Tumour development has long been recognised as an evolutionary process during which cells accumulate mutations and evolve into a mix of genetically distinct cell subpopulations. The resulting genetic intra-tumour heterogeneity poses a major challenge to cancer therapy, as it increases the chance of drug resistance. To study tumour evolution in more detail, reliable approaches to infer the life histories of tumours are needed. This dissertation focuses on computational methods for inferring trees of tumour evolution from single-cell and multi-sample sequencing data.

Recent advances in single-cell sequencing technologies have promised to reveal tumour heterogeneity at a much higher resolution, but single-cell sequencing data is inherently noisy, making it unsuitable for analysis with classic phylogenetic methods. The first part of the dissertation describes OncoNEM, a novel probabilistic method to infer clonal lineage trees from noisy single nucleotide variants of single cells. Simulation studies are used to validate the method and to compare its performance to that of other methods. Finally, OncoNEM is applied in two case studies.

In the second part of the dissertation, a comprehensive collection of existing multi-sample approaches is used to infer the phylogenies of metastatic breast cancers from ten patients. In particular, shallow whole-genome, whole exome and targeted deep sequencing data are analysed. The inference methods comprise copy number and point mutation based approaches, as well as a method that utilises a combination of the two. To improve the copy number based inference, a novel allele-specific multi-sample segmentation algorithm is presented. The results are compared across methods and data types to assess the reliability of the different methods.

In summary, this thesis presents substantial methodological advances to understand tumour evolution from genomic profiles of single cells or related bulk samples.