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Related Experiment Videos

Spread rate for a nonlinear stochastic invasion.

M A Lewis1

  • 1Department of Mathematics, University of Utah, JWB 233, Salt Lake City, UT 84112, USA. mlewis@math.utah.edu

Journal of Mathematical Biology
|January 11, 2001
PubMed
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Stochastic factors in ecological invasions, arising from individual interactions, can significantly slow population spread. This study provides analytical bounds showing slower invasion rates compared to deterministic models.

Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Ecological invasion models predominantly use deterministic equations, neglecting stochasticity.
  • Stochastic factors can be extrinsic (environmental) or intrinsic (population-based).
  • A conjecture suggests intrinsic stochasticity slows invasion spread, but lacks thorough analytical investigation.

Purpose of the Study:

  • To analytically investigate the effect of intrinsic stochastic factors on spatial ecological invasions.
  • To understand how local interactions among individuals influence invasion dynamics.
  • To derive bounds for expected population density and invasion spread rates.

Main Methods:

  • Formulation of equations for the dynamics of population spatial moments.

Related Experiment Videos

  • Application of moment closure and comparison methods to derive bounds.
  • Analysis of upper bounds to determine the rate of stochastic invasion spread.

    • Main Results:

    • Intrinsic stochastic factors demonstrably slow the rate of ecological invasion compared to deterministic models.
    • The effect is most pronounced with widely spaced, high-density invasion foci due to spatial correlations.
    • Derived upper bounds provide a limit on the spread rate of stochastic invasions.

    Conclusions:

    • Intrinsic stochasticity is a crucial factor in ecological invasions, leading to slower spread rates.
    • Spatial correlations amplify density-dependent effects even at low population densities.
    • A heuristic formula is proposed for estimating invasion spread in nonlinear stochastic processes.