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# Long-range dispersal, stochasticity and the broken accelerating wave of advance

Jacobs, Guy S. and Sluckin, Tim J. (2015) Long-range dispersal, stochasticity and the broken accelerating wave of advance. Theoretical Population Biology, 100, 39-55.

Record type: Article

## Abstract

Rare long distance dispersal events are thought to have a disproportionate impact on the spread of invasive species. Modelling using integrodifference equations suggests that, when long distance contacts are represented by a fat-tailed dispersal kernel, an accelerating wave of advance can ensue. Invasions spreading in this manner could have particularly dramatic effects. Recently, various authors have suggested that demographic stochasticity disrupts wave acceleration. Integrodifference models have been widely used in movement ecology, and as such a clearer understanding of stochastic effects is needed. Here, we present a stochastic non-linear one-dimensional lattice model in which demographic stochasticity and the dispersal regime can be systematically varied. Extensive simulations show that stochasticity has a profound effect on model behaviour, and usually breaks acceleration for fat-tailed kernels. Exceptions are seen for some power law kernels, $K(l) \propto |l|^{-\beta}$ with \$\beta

Other
pdf - Accepted Manuscript

e-pub ahead of print date: 24 December 2014
Published date: March 2015
Additional Information: Preprint version (October 2014) of TPB article accepted for publication December 2014
Keywords: q-bio.PE

## Identifiers

Local EPrints ID: 412485
URI: https://eprints.soton.ac.uk/id/eprint/412485
PURE UUID: 0b5b9ca9-6df4-40e6-8a54-e93fa623c4ab
ORCID for Tim J. Sluckin: orcid.org/0000-0002-9163-0061

## Catalogue record

Date deposited: 17 Jul 2017 13:59