Two-Sex Demographic Models

Abstract

Classical stable population theory, the standard model of population age structure and growth, is ill suited to addressing many issues that concern economists and demographers because it is a "one-sex" theory. This paper investigates the existence, uniqueness, and dynamic stability of equilibrium in the birth matrix-mating rule (BMMR) model, a new model of age structure and growth for two-sex, monogamously mating, populations. The paper shows, by means of examples, that the BMMR model can have multiple nontrivial equilibria and establishes sufficient conditions for uniqueness. It generalizes a theorem of W. Brian Arthur to nonlinear systems and uses it to establish sufficient conditions for local dynamic stability.