The dynamics of hierarchical age-structured populations

Research output: Contribution to journalArticle

67 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)705-729
Number of pages25
JournalJournal of Mathematical Biology
Volume32
Issue number7
DOIs
StatePublished - 1994

Fingerprint

Age-structured Population
Birth Rate
Age Distribution
Population Dynamics
Population Density
Mortality
Population
Existence-uniqueness
birth rate
intraspecific competition
Uniqueness Theorem
Population Size
Ordinary differential equations
Existence Theorem
Distribution functions
Distribution Function
Ordinary differential equation
population size
population dynamics
predation

Keywords

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

ASJC Scopus subject areas

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

Cite this

The dynamics of hierarchical age-structured populations. / Cushing, Jim M.

In: Journal of Mathematical Biology, Vol. 32, No. 7, 1994, p. 705-729.

Research output: Contribution to journalArticle

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