Cancer genomic medicine relies on targeting driver genes. However, current catalogues of cancer drivers are mostly based on indirect measurements of mutation frequencies, positions or types, rather than their effect on clonal expansions in vivo. Moreover, nongenetic drivers are largely unknown, as are the epigenetic and transcriptomic effects of genetic drivers. Here we perform spatial computational inference on multiomic data with matched whole-genome sequencing, ATAC-seq and RNA-seq. Using 436 samples, we directly quantify the contribution, or lack thereof, of putative driver genes to subclonal expansions in vivo in 30 colorectal carcinomas (4-33 samples per patient, median=15). Although subclonal neutral evolution was widespread (13/26 cases with sufficient data), there were cases with clear evidence of subclonal selection (6/26) in which we measured epigenetic and transcriptomic differences between subclones in vivo. In 7/26 cases we could not distinguish between neutral or selective evolution with the available data. We identified expanding subclones that were not driven by known genetic alterations, and propose candidate epigenetic drivers. We identified the distinguishing patterns of genomic heterogeneity produced in fast, exponentially growing tumours (7/26) versus neoplasms growing only at the periphery (19/26), as well as identifying clonally intermixed (16/28 cases with sufficient data) versus segregated malignancies (10/28). Our model-based approach measures genetic and non-genetic subclonal selection, or lack thereof, in space and time and allows in vivo comparisons of the emergent phenotypic properties of subclones within human tumours.