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Immigration and the stable population model

T J Espenshade, L F Bouvier, W B Arthur

    Demography
    |February 1, 1982
    PubMed
    Summary
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    This study extends stable population theory to include immigration. Constant immigration with below-replacement fertility results in a stationary population, regardless of immigration levels or net reproduction rates.

    Area of Science:

    • Demography
    • Population Dynamics
    • Mathematical Biology

    Background:

    • Stable population theory traditionally assumes closed populations.
    • Understanding population dynamics with immigration is crucial for policy and planning.
    • Previous models often simplified immigration's impact on population structure.

    Purpose of the Study:

    • To extend stable population theory by incorporating immigration.
    • To analyze the long-term population outcomes of constant immigration under specific fertility conditions.
    • To investigate the demographic mechanisms driving population stabilization with immigration.

    Main Methods:

    • Mathematical modeling based on stable population theory.
    • Simulation of population projection with defined immigration parameters.

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  • Analysis of age and generational distributions under immigration.

    • Main Results:

    • A constant number and age distribution of immigrants, with below-replacement fertility, leads to a stationary population.
    • The eventual stationary state is independent of the net reproduction rate or the size of annual immigration.
    • Immigrant fertility can exceed replacement levels temporarily, provided later generations maintain below-replacement fertility.

    Conclusions:

    • Immigration can be integrated into stable population models.
    • Below-replacement fertility is the key factor for achieving a stationary population, even with continuous immigration.
    • The age structure and generational dynamics of a population with immigration can be predicted and understood.