Population-level consequences of heterospecific density-dependent movements in predator-prey systems.
In this paper we elucidate how small-scale movements, such as those associated with searching for food and avoiding predators, affect the stability of predator-prey dynamics. We investigate an individual-based Lotka-Volterra model with density-dependent movement, in which the predator and prey populations live in a very large number of coupled patches. The rates at which individuals leave patches depend on the local densities of heterospecifics, giving rise to one reaction norm for each of the two species. Movement rates are assumed to be much faster than demographics rates. A spatial structure of predators and prey emerges which affects the global population dynamics. We derive a criterion which reveals how demographic stability depends on the relationships between the per capita covariance and densities of predators and prey. Specifically, we establish that a positive relationship with prey density and a negative relationship with predator density tend to be stabilizing. On a more mechanistic level we show how these relationships are linked to the movement reaction norms of predators and prey. Numerical results show that these findings hold both for local and global movements, i.e., both when migration is biased towards neighbouring patches and when all patches are reached with equal probability.
Department of Ecology and Environmental Science, Umeå University, 90187 Umeå, Sweden. Electronic address: henrik.sjodin@emg.umu.se.
Henrik
H
Sjödin
Department of Mathematics and Mathematical Statistics, Umeå University, 90187 Umeå, Sweden; Evolution and Ecology Program, International Institute for Applied Systems Analysis, 2361 Laxenburg, Austria.
Ke
K
Brännström
Department of Ecology and Environmental Science, Umeå University, 90187 Umeå, Sweden.
Mårten
M
Söderquist
Department of Ecology and Environmental Science, Umeå University, 90187 Umeå, Sweden. Electronic address: goran.englund@emg.umu.se.
Göran
G
Englund
D025041:Animal Migration / Q000502:physiology*; D000818:Animals; D011156:Population Density; D011235:Predatory Behavior / Q000502:physiology*; D013045:Species Specificity
Moment closure; Population dynamics; Spatial structure; Species coexistence; Stochastic processes