The dynamics of hierarchical age-structured populations
type: Item
instance of: scholarly article
title: The dynamics of hierarchical age-structured populations
zbMATH Open document ID: 0823.92018
DOI: 10.1007/BF00163023
published in: Journal of Mathematical Biology
publication date: 1995-10-31T00:00:00Z
review text: An age hierarchical population was defined as one in which the birth and death rates of an individual of age \(a\) are dependent upon the size of the class of individuals younger than \(a\) and/or the size of the class of individuals older than \(a\). Under this assumption a proof of the existence and uniqueness of a solution of the McKendrick model equations was given which yields a decoupled ordinary differential equation of the total population size. Thus, for this class of model populations our results provide a means by which the population level dynamics can be related to individual (age specific) vital rates. Moreover, because the equation for total population size is a scalar ordinary differential equation, these results also provide the possibility that the global asymptotic dynamics of the population can be determined. For example, in the autonomous case one of our theorems implies that only equilibrium dynamics are possible and shows how the asymptotic age distributions can be determined. Some examples illustrate how these kinds of models can be used to address certain interesting problems concerning intra-specific competition and prediction.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34E99
zbMATH DE Number: 665761
zbMATH Keywords: age-structured population dynamics
zbMATH Keywords: hierarchical models
zbMATH Keywords: cannibalism
zbMATH Keywords: existence and uniqueness
zbMATH Keywords: McKendrick model equations
zbMATH Keywords: decoupled ordinary differential equation of the total population size
zbMATH Keywords: global asymptotic dynamics
zbMATH Keywords: equilibrium dynamics
zbMATH Keywords: asymptotic age distributions
zbMATH Keywords: intra- specific competition
zbMATH Keywords: prediction
author: J. M. Cushing
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00163023
OpenAlex ID: W1991505140
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description: scientific article; zbMATH DE number 665761