ON THE CUMULANTS OF POPULATION-SIZE FOR THE STOCHASTIC POWER-LAW LOGISTIC MODEL

The deterministic power law logistic model is used to describe density -dependent population growth in cases where the ordinary logistic mode l is insufficient. This paper investigates an analogous stochastic pow er law logistic model. The exact (unconditional) population size distr ibutions and the cumulant functions for this stochastic model are intr actable far large population sizes. Approximating cumulant functions a re derived for populations of any size, and are illustrated with examp les of assumed Africanized honey bee population dynamics. Outstanding among the findings is that the approximations for the cumulant functio ns are very accurate for these examples. The stochastic power law logi stic model is very general and maybe applied to describe the growth of many other natural populations. (C) 1998 Academic Press.