AbstractOne of the great unsolved puzzles in cancer biology is not why cancers occur, but rather, explaining why so few cancers occur compared with the theoretical number that could occur given the number of progenitor cells in the body and the normal mutation rate. We hypothesised that a contributory explanation is that the tumour microenvironment (TME) is not fixed, and that this could impair the ability of neoplastic cells to retain a high enough fitness to become a cancer. The TME has implicitly been assumed to be static in most cancer evolution models, and we therefore developed a mathematical model of spatial cancer evolution assuming that the TME, and thus the optimum cancer phenotype, change over time. Based on simulations, we show how cancer cell populations adapt to diverse changing TME conditions and fitness landscapes. Compared with static TMEs which generate neutral dynamics, changing TMEs lead to complex adaptations with spatio-temporal heterogeneity involving variable sub-clonal fitness, mixing, competition and phylogeny patterns. In many cases, cancer cell populations fail to grow or undergo spontaneous regression, and even extinction. Our analyses predict that cancer evolution in a changing TME is challenging, and can help to explain why cancer is neither inevitable nor as common as expected. Should cancer driver mutations with effects dependent of the TME exist, they are likely to be selected. Anti-cancer prevention and treatment strategies based on changing the TME are feasible and potentially effective.