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Zbl 0823.92018
Cushing, J.M.
The dynamics of hierarchical age-structured populations. (English)
[J] J. Math. Biol. 32, No.7, 705-729 (1994). ISSN 0303-6812; ISSN 1432-1416/e

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. \par 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.

MSC 2000:: *92D25 Population dynamics
34D05 Asymptotic stability of ODE
34E99 Asymptotic theory of ODE

Keywords: age-structured population dynamics; hierarchical models; cannibalism; existence and uniqueness; McKendrick model equations; decoupled ordinary differential equation of the total population size; global asymptotic dynamics; equilibrium dynamics; asymptotic age distributions; intra- specific competition; prediction

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Zentralblatt MATH Berlin [Germany]