Small-scale spatial structure affects predator-prey dynamics and coexistence

Abstract

Small-scale spatial variability can affect community dynamics in many ecological and biological processes, such as predator-prey dynamics and immune responses. Spatial variability includes short-range neighbour-dependent interactions and small-scale spatial structure, such as clustering where individuals aggregate together, and segregation where individuals are spaced apart from one another. Yet, a large class of mathematical models aimed at representing these processes ignores these factors by making a classical mean-field approximation, where interactions between individuals are assumed to occur in proportion to their average density. Such mean-field approximations amount to ignoring spatial structure. In this work, we consider an individual based model of a two-species community that is composed of consumers and resources. The model describes migration, predation, competition and dispersal of offspring, and explicitly gives rise to varying degrees of spatial structure. We compare simulation results from the individual based model with the solution of a classical mean-field approximation, and this comparison provides insight into how spatial structure can drive the system away from mean-field dynamics. Our analysis reveals that mechanisms leading to intraspecific clustering and interspecific segregation, such as short-range predation and short-range dispersal, tend to increase the size of the resource species relative to the mean-field prediction. We show that under certain parameter regimes these mechanisms lead to the extinction of consumers whereas the classical mean-field model predicts the coexistence of both species.

Population dynamics with spatial structure and an Allee effect

“…The population dynamics arising from the IBM is analysed by considering the average density of individuals, Z 1 ( t ) = N ( t )/ L 2 . Information about the spatial configuration of the population can be studied in terms of the average density of pairs of individuals expressed as a pair correlation function, C (| ξ |, t ) [31,35,49,50]. The pair-correlation function denotes the average density of pairs of individuals with separation distance | ξ |, at a time, t , normalized by the density of pairs in a population with the complete absence of spatial structure.…”

“…In terms of spatial moments, the mean-field implies that we have Z2false(bold-italicξ,tfalse)=Z12false(tfalse) [30,31], which means that the expected death rate from equation (3.8) simplifies to, D1false(tfalse)=d+Z12false(tfalse)(∫ωcfalse(|bold-italicξ|false) dbold-italicξtrue)2+Z1false(tfalse)∫ωc2false(|bold-italicξ|false) dbold-italicξ. Similarly, the expected proliferation rate in equation (3.9) simplifies to P1false(tfalse)=p+Z1false(tfalse)∫ωpfalse(|bold-italicξ|false) dbold-italicξ. …”

“…In terms of spatial moments, the mean-field implies that we have Z 2 (ξ , t) = Z 2 1 (t) [30,31], which means that the expected death rate from equation (3.8) simplifies to,…”

“…When short-range interactions are present, such as shortrange competition, the mean-field approximation can become inaccurate [25][26][27][28]. Short-range interactions can lead to the development of spatial structure that can affect the overall population dynamics [29][30][31]. Spatial structure in biological populations includes both clustering and segregation [32][33][34][35][36][37].…”

Desempeño Del Modelo De Lotka-Volterra Y Holling Aplicado a Sistemas Presa-Depredador

“…Sin embargo, se espera a que alguna especie ganara en reproducción sobre la otra y es lo que sucede, siempre en teoría al suponer la presa sobre el depredador . Por lo tanto, se quiere demostrar en los tres modelos evaluados, que el primero es un modelo crítico estacionario donde las tasas de mortalidad y natalidad son variables y el segundo es un estudio de reducción paramétrica, donde se observa una variabilidad de x e y, presa y depredador, respectivamente (Surendran et al, 2020), el tercer modelo es desarrollado por el método Runge-Kutta, considerando la funcionalidad tipo II de Holling.…”