Dynamics of populations with changing rates: generalization of the stable population theory.

A general and complete exposition of the dynamics of populations with changing vital rates is given in the discrete time formulation. Results obtained are stronger than Lopez's or Hajnal's. In addition to the proof of existence of limits, an explicit expression for the age distribution is obtained by considering forward products of population projection matrices, while an explicit expression for the generalized reproductive values is obtained by considering backward products. The forward and backward characteristic equations respectively determine the forward and backward growth rates. The relative age distribution is compared to the alternative expression of Y.J. Kim (1986, Demography 23 (3), 451-461), which is the discrete version of S.H. Preston and A.J. Coale (1982, Pop. Index 48 (2), 217-259).