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    Co-operation, Competition and Crowding: A Discrete Framework Linking Allee Kinetics, Nonlinear Diffusion, Shocks and Sharp-Fronted Travelling Waves.

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    14
    15
    Author
    Johnston, ST; Baker, RE; McElwain, DLS; Simpson, MJ
    Date
    2017-02-14
    Source Title
    Scientific Reports
    Publisher
    Springer Science and Business Media LLC
    University of Melbourne Author/s
    Johnston, Stuart
    Affiliation
    School of Mathematics and Statistics
    Metadata
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    Document Type
    Journal Article
    Citations
    Johnston, S. T., Baker, R. E., McElwain, D. L. S. & Simpson, M. J. (2017). Co-operation, Competition and Crowding: A Discrete Framework Linking Allee Kinetics, Nonlinear Diffusion, Shocks and Sharp-Fronted Travelling Waves.. Sci Rep, 7 (1), pp.42134-. https://doi.org/10.1038/srep42134.
    Access Status
    Open Access
    URI
    http://hdl.handle.net/11343/254715
    DOI
    10.1038/srep42134
    Open Access at PMC
    http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5307329
    Abstract
    Invasion processes are ubiquitous throughout cell biology and ecology. During invasion, individuals can become isolated from the bulk population and behave differently. We present a discrete, exclusion-based description of the birth, death and movement of individuals. The model distinguishes between individuals that are part of, or are isolated from, the bulk population by imposing different rates of birth, death and movement. This enables the simulation of various co-operative or competitive mechanisms, where there is either a positive or negative benefit associated with being part of the bulk population, respectively. The mean-field approximation of the discrete process gives rise to 22 different classes of partial differential equation, which can include Allee kinetics and nonlinear diffusion. Here we examine the ability of each class of partial differential equation to support travelling wave solutions and interpret the long time behaviour in terms of the individual-level parameters. For the first time we show that the strong Allee effect and nonlinear diffusion can result in shock-fronted travelling waves. We also demonstrate how differences in group and individual motility rates can influence the persistence of a population and provide conditions for the successful invasion of a population.

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