Ecological interactions and spatial dynamics in microbial aggregates: A novel modelling framework

TL;DR

This paper introduces a PDE-based model to simulate ecological interactions and spatial patterns in microbial aggregates, capturing key features observed in individual-based models and analyzing wave dynamics.

Contribution

A novel PDE framework incorporating cross-diffusion and reaction terms to model microbial interactions and spatial dynamics, validated against IBM simulations and analyzed for wave behavior.

Findings

Model reproduces spatial patterns seen in IBMs

Captures competition and commensalism dynamics

Analyzes traveling wave speeds in one dimension

Abstract

We present a mathematical model based on a system of partial differential equations (PDEs) with cross-diffusion and reaction terms to describe ecological interactions between multiple bacterial species and substrates within microaggregates, where bacteria proliferate in response to substrate availability and undergo passive dispersal driven by population pressure gradients. The ecological interactions include interspecific competition for shared substrates, and commensalism, whereby one species benefits from the metabolic by-products of another. The main motivation comes from individual-based models (IBMs) of microbial aggregates, where simulations reveal that substrate-limited conditions can give rise to rich spatial patterns. Our numerical experiments demonstrate that our PDE-based model captures the key qualitative features of three verification scenarios that have previously been investigated with IBMs. Moreover, we formally derive a competition system from an on-lattice biased random walk, and establish local well-posedness for a parameter-symmetric subcase of it. We then formally analyse the travelling wave behaviour of this case in one spatial dimension and compare the minimal travelling wave speed with the wave speed measured in the simulations.