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.

肿瘤内异质性对癌症治疗提出了重大挑战。可以通过重建其突变历史来推断肿瘤的成分。当前方法的核心是无限位点假设，即每个基因组位置在肿瘤的整个生命周期中只能突变一次。该假设的有效性从未进行过定量评估。我们开发了严格的统计框架，以使用单细胞测序数据来测试无限位点假设。我们的框架考虑了此类数据中存在的高噪声和污染。对于来自多种人类癌症的12个单细胞测序数据集中的11个，我们发现了相同基因组位置在单个肿瘤中多次受到突变影响的有力证据。有7例涉及早期突变的丢失，其中五个发生在不受大规模基因组缺失影响的位点。四例病例显示出平行突变，可能表明在碱基对水平上趋同进化。我们的结果驳斥了无限位点假设的一般有效性，并表明需要更复杂的模型来充分量化肿瘤内异质性才能更有效地治疗癌症。