A regression based approach to phylogenetic reconstruction from multi-sample bulk DNA sequencing of tumors

We develop an approach to reconstruct phylogenetic trees from multi-sample bulk DNA sequencing data by separating the reconstruction problem into two parts: a structured regression problem for a fixed tree [Formula: see text], and an optimization over tree space. We derive an algorithm for the regression sub-problem by exploiting the unique, combinatorial structure of the matrices appearing within the problem. This algorithm has both asymptotic and empirical improvements over linear programming (LP) approaches to the problem. Using our algorithm for this regression sub-problem, we develop fastBE, a simple method for phylogenetic inference from multi-sample bulk DNA sequencing data. We demonstrate on simulated data with hundreds of samples and upwards of a thousand distinct sub-populations that fastBE outperforms existing approaches in terms of reconstruction accuracy, sample efficiency, and runtime. Owing to its scalability, fastBE enables both phylogenetic reconstruction directly from indvidual mutations without requiring the clustering of mutations into clones, as well as a new phylogeny constrained mutation clustering algorithm. On real data from fourteen B-progenitor acute lymphoblastic leukemia patients, fastBE infers mutation phylogenies with fewer violations of a widely used evolutionary constraint and better agreement to the observed mutational frequencies. Using our phylogeny constrained mutation clustering algorithm, we also find mutation clusters with lower distortion compared to state-of-the-art approaches. Finally, we show that on two patient-derived colorectal cancer models, fastBE infers mutation phylogenies with less violation of a widely used evolutionary constraint compared to existing methods.