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The Effects of Stochasticity on Pattern Formation in a Space- and Time-Discrete Predator–Prey System with Strong Allee Effect in the Prey

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Abstract

The effects of demographic and environmental noise on the vital dynamics and spatial pattern formation are studied for a predator–prey system with strong Allee effect in the prey species. Time and space are taken discrete. It is shown that noise can promote extinction depending on the growth and interaction parameters as well as the noise type and amplitude. The extinction risk increases with the noise amplitude; however, the environmental and demographic noise can have different effects on the risk of extinction. In space, the spatial structures obtained are blurred versions of the deterministic ones in most scenarios. In particular, the complex spatial structures that appear in the parameter domains where the deterministic local dynamics leads to extinction are robust to the density-dependent stochastic fluctuations but are disrupted with environmental noise.

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Acknowledgements

This research was supported by FAPERGS through Edital FAPERGS 012/2013 processes 0414-2551/14-0.

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Author notes

  1. Joice Chaves Marques

    Present address: PPGMap, UFRGS, Porto Alegre, Brazil

Authors and Affiliations

  1. Federal University of Santa Maria, Santa Maria, Brazil

    Joice Chaves Marques

  2. Institute of Environmental Systems Research, Osnabrück University, 49069, Osnabrück, Germany

    Horst Malchow

  3. Department of Mathematics, Federal University of Santa Maria, Santa Maria, Brazil

    Luiz Alberto Díaz Rodrigues & Diomar Cristina Mistro

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  1. Joice Chaves Marques
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  2. Horst Malchow
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  3. Luiz Alberto Díaz Rodrigues
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  4. Diomar Cristina Mistro
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Correspondence to Diomar Cristina Mistro.

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Marques, J.C., Malchow, H., Rodrigues, L.A.D. et al. The Effects of Stochasticity on Pattern Formation in a Space- and Time-Discrete Predator–Prey System with Strong Allee Effect in the Prey. Bull Math Biol 81, 1369–1393 (2019). https://doi.org/10.1007/s11538-018-00539-z

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  • DOI: https://doi.org/10.1007/s11538-018-00539-z

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