Use of birth-death-migration processes for describing the spread of insect populations

This paper models the spread of insect populations using stochastic birth-death-migration processes and presents statistical methodology for predicting population size. A birth-death-migration model for population growth and a stochastic compartmental model for population dispersal are developed and compared with Skellam's (1951, Biometrika 38:196-218) classic diffusion model. Statistical inferences are based on approximating gamma distributions. The birth-death-migration models have the advantages of incorporating more biological detail, accommodating releases from multiple sites, containing standard errors for predictions, and yielding inherent spatial correlation structure. A special case of the model is illustrated with data on the population dynamics of the Africanized honey bee, Apis mellifera L. The model is very general and has wide application to the range expansion and migration of other species because of its parameterization with generic birth, death, and migration rates