A Two-Sex, Age-Structured Population Model in Discrete-Time

Abstract

This work examines how the life history parameters effect the stable age distribution of the different classes and compares these results with the standard single sex model. The conditions necessary for a population projected forward in time to reach a stable age distribution is analyzed. The conditions for existence are dependent on the nature of the mating function, i.e. the rate at which the two sexes find each other and mate. In addition, the assumptions under which these mating functions are constructed have important implications for the dynamics of the population and ultimate age distribution, stable or not. An analysis of when including both sexes becomes essential to the understanding of reproductive strategies, examination of whether a population fulfils the necessary assumptions about mating to make certain statements about population growth, growth rates and relative fitness, and outlining an accessible approach to modeling the joint life histories will be of practical value. Toward this end, a framework for discrete-time two-sex models with age structure is developed. In addition a marriage (mating) function based on an analogy with foraging theory and preferences based on the predispositions of one age group for another is proposed. Some of the properties of these models and their solutions are also investigated.