  For proliferating cells subject to both division and death, how can one
estimate the average generation number of the living population without
continuous observation or a division-diluting dye? In this paper we provide a
method for cell systems such that at each division there is an unlikely,
heritable one-way label change that has no impact other than to serve as a
distinguishing marker. If the probability of label change per cell generation
can be determined and the proportion of labeled cells at a given time point can
be measured, we establish that the average generation number of living cells
can be estimated. Crucially, the estimator does not depend on knowledge of the
statistics of cell cycle, death rates or total cell numbers. We validate the
estimator and illustrate its features through comparison with published data
and physiologically parameterized stochastic simulations, using it to suggest
new experimental designs.
