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Spreading speed and linear determinacy for two-species competition models.

Mark A Lewis1, Bingtuan Li, Hans F Weinberger

  • 1Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA. mlewis@math.ualberta.ca

Journal of Mathematical Biology
|October 10, 2002
PubMed
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Invasive species spread rates are often estimated using a simplified formula. This study identifies conditions where this formula accurately predicts invasion speed in two-species competition models.

Area of Science:

  • Ecology
  • Mathematical Biology
  • Theoretical Ecology

Background:

  • Invasive species pose significant ecological threats.
  • Accurate prediction of species invasion rates is crucial for conservation and management.
  • A common heuristic for spread rate relies on linear determinacy, which simplifies complex competition dynamics.

Purpose of the Study:

  • To derive sufficient conditions for the validity of linear determinacy in spatially explicit, two-species competition models.
  • To understand the limitations of a common heuristic spread rate formula.
  • To identify ecological and dispersal parameters influencing invasion dynamics.

Main Methods:

  • Mathematical derivation of conditions for linear determinacy.
  • Analysis of spatially explicit, two-species competition models.

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  • Application of established mathematical results from companion research.

    • Main Results:

    • Sufficient conditions for linear determinacy were derived.
    • Linear determinacy requires higher invader dispersal relative to resident dispersal.
    • Weakened interactions between resident and invader species also promote linear determinacy.

    Conclusions:

    • The heuristic spread rate formula is not universally applicable for two-species competition.
    • Deviations from derived conditions can lead to invasion rates exceeding predictions.
    • Understanding these conditions is vital for accurate ecological modeling of invasions.