Cancer arises from a single cell of origin whose lineage accumulates somatic mutations in a step-wise manner over time. The evolutionary process towards cancer development is dynamic and the earliest mutation may arise decades before the onset for some cancers. This calls for a quantitative approach for probing early cancer evolution using measurable quantities in normal and precancerous tissues. Genetic alterations under positive selection in ostensibly healthy tissues have implica tions for cancer risk. However, total levels of positive selection across the genome remain unknown. How much positive selection elsewhere in the genome is missed by gene-focused sequencing panels? Synonymous passenger mutations that hitchhike to high variant allele frequency are influenced by any driver mutation, regardless of type or location in the genome, and can therefore be used to estimate total levels of positive selection in healthy tissues. By comparing observed numbers of synonymous passengers to the numbers expected due to driver mutations in canonical cancer genes, we showed in chapter 2 and 3 that it is possible to quantify missing selection left to be explained by unobserved drivers elsewhere in the genome. We analysed the variant allele frequency spectrum of synonymous mutations from physiologically healthy blood and oesophagus to quantify levels of missing positive selection. In blood we found that only ∼ 30% of synonymous passengers can be explained by SNVs in canonical driver genes, suggesting high levels of positive selection for other mutations elsewhere in the genome. In contrast, approximately half of all synonymous passengers in the oesophagus can be explained by just the two driver genes NOTCH1 and TP53, suggesting little positive selection elsewhere. In tissues with high levels of ‘missing’ selection, we showed that our framework can be used to guide targeted driver mutation discovery. In chapter 5 we used single-cell DNA sequencing of >2000 preleukemic haematopoietic stem cells across 8 DNMT3Amut/NPM1c acute myeloid leukemia (AML) patients to reveal the patterns of driver mutation co-occurrence in ostensibly healthy stem cells. We constructed phylogenetic trees using preleukemic HSCs for all eight patients and assigned cells to tree nodes based on both single-cell and bulk sequencing information. We found that in all cases the development of AML required a single cell to acquire 3-4 key driver events. Mutation co-occurrence patterns and mutation acquisition orders were consistent with findings from other studies. Using a model developed in chapter 4, we gained power in using evolutionary histories revealed by clonal trees to separate out parametrical influence of the two major parameters µ and s in preleukemic evolution. We showed that the k-hit staircase model makes many tractable predictions regarding variation across individuals and large variations are not unexpected from the inherent stochasticity of the process. We gained important insights into precancerous evolutionary dynamics by performing quantitative analyses on genetics data obtained from both normal and preleukemic tissues. What we presented here shows that quantitative approaches combined with clear model hypotheses carry explanatory powers to explain observed patterns in genetics data with reference to the mechanisms and processes of early cancers