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A New Method for Calculating Net Reproductive Rate from Graph Reduction with Applications to the Control of Invasive Species

Bulletin of Mathematical Biology volume 69, pages 1341–1354 (2007)Cite this article

Abstract

Matrix models are widely used for demographic analysis of age and stage structured biological populations. Dynamic properties of the model can be summarized by the net reproductive rate R 0. In this paper, we introduce a new method to calculate and analyze the net reproductive rate directly from the life cycle graph of the matrix. We show, with examples, how our method of analysis of R 0 can be used in the design of strategies for controlling invasive species.

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Authors and Affiliations

  1. Centre for Mathematical Biology and Department of Biological Sciences, University of Alberta, Edmonton, Alberta, T6G 2E9, Canada

    T. de-Camino-Beck & M. A. Lewis

  2. Centre for Mathematical Biology and Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada

    M. A. Lewis

Authors
  1. T. de-Camino-Beck
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  2. M. A. Lewis
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Correspondence to T. de-Camino-Beck.

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de-Camino-Beck, T., Lewis, M.A. A New Method for Calculating Net Reproductive Rate from Graph Reduction with Applications to the Control of Invasive Species. Bull. Math. Biol. 69, 1341–1354 (2007). https://doi.org/10.1007/s11538-006-9162-0

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  • DOI: https://doi.org/10.1007/s11538-006-9162-0

Keywords

  • Matrix models
  • Net reproductive rate
  • Invasion
  • Biological control