  We study a two-type branching process which provides excellent description of
experimental data on cell dynamics in skin tissue (Clayton et al., 2007). The
model involves only a single type of progenitor cell, and does not require
support from a self-renewed population of stem cells. The progenitor cells
divide and may differentiate into post-mitotic cells. We derive an exact
solution of this model in terms of generating functions for the total number of
cells, and for the number of cells of different types. We also deduce large
time asymptotic behaviors drawing on our exact results, and on an independent
diffusion approximation.
