Generalized stable population theory

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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 x 0(t) is the positive solution of the characteristic equation associated with the linear birth process at time t, then rapid convergence of x 0(t) to x 0 and convergence of mortality rates produce a stable exponential equilibrium with asymptotic growth rate x 0−1. Convergence of x 0(t) to x 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.

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