Green's cell division model for budding yeast

In Saccharomyces cerevisiae, cells divide by budding. When the daughter cell separates from the mother, it is generally smaller and requires a longer generation time before it is able to reproduce. Green (1981, J. Appl. Prob., 18, 799-808) has proposed a modification of the age-dependent branching process to model this process. The model assumes that

• The generation time of a mother cell is a random variable .


• The first generation time of a daughter cell is a random variable .
  represents the extra time that the daughter cell requires to increase in size sufficiently to begin the reproductive process. It is assumed that and are independent random variables.


• Once a daughter cell has produced its first offspring, it behaves as a mother cell for subsequent reproduction.


• Generation times of different cells are independent random variables.

Thus, at any time, the population consists of daughter cells, which have yet to produce their first offspring, and mother cells that have produced at least one previous offspring.