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Effects of Heterogeneity on Spread and Persistence in Rivers

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Abstract

The question how aquatic populations persist in rivers when individuals are constantly lost due to downstream drift has been termed the “drift paradox.” Recent modeling approaches have revealed diffusion-mediated persistence as a solution. We study logistically growing populations with and without a benthic stage and consider spatially varying growth rates. We use idealized hydrodynamic equations to link river cross-sectional area to flow speed and assume heterogeneity in the form of alternating patches, i.e., piecewise constant conditions. We derive implicit formulae for the persistence boundary and for the dispersion relation of the wave speed. We explicitly discuss the influence of flow speed, cross-sectional area and benthic stage on both persistence and upstream invasion speed.

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Authors and Affiliations

  1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2E1

    Frithjof Lutscher & Mark A. Lewis

  2. Department of Biological Sciences, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada, T2N 1N4

    Frithjof Lutscher & Edward McCauley

  3. Department of Biological Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2E1

    Mark A. Lewis

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  1. Frithjof Lutscher
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  2. Mark A. Lewis
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  3. Edward McCauley
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Correspondence to Frithjof Lutscher.

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Lutscher, F., Lewis, M.A. & McCauley, E. Effects of Heterogeneity on Spread and Persistence in Rivers. Bull. Math. Biol. 68, 2129–2160 (2006). https://doi.org/10.1007/s11538-006-9100-1

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  • DOI: https://doi.org/10.1007/s11538-006-9100-1

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