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The dynamics of hierarchical age-structured populations. (English) Zbl 0823.92018

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.

##### MSC:
 92D25 Population dynamics (general) 34D05 Asymptotic stability of ODE 34E99 Asymptotic theory of ODE
##### References:
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