Mathematical modeling of clonal evolution illustrates that linear evolution requires natural selection to occur in large populations but can occur through drift in small populations. (A-C) Simulations of a Moran model with 1000 cells and with increasing selective strength (increasing probability to self-renew upon acquisition of a mutation, α). When α = 0, evolution is neutral, and all cells have equal probability to self-renew whether mutant or not. When α > 0, mutated cells have an increased probability to expand (ie, mutations increase their fitness). (A) Linearity indices at t = 100 for selective strengths α = 0, α = 0.05, and α = 0.1. (B) Final clone frequency for all remaining clones across all simulations at t = 100 for selective strengths α = 0, α = 0.05, and α = 0.1. (C) Representative examples of clonal evolution in these simulations. The text above indicates the numbers of cells remaining and the linearity index at the end of the simulation. (D-F) Simulations with neutral evolution (α = 0) for 100, 1000, and 5000 SCs. (D) Linearity indices at t =100 for 100, 1000, and 5000 SCs. (E) Final clone frequency for all remaining clones across all simulations at t = 100 for 100, 1000, and 5000 SCs. (F) Representative example of clonal evolution for 100 cells, and 1 example of an outlier with a high linearity index.