In an age-dependent branching process, each individual lives for a random period of time L, termed the generation time, at the end of which it is replaced by a random number of offspring. M. A key assumption is that all random variables are independent, in particular:
These independence assumptions simplify the mathematical analysis of the process. The age-dependent branching process is also called the Bellman-Harris process.
For cell populations, we use the terms mothers and daughters for parent and offspring cells. The number of offspring is generally zero (i.e. the mother cell dies without reproducing) or two (the mother divides to produce two daughter cells).
In reality, cells go through a series of distinct stages between successive divisions (the cell cycle). Nonetheless, in applications where the details of the cell cycle can be ignored, the age-dependent branching process provides a useful model for populations of cells that reproduce by symmetric binary fission, such as Escherichia coli. However, an alternative model is more appropriate for cells that divide asymmetrically, such as Saccharomyces cerevisiae.