USE OF BIRTH-DEATH-MIGRATION PROCESSES FOR DESCRIBING THE SPREAD OF INSECT POPULATIONS

This paper models the spread of insect populations using stochastic bi rth-death-migration processes and presents statistical methodology for predicting population size. A birth-death-migration model for populat ion growth and a stochastic compartmental model for population dispers al are developed and compared with Skellam's (1951, Biometrika 38: 196 -218) classic diffusion model. Statistical inferences are based on app roximating gamma distributions. The birth-death-migration models have the advantages of incorporating more biological detail, accommodating releases from multiple sites, containing standard errors for predictio ns, and yielding inherent spatial correlation structure. A special cas e 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 othe r species because of its parameterization with generic birth, death, a nd migration rates.