On the derivation of a two-sex stable population model

Abstract

It is well known that the intrinsic rates of growth derived separately for the males and females in a population, when one assumes the continuation of their respective mortality and fertility experiences, usually turn out to be different. Noting that the phenomenon of human reproduction is a product of the cooperation between the two sexes, we have attempted in this paper to define the sex-age-specific fertility rates as a function not only of age but also of time, where the latter is implicitly introduced in the model through the sex composition of the reproductive population. It has been shown that a stable model can then be defined based on such changing sex-age-specific fertility rates and given sets of unchanging mortality rates. The fertility rates stabilize with time, and the common intrinsic rates of growth for the two sexes are found to lie in the interval generated by the corresponding rates of the two one-sex models. Several other interesting relationships among the parameters of this model have been presented in the paper. Among other alternatives, a least square solution has been presented for the values of sex-age-specific fertility rates that are minimally discrepant with the observed rates but are consistent in terms of the parametric estimates they generate. It is interesting to note that a relatively modest adjustment in the sex-age-specific fertility rates is all that it takes to eliminate the inconsistencies generated by the separate one-sex models. © 1978 Population Association of America.