GraPhyC: Using Consensus to Infer Tumor Evolution

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 do not have the same set of labels applied to the leaves of each tree. We describe several distance measures between these tumor trees. Our GraPhyC algorithm solves the consensus problem using a weighted directed graph where vertices are sets of mutations and edges are weighted based on the number of times a parental relationship is observed between their constituent mutations in the input trees. We find a minimum weight spanning arborescence in this graph and prove that it minimizes the total distance to all input trees for one of our distance measures. We also describe several extensions of our GraPhyC approach. On simulated data we show that GraPhyC outperforms a baseline method and demonstrate that GraPhyC can be an effective means of computing centroids in k-medians clustering. We analyze two real sequencing datasets and find that GraPhyC is able to identify a tree not included in the set of input trees, but that contains characteristics supported by other reported evolutionary reconstructions of this tumor.