Figure 4.
(A) Probabilities of reaching a large population (depicted by symbols) as a function of the death-to-birth ratio (r) for several values of the replication capacity k. A solid line plots the approximation (1 − r). (B) Probability that the maximum number of cells is greater than 109 (for most values of r the probability of reaching 109 cells is either zero or very close to the approximate probability of reaching a large size (1 − r)). (C) Probability that at least one mutation takes place P(M > 0). (D) Probability of escaping replication limits through a mutation that activates telomerase P(erl). For each of the values of k, P(erl) falls inside the corresponding grey band. The lines that form the boundary of the bands are calculated using the upper and lower bounds in Eq. 9. In (C,D) the mutation rate per cell division μ = 10−9. Results based on 104 simulations per point.