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Expected population size in the generation-dependent branching process.

J D Biggins, T Gotz

    Journal of Applied Probability
    |June 1, 1987
    PubMed
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    A new Malthusian parameter is introduced for general branching processes. This parameter helps analyze expected population size, with or without immigration, for better population dynamics understanding.

    Area of Science:

    • * Stochastic processes
    • * Population dynamics
    • * Mathematical biology

    Background:

    • * Branching processes are fundamental models for population growth.
    • * Understanding population size asymptotics is crucial for ecological and biological studies.
    • * Generation-dependent processes introduce complexities not captured by simpler models.

    Purpose of the Study:

    • * To introduce a Malthusian parameter for generation-dependent general branching processes.
    • * To analyze the asymptotic behavior of expected population size.
    • * To consider the impact of immigration on population dynamics.

    Main Methods:

    • * Development of a Malthusian parameter tailored for generation-dependent branching.
    • * Asymptotic analysis of expected population size using the new parameter.
    Keywords:
    Demographic FactorsDemographyEstimation TechnicsFamily And HouseholdFamily CharacteristicsGenerationsInternational MigrationMalthusianismMethodological StudiesMigrationModels, TheoreticalPopulationPopulation DynamicsPopulation ForecastPopulation GrowthPopulation Growth EstimationPopulation ProjectionPopulation SizePopulation TheoryResearch MethodologySocial SciencesWorld

    Related Experiment Videos

  • * Mathematical modeling of branching processes with and without immigration.

    • Main Results:

    • * The introduced Malthusian parameter provides insights into population growth rates.
    • * Asymptotic formulas for expected population size are derived.
    • * The study characterizes the influence of immigration on population size asymptotics.

    Conclusions:

    • * The Malthusian parameter is a valuable tool for analyzing complex branching processes.
    • * The findings offer a deeper understanding of population dynamics in stochastic environments.
    • * The results are applicable to models with or without immigration.