Structural genome alterations are determinants of cancer ontogeny and therapeutic response. While bulk genome sequencing has enabled delineation of structural variation (SV) mutational processes which generate patterns of DNA damage, we have little understanding of how these processes lead to cell-to-cell variations which underlie selection and rates of accrual of different genomic lesions. We analysed 309 high grade serous ovarian and triple negative breast cancer genomes to determine their mutational processes, selecting 22 from which we sequenced >22,000 single cell whole genomes across a spectrum of mutational processes. We show that distinct patterns of cell-to-cell variation in aneuploidy, copy number alteration (CNA) and segment length occur in homologous recombination deficiency (HRD) and fold-back inversion (FBI) phenotypes. Widespread aneuploidy through induction of HRD through BRCA1 and BRCA2 inactivation was mirrored by continuous whole genome duplication in HRD tumours, contrasted with early ploidy fixation in FBI. FBI tumours exhibited copy number distributions skewed towards gains, widespread clone-specific variation in amplitude of high-level amplifications, often impacting oncogenes, and break-point variability consistent with progressive genomic diversification, which we termed serriform structural variation (SSV). SSVs were consistent with a CNA-based molecular clock reflecting a continual and distributed process across clones within tumours. These observations reveal previously obscured genome plasticity and evolutionary properties with implications for cancer evolution, therapeutic targeting and response.

Cancer genomes exhibit extensive chromosomal copy number changes and structural variation, yet how allele specific alterations drive cancer genome evolution remains unclear. Here, through application of a new computational approach we report allele specific copy number alterations in 11,097 single cell whole genomes from genetically engineered mammary epithelial cells and 21,852 cells from high grade serous ovarian and triple negative breast cancers. Resolving single cell copy number profiles to individual alleles uncovered genomic background distributions of gains, losses and loss of heterozygosity, yielding evidence of positive selection of specific chromosomal alterations. In addition specific genomic loci in maternal and paternal alleles were commonly found to be altered in parallel with convergent phenotypic transcriptional effects. Finally we show that haplotype specific alterations trace the cyclical etiology of high level amplifications and reveal clonal haplotype decomposition of complex structures. Together, our results illuminate how allele and haplotype specific alterations, here determined across thousands of single cell cancer genomes, impact the etiology and evolution of structural variations in human tumours.