A two-sex renewal model and its population projection

Abstract

Population projections rely on one-sex renewal models. Consequently, changing the projection of male mortality does not affect the projection of birth, contradicting commonsense. A two-sex renewal model is presented in this paper to provide a better description of reproduction and more reasonable population projections. This model is nonlinear and includes the one-sex renewal models as special cases. In this model, age-specific birth rates are defined for two sexes jointly; total fertility, net reproduction rate, and intrinsic growth rate are also derived for two sexes jointly; and age-specific populations approach or converge to stable status. Applying the two-sex renewal model to Australia, it indicates that one-sex models underestimated the intrinsic growth rate by 14 percent. Compared to the results of one-sex models, the two-sex model would provide higher growth rate for low-fertility countries, and lower growth rate for high-fertility countries. In other words, the one-sex models are commonly biased. If the two-sex model is applied to all the countries, it would project smaller populations for the world in the future.