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The dynamics of hierarchical age-structured populations

Journal of Mathematical Biology volume 32, pages 705–729 (1994)Cite this article

Abstract

An age-structured population is considered in which the birth and death rates of an individual of age a is a function of the density of individuals older and/or younger than a. An existence/uniqueness theorem is proved for the McKendrick equation that governs the dynamics of the age distribution function. This proof shows how a decoupled ordinary differential equation for the total population size can be derived. This result makes a study of the population's asymptotic dynamics (indeed, often its global asymptotic dynamics) mathematically tractable. Several applications to models for intra-specific competition and predation are given.

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Authors and Affiliations

  1. Department of Mathematics, Interdisciplinary Program on Applied Mathematics, Building 89, University of Arizona, 85721, Tucson, AZ, USA

    J. M. Cushing

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Cushing, J.M. The dynamics of hierarchical age-structured populations. J. Math. Biol. 32, 705–729 (1994). https://doi.org/10.1007/BF00163023

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  • DOI: https://doi.org/10.1007/BF00163023

Key words

  • Age-structured population dynamics
  • McKendrick equations
  • Hierarchical models
  • Existence/uniqueness
  • Asymptotic dynamics
  • Global stability
  • Intra-specific competition
  • Cannibalism