The effect of "fear" on two species competition

Abstract

<abstract><p>Non-consumptive effects such as fear of depredation, can strongly influence predator-prey dynamics. There are several ecological and social motivations for these effects in competitive systems as well. In this work we consider the classic two species ODE and PDE Lotka-Volterra competition models, where <italic>one</italic> of the competitors is "fearful" of the other. We find that the presence of fear can have several interesting dynamical effects on the classical competitive scenarios. Notably, for fear levels in certain regimes, we show novel bi-stability dynamics. Furthermore, in the spatially explicit setting, the effects of several spatially heterogeneous fear functions are investigated. In particular, we show that under certain integral 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.</p></abstract>

Dynamical Analysis of a Lotka-Volterra Competition Model with both Allee and Fear Effect

“…It is worthwhile to comment to what degree the addition of the Allee effect changes the dynamical features of the model presented in [40], that is when there is only the fear effect present. We discuss this in terms of the classical scenarios of competitive exclusion, weak competition and strong competition, see Appendix B.…”

“…Similarly, by setting p(x) ≡ 1 and q(y) = 1 + py, we can obtain the Lotka-Volterra competition model for two competing species, where the species y is afraid of the species x [40]. On the other hand, if we set q(y) ≡ 1 and p(x) = p − x, we obtain a two species Lotka-Volterra ODE competition model that is subject to the Allee effect.…”

“…Such evidence motivates us to consider the fear effect in a purely competitive two-species model, in which one competitor causes fear to the other. Thus, Srivastava et al [40] considered the classical two-group Lotka-Volterra competition model with only one competitor causing fear to the other competitor:…”