The canonical route from normal tissue to cancer occurs through sequential acquisition of somatic mutations. Many studies have constructed a linear genetic model for tumorigenesis using the genetic alterations associated with samples at different stages of neoplastic progression from cross-sectional data. The common interpretation of these models is that they reflect the temporal order within any given tumor. Linear genetic methods implicitly neglect genetic heterogeneity within a neoplasm; each neoplasm is assumed to consist of one dominant clone. We modeled neoplastic progression of colorectal cancer using an agent-based model of a colon crypt and found clonal heterogeneity within our simulated neoplasms, as observed in vivo. Just 7.3% of cells within neoplasms acquired mutations in the same order as the linear model. In 41% of the simulated neoplasms, no cells acquired mutations in the same order as the linear model. We obtained similarly poor results when comparing the temporal order with oncogenetic tree models inferred from cross-sectional data. However, when we reconstructed the cell lineage of mutations within a neoplasm using several biopsies, we found that 99.7% cells within neoplasms acquired their mutations in an order consistent with the cell lineage mutational order. Thus, we find that using cross-sectional data to infer mutational order is misleading, whereas phylogenetic methods based on sampling intratumor heterogeneity accurately reconstructs the evolutionary history of tumors. In addition, we find evidence that disruption of differentiation is likely the first lesion in progression for most cancers and should be one of the few regularities of neoplastic progression across cancers.