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Single-cell sequencing provides a powerful approach for elucidating intratumor heterogeneity by resolving cell-to-cell variability. However, it also poses additional challenges including elevated error rates, allelic dropout and non-uniform coverage. A recently introduced single-cell-specific mutation detection algorithm leverages the evolutionary relationship between cells for denoising the data. However, due to its probabilistic nature, this method does not scale well with the number of cells. Here, we develop a novel combinatorial approach for utilizing the genealogical relationship of cells in detecting mutations from noisy single-cell sequencing data. Our method, called scVILP, jointly detects mutations in individual cells and reconstructs a perfect phylogeny among these cells. We employ a novel Integer Linear Program algorithm for deterministically and efficiently solving the joint inference problem. We show that scVILP achieves similar or better accuracy but significantly better runtime over existing methods on simulated data. We also applied scVILP to an empirical human cancer dataset from a high grade serous ovarian cancer patient. 

Phylogenetic networks extend phylogenetic trees to allow for modeling reticulate evolutionary processes such as hybridization. They take the shape of a rooted, directed, acyclic graph, and when parameterized with evolutionary parameters, such as divergence times and population sizes, they form a generative process of molecular sequence evolution. Early work on computational methods for phylogenetic network inference focused exclusively on reticulations and sought networks with the fewest number of reticulations to fit the data. As processes such as incomplete lineage sorting (ILS) could be at play concurrently with hybridization, work in the last decade has shifted to computational approaches for phylogenetic network inference in the presence of ILS. In such a short period, significant advances have been made on developing and implementing such computational approaches. In particular, parsimony, likelihood, and Bayesian methods have been devised for estimating phylogenetic networks and associated parameters using estimated gene trees as data. Use of those inference methods has been augmented with statistical tests for specific hypotheses of hybridization, like the D-statistic. Most recently, Bayesian approaches for inferring phylogenetic networks directly from sequence data were developed and implemented. In this chapter, we survey such advances and discuss model assumptions as well as methods’ strengths and limitations. We also discuss parallel efforts in the population genetics community aimed at inferring similar structures. Finally, we highlight major directions for future research in this area.