Graphical depiction of cell death and division events in (A) Moran A model, (B) Moran B model, and (C) branching process. Notation for all models: t, current time; T, time to next event; f (α, β), fitness of cell with α drivers and β passengers; Σf =Σk f (αk, βk). Notation for Moran models: N, constant cell count in the process; i, cell dying and to be replaced; j, cell replacing cell i; Notation for branching process: N (t), cell count at time t; i, cell chosen for division; {g0, g1, g2}, progeny count distribution; X, progeny count of cell i; N (t + T), cell count at time t + T after division event.

Statistics of the number of variants of a specific type.

The Site Frequency Spectrum (SFS). (A) Genealogy of a sample of n = 10 cells includes 14 mutational events, denoted by red dots. Time is running down the page. Mutations 1, 3, 4, 11, 13, and 14 (total of 6 mutations) are present in a single cell, mutations 2, 5, 7 and 12 (total of 4 mutations) are present in two cells, mutations 9 and 10 (2 mutations) are present in three cells, mutation 8 (1 mutation) is present in five cells and mutation 6 (1 mutation) is present in 9 cells. (B) The resulting site frequency spectrum, S10(1) = 6, S10(2) = 4, S10(3) = 2, S10(5) = 1, and S10(9) = 1, other Sn(k) equal to 0.

Comparisons between Moran and branching process (BP) models in the “neutral” setting. (A) Average cumulative tail of the mutational Site Frequency Spectra. (B) Distributions of allele counts at tf. (C) Distributions of singleton counts at tf. (D-F) Distributions of counts of driver mutations (D), passenger mutations (E) and divisions (F) within [t0, tf]. (G-N) Trajectories of the averages over time of population sizes (+/-std) (G), cumulative mutation counts (H), fitness (I), cumulative division/replacement counts (J), allele counts (K), percentage of singletons among all alleles (L), allele birth counts (M) and allele death counts (N). Allele death counts (lines) are categorized into mutation events (circles) and division/replacement events (diamonds). Dark blue = Moran A, green = Moran B, yellow = “binomial BP” with g0 = g2 = 0.25 (non-extinction), orange = “binomial BP” with g0 = g2 = 0.25 (N (tf) ∈ [90, 110]), purple = “fast BP” with g0 = g2 = 0.5 (N (tf) ∈ [90, 110]), cyan = “slow BP” with g0 = g2 = 0.05 (N (tf) ∈ [90, 110]), gray = “supercritical BP” with g0 = 0.2465, g1 = 0.5 and g2 = 0.2535 (non-extinction).

Statistics (mean ± standard deviation) for Figure 3 (neutral evolution). Model color code: dark blue = Moran A, green = Moran B, yellow = “binomial BP” with g0 = g2 = 0.25 (nonextinction), orange = “binomial BP” with g0 = g2 = 0.25 (N (tf) ∈ [90, 110]), purple = “fast BP” with g0 = g2 = 0.5 (N (tf) ∈ [90, 110]), cyan = “slow BP” with g0 = g2 = 0.05 (N (tf) ∈ [90, 110]), gray = “supercritical BP” with g0 = 0.2465, g1 = 0.5 and g2 = 0.2535 (non-extinction). Statistics: B = allele counts at tf, C = singleton counts at tf, D = driver mutation count within [t0, tf], E = passenger mutation count within [t0, tf], F = division count within [t0, tf].

Statistics for Figure 4 (balanced evolution)

Comparisons between Moran and branching process (BP) models in the “balanced” setting. (A) Average cumulative tail of the mutational Site Frequency Spectra. (B) Distributions of allele counts at tf. (C) Distributions of singleton counts at tf. (D-F) Distributions of counts of driver mutations (D), passenger mutations (E) and divisions (F) within [t0, tf]. (G-N) Trajectories of the averages over time of population sizes (+/-std) (G), cumulative mutation counts (H), fitness (I), cumulative division/replacement counts (J), allele counts (K), percentage of singletons among all alleles (L), allele birth counts (M) and allele death counts (N). Allele death counts (lines) are categorized into mutation events (circles) and division/replacement events (diamonds). Dark blue = Moran A, green = Moran B, yellow = “binomial BP” with g0 = g2 = 0.25 (non-extinction), orange = “binomial BP” with g0 = g2 = 0.25 (N (tf) ∈ [90, 110]), purple = “fast BP” with g0 = g2 = 0.5 (N (tf) ∈ [90, 110]), cyan = “slow BP” with g0 = g2 = 0.05 (N (tf) ∈ [90, 110]), gray = “supercritical BP” with g0 = 0.2465, g1 = 0.5 and g2 = 0.2535 (non-extinction).

