Our working hypothesis is that tumorigenesis is an evolutionary process that fundamentally couples few major driving events (point mutations, rearrangements) with a complex flux of minor aberrations, many of which are epigenetic. We believe that these minor events are critical factors in the emergence of the cancer phenotype, and that understanding them is essential to the characterization of the disease. In particular, we hypothesize that a quantitative and principled evolutionary model for carcinogenesis is imperative for understanding the heterogeneity within tumor cell populations and predicting the effects of cancer therapies. We will therefore develop an interdisciplinary scheme that combines theoretical models of cancer evolution with in vitro evolutionary experiments and new methods for assaying the population heterogeneity of epigenomic organization. By developing techniques to interrogate DNA methylation and its interaction with other key epigenetic marks at the single-cell level, we will allow quantitative theoretical predictions to be scrutinized and refined. By combining models describing epigenetic aberrations with direct measurements of chromatin organization using Hi-C and 4C-seq, we shall revisit fundamental questions on the causative nature of epigenetic changes during carcinogenesis. Ultimately, we will apply both theoretical and experimental methodologies to assay and characterize the evolutionary histories of tumor cell populations from multiple mouse models and clinical patient samples.