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Persistence in population models with demographic fluctuations.

T G Hallam, M Zhien

    Journal of Mathematical Biology
    |January 1, 1986
    PubMed
    Summary
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    This study introduces a population persistence and extinction theory for fluctuating demographic models. It establishes criteria to predict if populations will persist or face asymptotic extinction, crucial for toxic substance impact assessments.

    Area of Science:

    • Ecology
    • Mathematical Biology
    • Environmental Toxicology

    Background:

    • Population dynamics are influenced by temporal fluctuations in demographic parameters.
    • Understanding population persistence and extinction is vital for ecological risk assessment.

    Purpose of the Study:

    • To develop a theoretical framework for population persistence and extinction.
    • To establish criteria for predicting population fate under fluctuating conditions.
    • To apply this theory to assess the impact of toxic substances with oscillatory inputs.

    Main Methods:

    • Analytical studies of deterministic population models.
    • Development of a hierarchy of persistence criteria based on time-averaged fluctuations.
    • Identification of threshold values separating persistent from extinction-prone models.

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    Main Results:

    • Population models with fluctuating parameters may exhibit oscillations or stabilize.
    • Extinction, when it occurs, is an asymptotic process.
    • A threshold value can distinguish between persistent and extinction-bound population models.

    Conclusions:

    • The developed persistence and extinction theory provides a robust framework for analyzing population dynamics.
    • The theory is applicable to environmental toxicology, particularly for assessing risks from oscillatory toxicant inputs.
    • This work offers a quantitative approach to predict population responses to environmental variability and toxic stress.