Stochastic foundations in nonlinear density-regulation growth

TL;DR

This paper develops individual-based stochastic models for nonlinear density-regulation growth, linking microscopic interactions to macroscopic dynamics, analyzing extinction conditions, and deriving population distribution results.

Contribution

It introduces models that connect individual interactions with the generalized logistic growth and analyzes stochastic effects on long-term population dynamics.

Findings

Conditions for population extinction identified

Analytical expressions for population abundance distribution derived

Mean time to extinction calculated

Abstract

In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We also study the effect of internal fluctuations on the long-time dynamics for the different models that have been widely used in the literature, such as the theta-logistic and Savageau models. In particular, we determine the conditions for population extinction and calculate the mean time to extinction. If the population does not become extinct, we obtain analytical expressions for the population abundance distribution. Our theoretical results are based on WKB theory and the probability generating function formalism and are verified by numerical simulations.