  We consider a class of branching processes called Markovian binary trees, in
which the individuals lifetime and reproduction epochs are modeled using a
transient Markovian arrival process (TMAP). We estimate the parameters of the
TMAP based on population data containing information on age-specific fertility
and mortality rates. Depending on the degree of detail of the available data, a
weighted non-linear regression method or a maximum likelihood method is
applied. We discuss the optimal choice of the number of phases in the TMAP, and
we provide confidence intervals for the model outputs. The results are
illustrated using real data on human and bird populations.
