Fig. 1

Parametrically heterogeneous Malthusian growth model with respect to growth rate parameter c. Initial distribution is taken to be truncated exponential, with distribution parameter μ = 195. Initial population size is N(0) = 0.001. a Population of cells N(t), which remains at a negligible size until t ≈ 180. b The expected value E ^t[c] of Malthusian parameter c increases rapidly around the same time as the escape phase of tumor growth. c Variance Var ^t[c] also increases dramatically during the escape phase but then decreases the clone with the largest allowed value of c becomes selected (in this case it is E ^t[c] → 1, since the exponential distribution was taken to be truncated exponential on the interval c ∈ [0, 1]). d As the transition occurs, we can also see the distribution of cell clones change over time