A discrete time model of dispersal into a seasonal range with low probability of return

Insect species including fall armyworm (Spodoptera frugiperda), black cutworm (Agrotis ipsilon), and cotton leafworm (Alabama agrillacea) are seasonal residents of the northern United States and southern Canada, but the limits of their overwintering ranges are much farther south. Many of these species are economically important as crop pests, or ecologically important for the subsidies they provide to food webs in the seasonal range. We use discrete time models to investigate evolutionarily stable states for dispersal tendency in highly mobile species with large seasonal ranges and restricted overwintering ranges. When dispersal is introduced as a diffusive process, our models generate spatial and temporal population patterns qualitatively similar to those observed in the field. For reasonable sets of parameters, the return of an individual or its offspring from the northern part of the seasonal range may be a rare event and of little importance to the maintenance of the dispersal trait in the population.