title: Generalized stable population theory.
abstract: 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.
mesh_terms: D000367:Age Factors; D000375:Aging; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D009026:Mortality; D011153:Population; D011158:Population Growth; D013269:Stochastic Processes