Population Dynamics: 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 demographers because it is a ‘one-sex’ theory. Its basic building blocks are an age-specific fertility schedule and an age-specific mortality schedule for the female population. These schedules, which are assumed to remain constant, define a linear mapping of the female population vector in period t into the female population vector in period t+1. It is straightforward to show the existence of a ‘stable population’—an age structure that, once attained, will replicate itself in successive periods—and to show that this equilibrium is dynamically stable. Demography's ‘two-sex problem’ is to integrate men into this one-sex, female-based model. The birth matrix-mating rule (BMMR) model, a new model of age-structure and growth for two-sex populations, solves demography's two-sex problem. Because the BMMR model is inherently nonlinear, it is more complicated than classical stable population theory. Unlike classical stable population theory, however, the BMMR model accommodates the notion that female age-specific fertility rates are not constant but may be affected by a ‘marriage squeeze’ which changes the population balance between men and women.