Nonlocal pattern formation effects in evolutionary population dynamics

In this work, we derive a deterministic equation for a generalized nonlocal population dynamics that depends fundamentally on two lengths parameters (alpha, beta). We associate these parameters to the reproduction, competition, and pattern formation in bacterial dynamics. We propose that each set of parameters defines a state, and based on that, we formulate a stochastic cellular automaton for describing the evolutionary dynamics of a bacterial colony. It results in a selection of the bacteria more able to share space. In this way, we show that the evolution of the colony towards a maximum population allowed, in a given niche, defines the final pattern. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This work establishes a deterministic equation for a generalized nonlocal population dynamics that relies on two length parameters (alpha, beta) and associates these parameters with reproduction, competition, and pattern formation in bacterial dynamics. The proposed stochastic cellular automaton is formulated based on the states defined by each set of parameters, aiming to describe the evolutionary dynamics of a bacterial colony. The evolution of the colony towards a maximum population allowed in a given niche determines the final pattern, selecting for bacteria more capable of sharing space.