Implications of non-uniqueness in phylogenetic deconvolution of bulk DNA samples of tumors

Yuanyuan Qi, Dikshant Pradhan, Mohammed El-Kebir

Research output: Contribution to journalArticlepeer-review


Background: Tumors exhibit extensive intra-tumor heterogeneity, the presence of groups of cellular populations with distinct sets of somatic mutations. This heterogeneity is the result of an evolutionary process, described by a phylogenetic tree. In addition to enabling clinicians to devise patient-specific treatment plans, phylogenetic trees of tumors enable researchers to decipher the mechanisms of tumorigenesis and metastasis. However, the problem of reconstructing a phylogenetic tree T given bulk sequencing data from a tumor is more complicated than the classic phylogeny inference problem. Rather than observing the leaves of T directly, we are given mutation frequencies that are the result of mixtures of the leaves of T. The majority of current tumor phylogeny inference methods employ the perfect phylogeny evolutionary model. The underlying Perfect Phylogeny Mixture (PPM) combinatorial problem typically has multiple solutions. Results: We prove that determining the exact number of solutions to the PPM problem is #P-complete and hard to approximate within a constant factor. Moreover, we show that sampling solutions uniformly at random is hard as well. On the positive side, we provide a polynomial-time computable upper bound on the number of solutions and introduce a simple rejection-sampling based scheme that works well for small instances. Using simulated and real data, we identify factors that contribute to and counteract non-uniqueness of solutions. In addition, we study the sampling performance of current methods, identifying significant biases. Conclusions: Awareness of non-uniqueness of solutions to the PPM problem is key to drawing accurate conclusions in downstream analyses based on tumor phylogenies. This work provides the theoretical foundations for non-uniqueness of solutions in tumor phylogeny inference from bulk DNA samples.

Original languageEnglish (US)
Article number19
JournalAlgorithms for Molecular Biology
Issue number1
StatePublished - Sep 3 2019
Externally publishedYes


  • Copy-number aberration
  • Evolution
  • Inter-tumor heterogeneity
  • Intra-tumor heterogeneity
  • Metastasis
  • Phylogenetics
  • Single-nucleotide variant
  • Somatic mutations
  • Structural variant

ASJC Scopus subject areas

  • Structural Biology
  • Molecular Biology
  • Computational Theory and Mathematics
  • Applied Mathematics


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