Fig 1. Stochastic branching process model of tumor evolution.

(a) Stochastic branching process model for tumor expansion. Initiated tumor cells (blue) divide with birth rate b, die with death rate d, and accrue passenger mutations with mutation rate u. Type-1 cells, which carry the driver mutation, divide with birth rate b₁, die with death rate d₁, and accrue passenger mutations with mutation rate u. (b) The initiated tumor, or type-0, (blue) population growth is initiated from a single cell. A driver mutation occurs in a single type-0 cell at time t₁, starting the type-1 population (red). The tumor sample is collected and bulk sequenced at times t₁ + t and t₁ + t + Δ, where the driver fraction is α₁ and α₂, respectively. Tumor size (in number of cells) is M₁ and M₂ at first and second sample collection dates. (c) By the time the tumor is observed, it has a high level of genetic heterogeneity due to the mutations that have accrued in both type-0 (blue) and type-1 populations (red). Each yellow star represents a different passenger mutation.