the same model, we show that not all forms of density dependence lead to partial migration as an ESS/CSS. Most notably, partial migration is an ESS/CSS when migrants and non-migrants breed in isolation and experience density dependence only within their phenotype. In this case, phenotypes only interact through an allocation strategy, i.e., the trait that determines the fraction of each phenotype. When phenotypes compete directly during reproduction, partial migration is not an ESS/CSS. Instead, populations will be all migrant or all non-migrant. Prior residence density dependence, and its complimentary form late residence, lead to partial migration as an ESS/CSS only under certain conditions. These results can be used to generate predictions for many different species and provide a better understanding for the role of density dependence in the evolutionary stability of partial migration.