Intra-tumor heterogeneity poses substantial challenges for cancer treatment. A tumor’s composition can be deduced by reconstructing its mutational history. Central to current approaches is the infinite sites assumption that every genomic position can only mutate once over the lifetime of a tumor. The validity of this assumption has never been quantitatively assessed. We developed a rigorous statistical framework to test the infinite sites assumption with single-cell sequencing data. Our framework accounts for the high noise and contamination present in such data. We found strong evidence for the same genomic position being mutationally affected multiple times in individual tumors for 11 of 12 single-cell sequencing data sets from a variety of human cancers. Seven cases involved the loss of earlier mutations, five of which occurred at sites unaffected by large-scale genomic deletions. Four cases exhibited a parallel mutation, potentially indicating convergent evolution at the base pair level. Our results refute the general validity of the infinite sites assumption and indicate that more complex models are needed to adequately quantify intra-tumor heterogeneity for more effective cancer treatment.
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