Cancer is characterized by intra-tumor heterogeneity, the presence of distinct cell populations with distinct complements of somatic mutations, which include single-nucleotide variants (SNVs) and copy-number aberrations (CNAs). Single-cell sequencing technology enables one to study these cell populations at single-cell resolution. Phylogeny estimation algorithms that employ appropriate evolutionary models are key to understanding the evolutionary mechanisms behind intra-tumor heterogeneity.


We introduce Single-cell Phylogeny Reconstruction (SPhyR), a method for tumor phylogeny estimation from single-cell sequencing data. In light of frequent loss of SNVs due to CNAs in cancer, SPhyR employs the k-Dollo evolutionary model, where a mutation can only be gained once but lost k times. Underlying SPhyR is a novel combinatorial characterization of solutions as constrained integer matrix completions, based on a connection to the cladistic multi-state perfect phylogeny problem. SPhyR outperforms existing methods on simulated data and on a metastatic colorectal cancer.

Availability and implementation

SPhyR is available on

Supplementary information

Supplementary data are available at Bioinformatics online.

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