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Inspired by recent efforts to model cancer evolution with phylogenetic trees, we consider the problem of finding a consensus tumor evolution tree from a set of conflicting input trees. In contrast to traditional phylogenetic trees, the tumor trees we consider contain features such as mutation labels on internal vertices (in addition to the leaves) and allow multiple mutations to label a single vertex. We describe several distance measures between these tumor trees and present an algorithm to solve the consensus problem called GraPhyC. Our approach uses a weighted directed graph where vertices are sets of mutations and edges are weighted using a function that depends on the number of times a parental relationship is observed between their constituent mutations in the set of input trees. We find a minimum weight spanning arborescence in this graph and prove that the resulting tree minimizes the total distance to all input trees for one of our presented distance measures. We evaluate our GraPhyC method using both simulated and real data. On simulated data we show that our method outperforms a baseline method at finding an appropriate representative tree. Using a set of tumor trees derived from both whole-genome and deep sequencing data from a Chronic Lymphocytic Leukemia patient we find that our approach identifies a tree not included in the set of input trees, but that contains characteristics supported by other reported evolutionary reconstructions of this tumor.

A Consensus Approach to Infer Tumor Evolutionary Histories