Descent trees generated by individual women vary from one country to another. These differences can be investigated using stochastic models. We apply matrix analytic methods and show that the time-inhomogeneous Markovian binary tree model is suitable for modelling the lifetime of a woman and the long-term behaviour of a female family line generated by a single woman. Using this model, we introduce a formula to compute the mean family size generated by a newborn woman. The mean family size is analysed across selected time periods for which we also perform cross country comparisons. We also introduce a criterion to analyse the chance of survival of a family line generated by a woman of a given nationality.