Pattern formation and coexistence domains for a nonlocal population dynamics

TL;DR

This paper introduces a general nonlocal population dynamics model incorporating characteristic length parameters, analyzing pattern formation and coexistence domains, and compares the theoretical results with experimental data on E. coli diffusion.

Contribution

The paper develops a comprehensive nonlocal model with variable length parameters and identifies a coexistence curve analogous to thermodynamics, linking theory with experimental data.

Findings

Identified a coexistence curve in parameter space for pattern formation.

Established an analogy between population dynamics and thermodynamics.

Validated the model with experimental data on E. coli diffusion.

Abstract

In this communication we propose a most general equation to study pattern formation for one-species population and their limit domains in systems of length L. To accomplish this we include non-locality in the growth and competition terms where the integral kernels are now depend on characteristic length parameters alpha and beta. Therefore, we derived a parameter space (alpha,beta) where it is possible to analyze a coexistence curve alpha*=alpha*(\beta) which delimits domains for the existence (or not) of pattern formation in population dynamics systems. We show that this curve has an analogy with coexistence curve in classical thermodynamics and critical phenomena physics. We have successfully compared this model with experimental data for diffusion of Escherichia coli populations.