A multi-class extension of the mean field Bolker-Pacala population model

TL;DR

This paper extends the mean field Bolker-Pacala population model to multiple classes, analyzing equilibria, stability, and ergodicity, with implications for understanding complex population interactions.

Contribution

It introduces a multi-class extension of the mean field Bolker-Pacala model, providing new equilibrium analysis and stability results for systems with multiple interacting classes.

Findings

Existence of a symmetric non-trivial equilibrium for N ≥ 2

Calculation of all equilibria for the case N=2

Proven geometric ergodicity when no suppression occurs across classes

Abstract

We extend our earlier mean field approximation of the Bolker-Pacala model of population dynamics by dividing the population into N classes, using a mean field approximation for each class but also allowing migration between classes as well as possibly suppressive influence of the population of one class over another class. For N at least 2, we obtain one symmetric non-trivial equilibrium for the system and give global limit theorems. For N=2, we calculate all equilibrium solutions, which, under additional conditions, include multiple non-trivial equilibria. Lastly, we prove geometric ergodicity regardless of the number of classes when there is no population suppression across the classes.