The probability of cancer initiation along the four evolutionary trajectories. The figure shows the time course of the probability of cancer initiation via the four trajectories. The scenarios are enumerated as in . All probabilities increase with time but the slopes are different. The curves represent the predictions by the formulas ( for scenario *i*, in which an HSC accumulates the JAK2V617F mutation; for scenario *ii*, in which a progenitor accumulates first a mutation conferring self-renewal followed by the JAK2V617F mutation; for scenario *iii*, in which a progenitor first accumulates the JAK2V617F mutation followed by the mutation conferring self-renewal; and for scenario *iv*, in which an HSC first accumulates the mutation conferring self-renewal, followed by the JAK2V617F arising in a progenitor). The circles show the results of the direct computer simulations. (*Left*) Demonstrates the fit between predictions and simulations. (*Right*) Investigates the importance of the trajectories for the most accurate parameter values of the hematopoietic system. Parameter values are *N* = 100, τ = 5, *u*_{a} = *u*_{b} = 2 × 10^{−6}, *d* = 0.1, *z* = 9, γ = 3, and α = 1 (*Left*) and *N* = 500,000, τ = 300, *u*_{a} = *u*_{b} = 5 × 10^{−8}, *d* = 0.1, *z* = 15, γ = 5, and α = 0.5 (*Right*).

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