Tumors frequently develop clonal dominance, meaning that most cells descend from a small fraction of initial clones. Such dominance also occurred in published in vitro iterated growth and passage experiments with tumor cells in which lineage tracing was performed using genetic barcodes. A potential source for such heterogeneity is that dominant clones derive from cancer stem cells with an unlimited self-renewal capacity. Alternatively, clonal dominance may be caused by heterogeneity of division rates between clones. To test which hypothesis can explain the development of clonal dominance, we build a computational model that accurately simulates the iterated growth and passage experiments in which clonal dominance emerged. With this model we show that clonal dominance does not develop in a model where all cells grow at a uniform rate, even when the population is subdivided in cancer stem cells and differentiated cells. However, when the division rates vary between clones and are inherited from parent cells, clonal dominance develops and increases over time. The experimentally observed evolution of clone loss, clonal dominance, and the clonal overlap across biological replicates are closely matched by our simulations. Thus, our findings suggest that tumor cells exhibit a heritable variation in the division rates of individual cells.