Quadratic transformations: a model for population growth. I

A reasonably general but greatly simplified model for a finite sexually reproducing population is considered. We restrict ourselves to the case where there are distinct, non-overlapping generations, but there is hope that the techniques will also be applicable to some very simple minded continuous time models with overlapping generations (see also Section 5, Example 3). There aret∞< ∞ different types of females andt1< ∞ types of males and our main concern is the asymptotic behavior of the variables and