Statistics for Figure 5 (driver domination)

Comparisons between Moran and branching process (BP) models in the “selective” setting. (A) Average cumulative tail of the mutational Site Frequency Spectra. (B) Distributions of allele counts at tf. (C) Distributions of singleton counts at tf. (D-F) Distributions of counts of driver mutations (D), passenger mutations (E) and divisions (F) within [t0, tf]. (G-N) Trajectories of the averages over time of population sizes (+/-std) (G), cumulative mutation counts (H), fitness (I), cumulative division/replacement counts (J), allele counts (K), percentage of singletons among all alleles (L), allele birth counts (M) and allele death counts (N). Allele death counts (lines) are categorized into mutation events (circles) and division/replacement events (diamonds). Dark blue = Moran A, green = Moran B, yellow = “binomial BP” with g0 = g2 = 0.25 (non-extinction), orange = “binomial BP” with g0 = g2 = 0.25 (N (tf) ∈ [90, 110]), purple = “fast BP” with g0 = g2 = 0.5 (N (tf) ∈ [90, 110]), cyan = “slow BP” with g0 = g2 = 0.05 (N (tf) ∈ [90, 110]), gray = “supercritical BP” with g0 = 0.2465, g1 = 0.5 and g2 = 0.2535 (non-extinction).

Comparisons between Moran and branching process (BP) models in the “deleterious” setting. (A) Average cumulative tail of the mutational Site Frequency Spectra. (B) Distributions of allele counts at tf. (C) Distributions of singleton counts at tf. (D-F) Distributions of counts of driver mutations (D), passenger mutations (E) and divisions (F) within [t0, tf]. (G-N) Trajectories of the averages over time of population sizes (+/-std) (G), cumulative mutation counts (H), fitness (I), cumulative division/replacement counts (J), allele counts (K), percentage of singletons among all alleles (L), allele birth counts (M) and allele death counts (N). Allele death counts (lines) are categorized into mutation events (circles) and division/replacement events (diamonds). Dark blue = Moran A, green = Moran B, yellow = “binomial BP” with g0 = g2 = 0.25 (non-extinction), orange = “binomial BP” with g0 = g2 = 0.25 (N (tf) ∈ [90, 110]), purple = “fast BP” with g0 = g2 = 0.5 (N (tf) ∈ [90, 110]), cyan = “slow BP” with g0 = g2 = 0.05 (N (tf) ∈ [90, 110]), gray = “supercritical BP” with g0 = 0.2465, g1 = 0.5 and g2 = 0.2535 (non-extinction).

Statistics for Figure 6 (passenger domination)

Results from fitting the SFS from sample G2. (A) Heatmap of error between data SFS tail and average SFS tail for distinct (s, d) combinations in Moran A. Dark blue squares: 100 best (s, d) combinations, with linear regression. Dark red square: best (s, d) combination. (B) Comparison between sample SFS (black line), average SFS under Moran A from 100 best (s, d) combinations (dark blue dots) and the best (s, d) combination (dark red dots). (C) Comparison between sample SFS (black line), average SFS under “binomial BP” (g0 = g2 = 0.25, N (tf) ∈ [90, 110]) from 100 best (s, d) combinations (red dots) and the best (s, d) combination (dark red dots). Each SFS from Moran A or binomial BP is averaged from 1,000 simulations.

Results from fitting the SFS from sample G32. (A) Heatmap of error between data SFS and average SFS for distinct (s, d) combinations in Moran A. Dark blue squares: 100 best (s, d) combinations, with linear regression. Dark red square: best (s, d) combination. (B) Comparison between sample SFS (black line), average SFS under Moran A from 100 best (s, d) combinations (dark blue dots) and the best (s, d) combination (dark red dots). (C) Comparison between sample SFS (black line), average SFS under “binomial BP” (g0 = g2 = 0.25, N (tf) ∈ [90, 110]) from 100 best (s, d) combinations (red dots) and the best (s, d) combination (dark red dots). Each SFS from Moran A or binomial BP is averaged from 1,000 simulations.

Results from fitting the SFS from sample G41. (A) Heatmap of error between data SFS and average SFS for distinct (s, d) combinations in Moran A. Dark blue squares: 100 best (s, d) combinations, with linear regression. Dark red square: best (s, d) combination. (B) Comparison between sample SFS (black line), average SFS under Moran A from 100 best (s, d) combinations (dark blue dots) and the best (s, d) combination (dark red dots). (C) Comparison between sample SFS (black line), average SFS under “binomial BP” (g0 = g2 = 0.25, N (tf) ∈ [90, 110]) from 100 best (s, d) combinations (red dots) and the best (s, d) combination (dark red dots). Each SFS from Moran A or binomial BP is averaged from 1,000 simulations.