On the distribution of completed parities when fertility is heritable.

"Over the last one hundred years, there has been, in many developed countries, a demographic convergence towards the two child family. The possible implications for population growth of such a tendency are considered in this paper in terms of both family limitation and also the intergenerational transmission of fertility. These two effects interact so that as the proportion of two-child families increases, the possible influence of mother-daughter fertility associations on population growth decreases, though even now it could override otherwise significant changes in either or both of the birth and death intensities. In particular, it is shown that according...to how fertility is transmitted through generations, it is still possible to have zero growth rates consistently with a widely dispersed stable distribution of family size as well as a typical mortality regime." (SUMMARY IN FRE)

Population growth with variable family size.

"The Sharpe-Lotka continuous time deterministic model of population growth is developed to take account of some possible forms of mother-daughter fertility association.... Model specific results relating the intergenerational fertility effect to the long term population growth rate and magnitude are established. The quantitative implications of the theory are illustrated by a consideration of a general bilinear form of A and in this context numerical results illustrating the finite time growth and also the long term distribution of fertility levels in the stable female population are obtained. In particular, it is shown that different fertility specific subpopulations can coexist indefinitely."