Stochastic effects in mean-field population growth: The quasi-Gaussian approximation to the case of a Taylor’s law-distributed substrate

Abstract

We analyze the effect of the stochastic growth rates, which may originate from heterogeneity of resource distribution on the average unrestricted growth of an ensemble of non-interacting sub-populations of consumers with Holling I and II functional responses, assuming normal (Gaussian) and anomalous (Tweedie) density distributions of resources. We show that the variation in the resource availability between the sub-population habitats leads to a non-Malthusian dynamics of the initial phase of the average biomass growth, and that this phase of growth can be successfully approximated using quasi-Gaussian approach. This conclusion is illustrated by numerical simulations.