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Most cancers are caused by a combination of inherited germline variants and somatically acquired mutations that drive cellular dysregulation. Cancer genomics aims to distinguish functional cancer-causing genetic variants from the millions of benign passenger mutations. This thesis incorporates measures of evolutionary selection into genetic analysis to identify germline and somatic variants that are preferentially retained during cancer development. Loss-of-heterozygosity (LOH) describes when one copy of a locus is either deleted or replaced by the other copy. By studying patterns of LOH across almost 10,000 human cancers from The Cancer Genome Atlas (TCGA), this thesis quantifies preferential allelic imbalance, and in doing so identifies germline variants that are important to the developing tumour. Initial analysis discovered widespread sequencing biases and cross-sample contamination in the TCGA dataset. Consequently, a rigorous filtering pipeline was developed to mitigate their influence. In total, 1,678 pairs of tumour-normal samples (14.7%) were found to be contaminated or affected by experimental error. Subsequent analysis identified damaging variants in DNA double strand break repair genes as the most common targets of biased LOH. This result suggests a ratchet-like process where heterozygous germline mutations in these genes reduce the efficacy of DNA double-strand break repair, increasing the likelihood of a second hit. Recent work revealed that strand-specific DNA damage segregates independently into daughter cells resulting in the chromosome-scale phasing of mutations. By analysing strand inheritance in genomic segments with and without a potential driver mutation, this thesis developed and applied a statistical approach to quantify oncogenic selection of somatic mutations in a manner agnostic to functional annotation and without the requirement of LOH. Together this work provides insight into the interplay of mutation and selection in cancer evolution, revealing common routes to oncogenesis, and delineating the early stages of cancer development.

Chromosomal instability (CIN), defined as the process of losing or gaining whole or parts of chromosomes, is one of the earliest molecular characteristics to be described in cancer. Since its detection by light microscopy in the late 19th century, technological advances have facilitated the observation of CIN at increasing resolution, revealing an extreme genomic complexity which we are only beginning to understand. As such, CIN has become a hallmark of cancer. Despite its major influence in cancer evolution, fundamental questions as to the frequency of CIN across human cancers, the number of detectable types in a genome, and the possibility of their co-occurrence, remain only partially answered. In this thesis, I present a comprehensive compendium of CIN in cancer using genomic profiling of over 10,000 patient tumours. Firstly, I establish an empirical threshold to detect chromosomal instability which shows that 80% of all tumours have detectable levels of CIN. Secondly, I derive robust genomic signatures of 17 different types of CIN. I discover that chromosomal instability is overwhelmingly driven by two signatures: errors during mitosis through telomere attrition or chromosome missegregation, and non-mitotic errors via impaired homologous recombination. Analysing the co-occurrence of signatures, I find that the remaining signatures (except one) co-occur significantly more often with either one of these two signatures. These results reveal two dominant modes of CIN in human cancers. To interrogate different types of CIN, I develop a triangulation-based framework by integrating diverse sets of genomic features from public data. This allows me to propose putative aetiologies underpinning the signatures and link them to the existing literature. Finally, I show that combinations of signatures distinguish complex genotypes, such as BRCA1 from BRCA2 germline mutant cancers, or sarcoma cancer subtypes known as one of the most karyotypically complex cancers. The extensive complexity of highly unstable tumours has so far restricted the effectiveness of targeted therapies and improvements in patient survival. This thesis facilitates a deeper understanding of one of the most crucial hallmarks of cancer. My results illuminate the fundamental structure underlying genomic complexity, to guide future research efforts on mitosis and homologous recombination.