Clustering determines the survivor for competing Brownian and L\'evy walkers

TL;DR

This study investigates how spatial clustering influences competition outcomes between species with different movement patterns, revealing that clustering can determine which species survives or if coexistence is possible.

Contribution

It demonstrates that spatial clustering, rather than movement type alone, determines competitive success and coexistence in species with Brownian or Lévy flight movement.

Findings

Clustering leads to competitive advantage for more concentrated species.

Type of motion has no effect in well-mixed populations.

Coexistence occurs under specific spatial conditions.

Abstract

The competition between two ecologically similar species that use the same resources and differ from each other only in the type of spatial motion they undergo is studied. The latter is assumed to be described either by Brownian motion or L\'evy flights. Competition is taken into account by assuming that individuals reproduce in a density-dependent fashion. It is observed that no influence of the type of motion occurs when the two species are in a well-mixed unstructured state. However, as soon as the species develop spatial clustering, the one forming more concentrated clusters gets a competitive advantage and eliminates the other. Similar competitive advantage would occur between walkers of the same type but with different diffusivities if this leads also to different clustering. Coexistence of both species is also possible under certain conditions.