Pair Formation Models

Abstract

The stable population model can be extended to take into account marriage phenomena. However, this proves unsatisfactory as these linear models are essentially one-sex models that neglect the process of pair formation between the sexes. In reality, the mating chances depend on the existence of the other sex. It is not self-evident why persistent population growth, as observed in the real world, is possible under this model of pair formation between the sexes. Various questions cannot be answered by linear population models, such as those regarding the laws of pair formation that make persistent growth possible, the two-sex Malthusian growth rate, and the result of an imbalanced sex ratio. Although two-sex population dynamics models without age structures have been developed by several authors, it is very difficult to study age-structured two-sex models. Thus, there is not yet a satisfactory two-sex nonlinear demographic theory. Temporary or persistent pair formation also plays an important role in understanding the spread of sexually transmitted diseases, so there are a number of studies about pair formation phenomena in the context of epidemic models. In this chapter, however, we focus on pure continuous-time demographic theories.