Facial reconstruction

Search LJMU Research Online

Browse Repository | Browse E-Theses

Coexistence of competitors mediated by nonlinear noise

Siekmann, I and Bengfort, M and Malchow, H (2017) Coexistence of competitors mediated by nonlinear noise. European Physical Journal - Special Topics, 226 (9). pp. 2157-2170. ISSN 1951-6355

[img] Text
SiekBenMal2017.pdf - Accepted Version
Restricted to Repository staff only until 21 June 2018.

Download (4MB)

Abstract

Stochastic reaction-diffusion equations are a popular modelling approach for studying interacting populations in a heterogeneous environment under the influence of environmental fluctuations. Although the theoretical basis of alternative models such as Fokker- Planck diffusion is not less convincing, movement of populations is most commonly modelled using the diffusion law due to Fick. An interesting feature of Fokker-Planck diffusion is the fact that for spatially varying diffusion coefficients the stationary solution is not a homogeneous distribution – in contrast to Fick’s law of diffusion. Instead, concentration accumulates in regions of low diffusivity and tends to lower levels for areas of high diffusivity. Thus, we may interpret the stationary distribution of the Fokker-Planck diffusion as a reflection of different levels of habitat quality. Moreover, the most common model for environmental fluctuations, linear multiplicative noise, is based on the assumption that individuals respond independently to stochastic environmental fluctuations. For large population densities the assumption of independence is debatable and the model further implies that noise intensities can increase to arbitrarily high levels. Therefore, instead of the commonly used linear multiplicative noise model, we implement environmental variability by an alternative nonlinear noise term which never exceeds a certain maximum noise intensity. With Fokker-Planck diffusion and the nonlinear noise model replacing the classical approaches we investigate a simple invasive system based on the Lotka-Volterra competition model. We observe that the heterogeneous stationary distribution generated by Fokker-Planck diffusion generally facilitates the formation of segregated habitats of resident and invader. However, this segregation can be broken by nonlinear noise leading to coexistence of resident and invader across the whole spatial domain, an effect that would not be possible in the non-spatial version of the competition model for the parameters considered here.

Item Type: Article
Uncontrolled Keywords: 01 Mathematical Sciences, 02 Physical Sciences
Subjects: Q Science > QA Mathematics
Divisions: Applied Mathematics
Publisher: EDP Sciences
Related URLs:
Date Deposited: 20 Sep 2017 11:04
Last Modified: 20 Sep 2017 11:04
DOI or Identification number: 10.1140/epjst/e2017-70038-6
URI: http://researchonline.ljmu.ac.uk/id/eprint/7132

Actions (login required)

View Item View Item