A reformulation of the two-sex problem

The ability of classical stable population theory to determine the equilibrium growth rate and age structure of a population from its vital rates in a single period depends on assuming that the observed maternity rates are equilibrium rates. This paper resolves the two-sex problem by replacing the fixed, age-specific fertility schedule of classical stable population theory by two basic relationships: a “birth matrix” and a “mating rule.” Placing certain restrictions on the birth matrix and the mating rule (BMMR), I establish that under certain plausible conditions, the BMMR model solves the two-sex problem by allowing matings and births to adjust to changes in population structure. The BMMR model thus provides an equilibrating mechanism in place of a fixed maternity schedule of classical stable population theory.