Toward a General Model for Populations with Changing Rates

Formal demography has yet to move beyond assuming that demographic rates are constant over time, an assumption that is both unrealistic and constraining. To generalize the fixed rate stable model to the changing rate dynamic model, this paper explores the mathematical regularities that underlie the behavior of all populations. At any time, the composition of a population can be expressed in terms of current circumstances, using the rates of a "latent" stable model. Closed form solutions for the equations governing dynamic multistate models are not always possible, but are presented for certain special cases. Those solutions provide opportunities for specifying dynamic models of potentially great value, especially for analyses of cyclical and hierarchical populations.