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STEM CELLS: POPULATION GENETICS 281

k = n 1 2 n 2 total cells

n 2 transit cell divisions

/ /
0 1 2 n 1 -1 n 1
n 1 stem cell divisions

Figure 13.5 The pattern of cell division giving rise to a total of k cells. The
single, initial cell divides to produce a stem cell and a transit lineage. Each
transit lineage divides n 2 times, yielding 2 n 2 cells. The stem lineage divides n 1
times, producing a total of k = n 1 2 n 2 cells. Redrawn from Frank et al. (2003).

Given the need to make k cells, consider how natural selection might
increase benefit. Suppose short-lived transit lineages pose little risk.
An improved design would add more cell divisions to those low-risk
transit lineages and reduce the number of divisions in the long-lived
stem lineage, that is, decrease n 1 and increase n 2 .
In general, suppose we may choose to add one additional cell division
to any lineage, with the goal to minimize cancer risk (Frank et al. 2003).
If cancer requires n rate-limiting steps, and each step happens only dur-
n
ing cell division, the risk rises with d , where d is the number of cell
divisions. Risk increases exponentially with number of cell divisions in
a lineage, thus natural selection favors prevention of long lineages. It is
always most advantageous to add any new cell division to the shortest
extant lineage. This optimal design maintains equal length among cell
lineages.
In terms of tissue architecture, if we start with one cell, then the best
design follows perfect binary cell division with all lineages remaining
the same length, such that k = 2 , where n 2 is the number of rounds
n 2
of cell division. No stem divisions would occur except the first to seed
the transit lineages.