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Time scales, persistence and patchiness

H M Hastings, R Pekelney, R Monticciolo

    Bio Systems
    |January 1, 1982
    PubMed
    Summary
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    This study explores ecological competition models, revealing that maximizing the diffusion-extinction ratio is an evolutionarily stable strategy for species persistence. Fractal geometry helps measure ecological successional stages.

    Area of Science:

    • Ecology
    • Theoretical Ecology
    • Mathematical Biology

    Background:

    • Ecological competition models are crucial for understanding species dynamics.
    • Patch-dynamical and diffusion-extinction models offer insights into ecological processes.
    • Levin's 1978 model provides a foundational framework for spatial ecology.

    Purpose of the Study:

    • To reformulate and extend Levin's basic model using geometric diffusion.
    • To analyze ecological dynamics across three distinct time scales.
    • To introduce fractal geometry for modeling long-term ecological effects and persistence.

    Main Methods:

    • Reformulation of Levin's 1978 model with geometric diffusion.
    • Analysis of diffusion-extinction ratios for evolutionary stability.

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  • Application of fractal geometry (Mandelbrot's 1977) to ecological models.
  • Development of the fractal exponent H as a measure of successional stage.

    • Main Results:

    • Diffusion drives short-term ecological dynamics.
    • Maximizing the diffusion-extinction ratio is an Evolutionarily Stable Strategy (ESS).
    • Organism-environment interactions become critical over longer time scales.
    • Relative patchiness is linked to ecological persistence via fractal dimensions.

    Conclusions:

    • Ecological models incorporating diffusion and extinction reveal complex dynamics across multiple time scales.
    • Evolutionarily stable strategies in competition are influenced by the balance of dispersal and local extinction.
    • Fractal geometry provides a novel framework for quantifying ecological succession and persistence.