Journal of Mathematical Biology

, Volume 73, Issue 2, pp 491–523 | Cite as

Inferring average generation via division-linked labeling



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 explore the estimator’s features through comparison with physiologically parameterized stochastic simulations and extrapolations from published data, using it to suggest new experimental designs.


Average generation inference Branching processes Stochastically decorated trees 

Mathematics Subject Classification

92D25 60J85 



The authors thank Søren Asmussen (Aarhus University) for drawing their attention to Asmussen (1998). The work of T.W., L.P. and K.D. was supported by Human Frontier Science Program Grant RGP0060/2012. K.D. was also supported by Science Foundation Ireland Grant 12 IP 1263.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Hamilton InstituteMaynooth UniversityMaynoothIreland
  2. 2.Division of ImmunologyNetherlands Cancer InstituteAmsterdamThe Netherlands
  3. 3.Department of Theoretical Biology and BioinformaticsUtrecht UniversityUtrechtThe Netherlands
  4. 4.Institut Curie, PSL Research University, CNRS UMR168ParisFrance

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