Population-level consequences of heterospecific density-dependent movements in predator–prey systems

Abstract

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 neighboring patches and when all patches are reached with equal probability.

Only strict quarantine measures can curb the coronavirus disease (COVID-19) outbreak in Italy, 2020

“…To account for the importance of stochasticity in individual-based processes within smaller cities and within households, we modelled the outbreak progression as a continuous-time Markov process, specifically by developing a susceptible-exposed-infectious-recovered (SEIR) epidemiological model in the form of a Master equation [3][4][5] (Supplement 1). The model was parameterised to COVID-19 based on published data on incubation time and infectious period [6,7].…”

Space race functional responses

“…R. Soc. B 282: 20142121 movements [15,24,25]. Dividing equation (3.1) by P gives the rate at which individual predators encounter prey, which is conventionally referred to as the 'encounter rate'.…”

“…concerns only movements in response to densities of heterospecifics and does not involve reactions to conspecifics, the prey's resources or other environmental factors. Our analyses are based on an approximation of the spatial covariance between predators and prey, which was derived in [15]. We show how empirically documented emigration responses give rise to a new nonlinear functional response which we compare with the Holling type II and DeAngelis-Beddington responses.…”

“…This conflict of interest leads to a spatial game that has been termed a space race [13]. Space races between predators and prey are dominant drivers of small-scale spatial distributions [14], and have significant effects on predator-prey encounter rates [15]. Although the importance of space races is widely recognized, it remains unclear how they affect functional responses.…”

Holocene extinctions of a top predator—Effects of time, habitat area and habitat subdivision

“…This is illustrated by the longstanding 'SLOSS' debate about reserve design, which focused on the relative merits of a single large habitat patch and several small patches for population persistence (Ovaskainen, 2002), and more recently by the related debate about the role of fragmentation per se (Fahrig, 2017;Fletcher et al, 2018;Hanski, 2015). An important lesson from theoretical studies is that dispersal capacity is crucial for how organisms respond to changes in the spatial structure of the habitat (Keeling, Wilson, & Pacala, 2002;Sjödin, Brännström, Söderquist, & Englund, 2014). For example, species with either high or low dispersal capacities may experience the same landscape as consisting of a single large habitat or many small isolated habitats respectively (MacDonald, Anderson, Acorn, & Nielsen, 2018;Öckinger, Franzen, Rundlöf, & Smith, 2009;Thomas, 2000).…”