SUMMARYCancers arise through a process of somatic evolution that can result in substantial sub-clonal heterogeneity within tumors. The mechanisms responsible for the coexistence of distinct sub-clones and the biological consequences of this coexistence remain poorly understood. Here we used a mouse xenograft model to investigate the impact of sub-clonal heterogeneity on tumor phenotypes and the competitive expansion of individual clones. We found that tumor growth can be driven by a minor cell subpopulation, which enhances the proliferation of all cells within a tumor by overcoming environmental constraints and yet can be outcompeted by faster proliferating competitors, resulting in tumor collapse. We then developed a mathematical modeling framework to identify the rules underlying the generation of intratumor clonal heterogeneity. We found that non-cell autonomous driving, together with clonal interference, stabilizes sub-clonal heterogeneity, thereby enabling inter-clonal interactions that can lead to new phenotypic traits.

Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.