Establishment and Fecundity in Spatial Ecological Models: Statistical Approach and Kinetic Equations

TL;DR

This paper develops a statistical approach to spatial ecological models, deriving kinetic equations to describe population dynamics influenced by establishment and fecundity, with analysis of dispersion and mesoscopic limits.

Contribution

It introduces a novel method for deriving and analyzing Vlasov-type kinetic equations for spatial ecological systems with birth-death processes.

Findings

Derived Vlasov-type kinetic equations for ecological models

Analyzed mesoscopic limits of stochastic spatial dynamics

Studied effects of establishment and fecundity mechanisms

Abstract

We consider spatial population dynamics given by Markov birth-and-death process with constant mortality and birth influenced by establishment or fecundity mechanisms. The independent and density dependent dispersion of spreading are studied. On the base of general methods of [14], we construct the state evolution of considered microscopic ecological systems. We analyze mesoscopic limit for stochastic dynamics under consideration. The corresponding Vlasov-type non-linear kinetic equations are derived and studied.