Spatial clustering of interacting bugs: Levy flights versus Gaussian jumps

TL;DR

This study compares how Gaussian and Levy flight-based movements influence spatial pattern formation in a biological competition model, revealing that resource competition primarily drives collective behavior over movement type.

Contribution

It introduces a model analyzing the effects of Gaussian versus Levy flight dispersal on spatial patterns in a competitive biological system.

Findings

Periodic patterns form under both diffusion types.

Resource competition dominates over movement type in pattern formation.

Differences between Gaussian and Levy flights are discussed.

Abstract

A biological competition model where the individuals of the same species perform a two-dimensional Markovian continuous-time random walk and undergo reproduction and death is studied. The competition is introduced through the assumption that the reproduction rate depends on the crowding in the neighborhood. The spatial dynamics corresponds either to normal diffusion characterized by Gaussian jumps or to superdiffusion characterized by L\'evy flights. It is observed that in both cases periodic patterns occur for appropriate parameters of the model, indicating that the general macroscopic collective behavior of the system is more strongly influenced by the competition for the resources than by the type of spatial dynamics. However, some differences arise that are discussed.