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 model is insufficient. This paper investigates an analogous stochastic power law logistic model. The exact (unconditional) population size distributions and the cumulant functions for this stochastic model are intractable for large population sizes. Approximating cumulant functions are derived for populations of any size, and are illustrated with examples of assumed Africanized honey bee population dynamics. Outstanding among the findings is that the approximations for the cumulant functions are very accurate for these examples. The stochastic power law logistic model is very general and may be applied to describe the growth of many other natural populations.