Small-scale spatial structure influences large-scale invasion rates
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ORIGINAL PAPER
Small-scale spatial structure influences large-scale invasion rates Michael J. Plank1,2
· Matthew J. Simpson3 · Rachelle N. Binny2,4
Received: 6 September 2019 / Accepted: 21 January 2020 © Springer Nature B.V. 2020
Abstract Local interactions among individual members of a population can generate intricate small-scale spatial structure, which can strongly influence population dynamics. The two-way interplay between local interactions and population dynamics is well understood in the relatively simple case where the population occupies a fixed domain with a uniform average density. However, the situation where the average population density is spatially varying is less well understood. This situation includes ecologically important scenarios such as species invasions, range shifts, and moving population fronts. Here, we investigate the dynamics of the spatial stochastic logistic model in a scenario where an initially confined population subsequently invades new, previously unoccupied territory. This simple model combines density-independent proliferation with dispersal, and density-dependent mortality via competition with other members of the population. We show that, depending on the spatial scales of dispersal and competition, either a clustered or a regular spatial structure develops over time within the invading population. In the short-range dispersal case, the invasion speed is significantly lower than standard predictions of the mean-field model. We conclude that mean-field models, even when they account for non-local processes such as dispersal and competition, can give misleading predictions for the speed of a moving invasion front. Keywords Density dependence · Dispersal · Mean-field model · Plant populations · Species range shifts · Stochastic model
Introduction Spatial structure can affect population dynamics. Common examples of spatial structure are clustering, where individuals tend to occur in tightly packed groups, and regular structure, where individuals tend to be evenly spaced from one another (Pacala and Silander 1985; Mahdi and Law 1987; Purves and Law 2002). Spatial structure can arise from individual-level processes and interactions that occur locally in space, such as competition (Yokozawa et al. 1999; Adams et al. 2013), dispersal (Lewis and Pacala 2000), adhesion (Johnston et al. 2013), and crowding (Binny et al. Michael J. Plank
[email protected] 1
School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand
2
Te P¯unaha Matatini, Centre of Research Excellence, Auckland, New Zealand
3
School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
4
Manaaki Whenua, Lincoln, New Zealand
2016a). These local interactions typically generate smallscale spatial structure that occurs at a length scale of the order one to ten times an individual’s size. Despite being local in origin, spatial structure can have significant largescale effects on population size, and even determine whether the population
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