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Individual Variability in Dispersal and Invasion Speed

Author

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  • Aled Morris

    (Centre for Biomathematics, College of Science, Swansea University, Swansea SA2 8PP, UK
    Department of Mathematics, College of Science, Swansea University, Swansea SA2 8PP, UK)

  • Luca Börger

    (Centre for Biomathematics, College of Science, Swansea University, Swansea SA2 8PP, UK
    Department of Biosciences, College of Science, Swansea University, Swansea SA2 8PP, UK)

  • Elaine Crooks

    (Centre for Biomathematics, College of Science, Swansea University, Swansea SA2 8PP, UK
    Department of Mathematics, College of Science, Swansea University, Swansea SA2 8PP, UK)

Abstract

We model the growth, dispersal and mutation of two phenotypes of a species using reaction–diffusion equations, focusing on the biologically realistic case of small mutation rates. Having verified that the addition of a small linear mutation term to a Lotka–Volterra system limits it to only two steady states in the case of weak competition, an unstable extinction state and a stable coexistence state, we exploit the fact that the spreading speed of the system is known to be linearly determinate to show that the spreading speed is a nonincreasing function of the mutation rate, so that greater mixing between phenotypes leads to slower propagation. We also find the ratio at which the phenotypes occur at the leading edge in the limit of vanishing mutation.

Suggested Citation

  • Aled Morris & Luca Börger & Elaine Crooks, 2019. "Individual Variability in Dispersal and Invasion Speed," Mathematics, MDPI, vol. 7(9), pages 1-21, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:795-:d:262855
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    References listed on IDEAS

    as
    1. Elizabeth C Elliott & Stephen J Cornell, 2013. "Are Anomalous Invasion Speeds Robust to Demographic Stochasticity?," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-8, July.
    2. Camille Parmesan & Gary Yohe, 2003. "A globally coherent fingerprint of climate change impacts across natural systems," Nature, Nature, vol. 421(6918), pages 37-42, January.
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    1. Pablo Bonilla-Escribano & David Ramírez & Alejandro Porras-Segovia & Antonio Artés-Rodríguez, 2020. "Assessment of Variability in Irregularly Sampled Time Series: Applications to Mental Healthcare," Mathematics, MDPI, vol. 9(1), pages 1-18, December.

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