The dynamics of hierarchical age-structured populations

J. M. Cushing

Research output: Contribution to journalArticlepeer-review

78 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)705-729
Number of pages25
JournalJournal of mathematical biology
Issue number7
StatePublished - Aug 1994


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

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


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