Extended Data Fig. 9: A mathematical method to quantify the chronology of metastatic seeding, t_s.

a, Schematic of the parameters used to quantify metastatic timing t_s (number of years prior to primary tumor diagnosis). We assume metastatic spread occurs at t_m following the emergence of malignant founder of primary carcinoma (denoted t = 0). Let T be the time from emergence of malignant founder to diagnosis of the primary tumor, thus t_s = T-t_m. Let L_p and L_m be the number of private clonal sSNVs in a bulk sample from primary tumor and metastasis, respectively. L_p represents the number of sSNVs that occurred from emergence of the primary tumor founder to the most recent common ancestor (PMRCA) of cell lineages in a bulk sample. This time span is denoted as t_p. Similarly, L_m denotes the number of SSNVs occurred from the emergence of primary tumor founder to the MRCA in a bulk sample from the metastasis (denoted MMRCA). L_m includes the number of M-private clonal mutations that occur: (i) within the primary tumor (L_m1) and (ii) after cells have disseminated from the primary tumor (L_m2), thus L_m = L_m1 + L_m2. b, Estimation of α by simulating an agent-based model of tumor evolution (Methods). The mean α and standard deviation from 1000 simulated tumors are shown.