Inferring models of multiscale copy number evolution for single-tumor phylogenetics

*To whom correspondence should be addressed. Motivation: Phylogenetic algorithms have begun to see widespread use in cancer research to re-construct processes of evolution in tumor progression. Developing reliable phylogenies for tumor data requires quantitative models of cancer evolution that include the unusual genetic mechanisms by which tumors evolve, such as chromosome abnormalities, and allow for heterogeneity between tumor types and individual patients. Previous work on inferring phylogenies of single tumors by copy number evolution assumed models of uniform rates of genomic gain and loss across different genomic sites and scales, a substantial oversimplification necessitated by a lack of algorithms and quantitative parameters for fitting to more realistic tumor evolution models. Results: We propose a framework for inferring models of tumor progression from single-cell gene copy number data, including variable rates for different gain and loss events. We propose a new algorithm for identification of most parsimonious combinations of single gene and single chromo-some events. We extend it via dynamic programming to include genome duplications. We implement an expectation maximization (EM)-like method to estimate mutation-specific an