Non-local interaction effects in models of interacting populations

TL;DR

This paper investigates non-local interaction models for two species, revealing that non-locality induces spatial structures, promotes species survival, and leads to complex spatio-temporal patterns beyond classical local models.

Contribution

It introduces non-local interaction terms into classical population models, demonstrating their effects on spatial pattern formation and species survival.

Findings

Non-local interactions induce spatial structures.

Non-locality can prevent extinction in competitive or predatory scenarios.

Spatio-temporal patterns emerge without oscillations in local models.

Abstract

We consider a couple of models for the dynamics of the populations of two interacting species, inspired by Lotka-Volterra's classical equations. The novelty of this work is that the interaction terms are non local and the interaction occurs within a bounded range. These terms include the competitive intraspecific interaction among individuals and the interspecific terms for which we consider two cases: Competition and predation. The results show that not only the non-locality induces spatial structures but also allows for the survival of the species when due to predation or the competitive exclusion extinction was expected, and even promotes spatio-temporal patterns not linked to eventual temporal oscillations in the local case. In this work we also explore some interesting details about the behavior of the population dynamics that shows spatial patterns that interfere in a way that leads to non-trivial results.