Abstract: It has long been suspected that cellular senescence is an anticancer mechanism; however, it has been difficult to understand the advantage for the organism of retaining mutant cells in a postmitotic state rather than simply deleting them by apoptosis. It is proposed that in certain circumstances apoptosis promotes neoplasia by causing cells adjacent to the deleted cell to divide and that the role of cellular senescence is to prevent this. This may be particularly important in mammalian stem cell niches. After loss of a stem cell from a niche, another stem cell within the same niche divides symmetrically to restore the original number. The most important human malignancies arise from tissues maintained by stem cells, and there is increasing evidence that stem cells are the targets for at least the initial genetic changes that occur during carcinogenesis. If a subset of stem cells within a niche arises containing an oncogenic mutation, then tumor suppressor mechanisms promote apoptosis of these cells, and the niche restores the original number of stem cells by replication of both normal and mutated stem cells. Thus, paradoxically apoptosis increases turnover of mutant cells with associated risk of further genetic changes. However, if in addition mutant cells can become senescent, then the niche is progressively filled by senescent cells until either the mutant cells are eliminated or the niche is completely occupied by postmitotic cells, thereby preventing further evolution of the neoplastic clone. The consequences of this hypothesis are explored by computer modeling.