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Modeling invasive species spread in Lake Champlain via evolutionary computations

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Abstract

We use a reaction diffusion equation, together with a genetic algorithm approach for model selection to develop a general modeling framework for biological invasions. The diffusion component of the reaction diffusion model is generalized to include dispersal and advection. The reaction component is generalized to include both linear and non-linear density dependence, and Allee effect. A combination of the reaction diffusion and genetic algorithm is able to evolve the most parsimonious model for invasive species spread. Zebra mussel data obtained from Lake Champlain, which demarcates the states of New York and Vermont, is used to test the appropriateness of the model. We estimate the minimum wave spread rate of Zebra mussels to be 22.5 km/year. In particular, the evolved models predict an average northward advection rate of 60.6 km/year (SD ± 1.9), which compares very well with the rate calculated from the known hydrologic residence time of 60 km/year. A combination of a reaction diffusion model and a genetic algorithm is, therefore, able to adequately describe some of the hydrodynamic features of Lake Champlain and the spread of a typical invasive species—Zebra mussels within the lake.

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Acknowledgments

This work was supported in part by grants from the National Science Foundation (DUE 0436330) to DEB; United States Department of Agriculture Hatch and the University of Vermont Department of Energy Computational Biology grants to JPH, and DEB and support from Eastern Connecticut State University to OBM

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Eastern Connecticut State University, 83 Wndham St, Willimantic, CT, 06226, USA

    B. M. Osei

  2. Department of Plant Biology, The University of Vermont, 63 Carrigan Dr., Burlington, VT, 05405, USA

    C. D. Ellingwood

  3. Sustainability Programs, 239 Montauk Highway, Stony Brook Southampton, Southampton, NY, 11968, USA

    J. P. Hoffmann

  4. Department of Mathematics and Statistics, The University of Vermont, 16 Colchester Av, Burlington, VT, 05405, USA

    D. E. Bentil

Authors
  1. B. M. Osei
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  2. C. D. Ellingwood
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  3. J. P. Hoffmann
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  4. D. E. Bentil
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Correspondence to B. M. Osei.

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Osei, B.M., Ellingwood, C.D., Hoffmann, J.P. et al. Modeling invasive species spread in Lake Champlain via evolutionary computations. Theory Biosci. 130, 145–152 (2011). https://doi.org/10.1007/s12064-011-0122-3

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  • DOI: https://doi.org/10.1007/s12064-011-0122-3

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