Supplementary material from "Sweepstake evolution revealed by population-genetic analysis of copy-number alterations in single genomes of breast cancer"

Single-cell sequencing is a promising technology that can address cancer cell evolution by identifying genetic alterations in individual cells. In a recent study, genome-wide DNA copy numbers of single cells were accurately quantified by single-cell sequencing in breast cancers. Phylogenetic-tree analysis revealed genetically distinct populations, each consisting of homogeneous cells. Bioinformatics methods based on population genetics should be further developed to quantitatively analyse the single-cell sequencing data. We developed a bioinformatics framework that was combined with molecular-evolution theories to analyse copy-number losses. This analysis revealed that most deletions in the breast cancers at the single-cell level were generated by simple stochastic processes. A non-standard type of coalescent theory, the multiple-merger coalescent model, aided by approximate Bayesian computation fit well with the data, allowing us to estimate the population-genetic parameters in addition to false-positive and false-negative rates. The estimated parameters suggest that the cancer cells underwent sweepstake evolution, where only one or very few parental cells produced a descendent cell population. We conclude that breast cancer cells successively substitute in a tumour mass, and the high reproduction of only a portion of cancer cells may confer high adaptability to this cancer.