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Turing patterns in a predator-prey model with seasonality.

Xiaoying Wang1, Frithjof Lutscher2,3

  • 1Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, K1N 6N5, Canada. xwang4@uottawa.ca.

Journal of Mathematical Biology
|August 30, 2018
PubMed
Summary
This summary is machine-generated.

Seasonal variations can drive ecological pattern formation. A new model shows that low resource survival in winter enhances this pattern development, even with similar predator and prey diffusion rates.

Keywords:
Consumer-resourceDiscrete systemImpulsive reproductionPattern formationReaction–diffusion equationTuring bifurcation

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Ecological systems often exhibit non-uniform population distributions.
  • Diffusion-driven instabilities are known mechanisms for pattern formation in biology, but less explored in ecology due to restrictive conditions.
  • The impact of seasonal variation on ecological pattern formation remains largely uninvestigated.

Purpose of the Study:

  • To explore pattern formation in ecological systems influenced by seasonal variation.
  • To analyze an impulsive reaction-diffusion model for a resource and consumer in a two-season environment.
  • To determine conditions for diffusion-driven instability and pattern emergence.

Main Methods:

  • Formulation and analysis of an impulsive reaction-diffusion system.
  • Modeling a resource with seasonal growth and a consumer with annual reproduction.
  • Derivation of conditions for diffusion-driven instability using a Beddington-DeAngelis functional response.

Main Results:

  • Pattern formation is demonstrated to be possible within the two-season model.
  • A low overwinter survival probability for the resource significantly enhances the propensity for pattern formation.
  • Diffusion-driven instability can occur even when resource and consumer diffusion rates are comparable.

Conclusions:

  • Seasonal variation, particularly low resource overwinter survival, can promote pattern formation in ecological systems.
  • Impulsive reaction-diffusion models are valuable tools for understanding ecological pattern dynamics.
  • The study expands the understanding of diffusion-driven instabilities in ecological contexts.