Phylogenetic techniques are increasingly applied to infer the somatic mutational history of a tumor from DNA sequencing data. However, standard phylogenetic tree reconstruction techniques do not account for the fact that bulk sequencing data measures mutations in a population of cells. We formulate and solve the multi-state perfect phylogeny mixture deconvolution problem of reconstructing a phylogenetic tree given mixtures of its leaves, under the multi-state perfect phylogeny, or infinite alleles model. Our somatic phylogeny reconstruction using combinatorial enumeration (SPRUCE) algorithm uses this model to construct phylogenetic trees jointly from single-nucleotide variants (SNVs) and copy-number aberrations (CNAs). We show that SPRUCE addresses complexities in simultaneous analysis of SNVs and CNAs. In particular, there are often many possible phylogenetic trees consistent with the data, but the ambiguity decreases considerably with an increasing number of samples. These findings have implications for tumor sequencing strategies, suggest caution in drawing strong conclusions based on a single tree reconstruction, and explain difficulties faced by applying existing phylogenetic techniques to tumor sequencing data.

Metastasis is the migration of cancerous cells from a primary tumor to other anatomical sites. While metastasis was long thought to result from monoclonal seeding, or single cellular migrations, recent phylogenetic analyses of metastatic cancers have reported complex patterns of cellular migrations between sites, including polyclonal migrations and reseeding. However, accurate determination of migration patterns from somatic mutation data is complicated by intra-tumor heterogeneity and discordance between clonal lineage and cellular migration. We introduce MACHINA, a multi-objective optimization algorithm that jointly infers clonal lineages and parsimonious migration histories of metastatic cancers from DNA sequencing data. MACHINA analysis of data from multiple cancers reveals that migration patterns are often not uniquely determined from sequencing data alone, and that complicated migration patterns among primary tumors and metastases may be less prevalent than previously reported. MACHINA’s rigorous analysis of migration histories will aid in studies of the drivers of metastasis.