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Pushing the Boundaries: Models for the Spatial Spread of Ecosystem Engineers

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Abstract

Ecosystems engineers are species that can substantially alter their abiotic environment and thereby enhance their population growth. The net growth rate of obligate engineers is even negative unless they modify the environment. We derive and analyze a model for the spread and invasion of such species. Prior to engineering, the landscape consists of unsuitable habitat; after engineering, the habitat is suitable. The boundary between the two types of habitat is moved by the species through their engineering activity. Our model is a novel type of a reaction–diffusion free boundary problem. We prove the existence of traveling waves and give upper and lower bounds for their speeds. We illustrate how the speed depends on individual movement and engineering behavior near the boundary.

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Acknowledgements

FL wishes to thank Chris Cosner for some initial discussions on this topic after attending several talks on using free boundary problems to model population spread. FL gratefully acknowledges funding from the Natural Sciences and Engineering Research Council of Canada (NSERC) through a Discovery Grant (RGPIN-2016-04795) and a Discovery Accelerator Supplement (RGPAS 492878-2016). JF gratefully acknowledges support from the German Academic Exchange Service (DAAD) Rise Worldwide Internship program. YZ gratefully acknowledges funding from the Chinese Scholarship Council (201707535005) and the National Natural Science Foundation of China (NSFC No. 41701054).

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Author notes

  1. Justus Fink

    Present address: Institute of Integrative Biology, ETH Zurich, 8092, Zurich, Switzerland

  2. Yingjie Zhu

    Present address: College of Science, Changchun University, Changchun, 130022, China

Authors and Affiliations

  1. Department of Mathematics and Statistics, Department of Biology, University of Ottawa, Ottawa, ON, K1N 6N5, Canada

    Frithjof Lutscher

  2. Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, K1N 6N5, Canada

    Justus Fink & Yingjie Zhu

Authors
  1. Frithjof Lutscher
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  2. Justus Fink
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Correspondence to Frithjof Lutscher.

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Lutscher, F., Fink, J. & Zhu, Y. Pushing the Boundaries: Models for the Spatial Spread of Ecosystem Engineers. Bull Math Biol 82, 138 (2020). https://doi.org/10.1007/s11538-020-00818-8

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