Generalized stable population theory
Copyright policy )Generalized stable population theory
In generalizing stable population theory we give sufficient, then necessary conditions under which a population subject to time dependent vital rates reaches an asymptotic stable exponential equilibrium (as if mortality and fertility were constant). If chi 0 (t) is the positive solution of the characteristic equation associated with the linear birth process at time t, then rapid convergence of chi 0 (t) to chi 0 and convergence of mortality rates produce a stable exponential equilibrium with asymptotic growth rate chi 0-1. Convergence of chi 0 (t) to chi 0 and convergence of mortality rates are necessary. Therefore the two sets of conditions are very close. Various implications of these results are discussed and a conjecture is made in the continuous case.
- University of North Carolina at Chapel Hill United States
Aging, Stochastic Processes, Necessary and sufficient conditions, rapid convergence, Leslie matrix, Population, Age Factors, convergence of mortality rates, stochastic matrix, Generalization of stable population theory, Models, Biological, Population dynamics (general), asymptotic stable exponential equilibrium, dominant eigenvalue, ergodicity, Humans, Mortality, Population Growth, time dependent vital rates, Mathematics
Aging, Stochastic Processes, Necessary and sufficient conditions, rapid convergence, Leslie matrix, Population, Age Factors, convergence of mortality rates, stochastic matrix, Generalization of stable population theory, Models, Biological, Population dynamics (general), asymptotic stable exponential equilibrium, dominant eigenvalue, ergodicity, Humans, Mortality, Population Growth, time dependent vital rates, Mathematics
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