Optimization of Seasonal Migratory Behavior

Abstract

A theoretical model is constructed for the dependence of the long term survival of a population on the fraction which migrate during the non-breeding season. The surviving fraction of the migrating fraction, Vm, and of the non-migrating fraction, Vs, are assumed to be independent random variables. The migration fraction which maximizes long term survival, Mm, is 1 when [image] [greater than or equal to] E(Vs), it is O when [image] [greater than or equal to] E(Vm), and is between O and 1 when [image] < E(Vs) and [image] < E(Vm), where E is the expectation. O < MM < 1 becomes more likely as the variance of either Vm or Vs increases and conversely. When a correlation exists between conditions at the time the decision to migrate is being made and the survival fraction during the following winter, MM varies according to the nature of this correlation, which may be different in different years. As the degree of correlation increases, MM is more likely to be either O or 1, and the survival expectation increases. The model is also applied to the problem of dispersal in general.