Perfect agreement between the analytical approximations given by and (lines) and exact numerical simulation (points). We perform a stochastic simulation for the cancer initiation process described in the main text and illustrated in . In each time step, a random event is chosen proportionally to its rate. Before clonal expansion, there is only one (stem) cell. Initially, this cell is of type *X*_{0}. Mutation to *X*_{1} or *Y*_{1} occurs with probabilities *u*_{1} and *u*_{c}, respectively. A *Y*_{0} cell can mutate to a *Y*_{1} cell with probability *u*_{1}. An *X*_{1} cell can mutate to an *X*_{2} cell with probability *u*_{2} or to a *Y*_{1} cell with probability *u*_{c}. A *Y*_{1} cell can mutate to a *Y*_{2} cell with probability *u*_{3}. An *X*_{2} cell initiates clonal expansion; cells divide with rate *a* and die with rate *b*. Similarly, a *Y*_{2} cell initiates clonal expansion; cells divide with rate *c* and die with rate *d*. The simulation is stopped if the clone has died out or has reached *M* cells. The figure shows the probability that a single (stem) cell has given rise to a stable lesion or a CIN lesion. Parameter values are *u*_{1} = 2 × 10^{−7}, *u*_{2} = 10^{−6}, *u*_{3} = 10^{−2}, *u*_{c} = 5*u*_{1}, *a* = 1, *b* = 0.1, *c* = 0.5, *d* = 0.1, and *M* = 10^{6}. The probability is evaluated over 10^{7} runs.

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