On the formulation and computer implementation of an age-dependent two-sex demographic model

A two-sex age-dependent demographic model is formulated within the framework of a stochastic population process, including both time-homogeneous and time-inhomogeneous laws of evolution. An outline of the parametric components of the system, which expedite computer implementation and experimentation, is also given. New features of the model include a component for couple formation, using the class of Farlie-Morgenstern bivariate distributions to accommodate age preferences in selecting marriage partners, a component for couple dissolution due to separation or divorce, and an outline of techniques for initializing a two-sex projection given scanty information. For the case of time-homogeneous laws of evolution, stability properties of two-sex models that are analogs of those for one-sex models are difficult to prove mathematically due to nonlinearities. But computer experiments in this case suggest that these properties continue to hold for two-sex models for such widely used demographic indicators as period crude birth rates, period rates of natural increase, and period age distributions, which converge to constant forms in long-term projections. The values of the stable crude birth rate, rate of natural increase, and quantiles of the stable age distribution differ markedly among projections that differ only in selected values of parameters governing couple formation and dissolution. Such experimental results demonstrate that two-sex models are not merely intellectual curiosities but exist in their own right and lead to insights not attainable in simpler one-sex formulations.