Partial migration and transient coexistence of migrants and residents in animal populations.

Partial migration, whereby a proportion of the population migrates, is common across the animal kingdom. Much of the focus in the literature has been on trying to explain the underlying mechanisms for the coexistence of migrants and residents. In addition, there has been an increasing number of reports on the prevalence and frequency of partially migratory populations. One possible explanation for the occurrence of partial migration, which has received no attention in the literature, is that of 'transient coexistence' during the invasion phase of a superior behaviour. In this study we develop a theoretical basis for explaining partial migration as a transient coexistence and derive a method to predict the frequency of residents and migrants in partially migrating populations. This method is useful to predict the frequencies of migrants and residents in a small set of populations as a complementing hypothesis to 'an Evolutionary Stable Strategy (ESS)'. We use the logistic growth equation to derive a formula for predicting the frequencies of residents and migrants. We also use simulations and empirical data from white perch (Morone americana), moose (Alces alces) and red deer (Cervus elaphus) to demonstrate our approach. We show that the probability of detecting partial migration due to transient coexistence depends upon a minimum number of tracked or marked individuals for a given number of populations. Our approach provides a starting point in searching for explanations to the observed frequencies, by contrasting the observed pattern with both the predicted transient and the uniform random pattern. Aggregating such information on observed patterns (proportions of migrants and residents) may eventually lead to the development of a quantitative theory for the equilibrium (ESS) populations as well.