The effect of "fear" on two species competition

TL;DR

This paper explores how fear influences competition dynamics between two species, revealing complex behaviors like bi-stability and potential shifts from coexistence to exclusion, with implications for ecology and social systems.

Contribution

It introduces the first analysis of fear effects in classical competition models, demonstrating novel dynamical phenomena and spatial heterogeneity impacts.

Findings

Fear can induce bi-stability between coexistence and exclusion.

Spatial heterogeneity in fear can alter competition outcomes.

Fear effects extend to ecological and sociopolitical contexts.

Abstract

Non-consumptive effects such as fear of depredation, can strongly influence predator-prey dynamics. These effects have not been as well studied in the case of purely competitive systems, despite ecological and social motivations for the same. In this work we consider the classic two species ODE and PDE Lokta-Volterra competition models, where \emph{one} of the competitors is "fearful" of the other. We find that the presence of fear can have several interesting dynamical effects on the classical scenarios of weak and strong competition, and competitive exclusion. Notably, for fear levels in certain regimes, we show bi-stability between interior equilibrium and boundary equilibrium is possible - contrary to the classical strong competition situation where bi-stability is only possible between boundary equilibrium. Furthermore, in the spatially explicit setting, the effects of several spatially heterogeneous fear functions are investigated. In particular, we show that under certain $\mathbb{L}^{1}$ restrictions on the fear function, a weak competition type situation can change to competitive exclusion. Applications of these results to ecological as well as sociopolitical settings are discussed, that connect to the "landscape of fear" (LOF) concept in ecology.