Migration effects in a stochastic multipopulation model for African bee population dynamics

The rate of northern migration of the Africanized honey bee (AHB) in the United States has recently slowed dramatically. This paper investigates the impact of migration on the equilibrium size distributions of a particular stochastic multipopulation model, namely a coupled logistic power law model. The bivariate equilibrium size distribution of the model is derived and illustrated with parameter values used to describe AHB population dynamics. In the model, the difference between the equilibrium sizes of the two populations is a measure of the effect of migration. The distribution of this difference may be approximated by a normal distribution. The mean and variance parameters for the normal are predicted accurately by a second-order regression model based on the migration rate and the maximum size of the first population. The methodology is general, and should be useful in studying the migration effect in many other applications with one-way migration.