Parametrizing the Net Maternity Function

Abstract

The net maternity function represents the chance of a newborn female surviving to a certain age class, multiplied by the average number of female babies she is likely to bear while sojourning in that age class. Although the net maternity function does not lend itself well to modeling in terms of conventional time, it may be parametrized effectively as a function of the logarithm of a mother's age. Choice of this independent variable leads to absolute dimensionless quantities that do not have to be rescaled when the units of time are changed. The parametrized model provides a close fit to the real net maternity function for stable populations, while divergences between the model and actual function may serve as a diagnostic for new features within a population. Reduction of the specification of the net maternity function to a small number of parameters enables those parameters to be tracked in long-term historical studies, and also serves as the basis of techniques for predicting future states of a population. Among the parameters, a new logarithmic generation time emerges as an important population variable.