Cancer is an evolutionary process where cells acquire somatic mutations over time. As a result of this process, tumors are often highly heterogeneous — containing cell populations with different sets of mutations. While tumor evolution cannot be directly observed, high-throughput DNA sequencing provides a measure of tumor heterogeneity. In this thesis, we introduce three algorithms that leverage tumor heterogeneity to infer the phylogenetic history of cancer. These algorithms account for specific issues in the two technologies for cancer DNA sequencing — bulk sequencing, where thousands of cells from a single tumor are sequenced simultaneously, and single-cell sequencing. First, we introduce an algorithm, PASTRI, that simultaneously deconvolves bulk sequencing data and constructs a tumor phylogeny based on somatic single-nucleotide variants (SNVs); PASTRI uses a hybrid probabilistic-combinatorial approach to more accurately model sequencing noise compared to existing combinatorial approaches. In addition to SNVs, tumors often contain copy-number aberrations (CNAs), a structural variation where larger regions of the genome are duplicated or deleted. Most existing phylogenetic inference algorithms use either SNVs or CNAs alone; however CNAs often overlap SNVs and failure to model these interactions between the two types of mutations can lead to inaccurate phylogenies. We introduce two algorithms, SPRUCE and SCARLET, that integrate SNVs and CNAs using bulk sequencing data and single-cell sequencing data, respectively. Finally, we investigate technical biases in single-cell DNA sequencing data and demonstrate how these biases can be used to phase genomic variants.
