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A Structured Threshold Model for Mountain Pine Beetle Outbreak

Bulletin of Mathematical Biology volume 72, pages 565–589 (2010)Cite this article

Abstract

A vigor-structured model for mountain pine beetle outbreak dynamics within a forest stand is proposed and analyzed. This model explicitly tracks the changing vigor structure in the stand. All model parameters, other than beetle vigor preference, were determined by fitting model components to empirical data. An abrupt threshold for tree mortality to beetle densities allows for model simplification. Based on initial beetle density, model outcomes vary from decimation of the entire stand in a single year, to inability of the beetles to infect any trees. An intermediate outcome involves an initial infestation which subsequently dies out before the entire stand is killed. A model extension is proposed for dynamics of beetle aggregation. This involves a stochastic formulation.

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Authors and Affiliations

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

    Mark A. Lewis

  2. Department of Biological Sciences, University of Alberta, Edmonton, Canada

    William Nelson & Cailin Xu

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  1. Mark A. Lewis
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  2. William Nelson
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  3. Cailin Xu
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Correspondence to Mark A. Lewis.

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Lewis, M.A., Nelson, W. & Xu, C. A Structured Threshold Model for Mountain Pine Beetle Outbreak. Bull. Math. Biol. 72, 565–589 (2010). https://doi.org/10.1007/s11538-009-9461-3

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  • DOI: https://doi.org/10.1007/s11538-009-9461-3

Keywords

  • Mountain pine beetle
  • Structured population model
  • Integrodifference equation