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Deep sequencing can detect somatic DNA mutations in tissues permitting inference of clonal relationships. This has been applied to human epidermis, where sun exposure leads to the accumulation of mutations and an increased risk of skin cancer. However, previous studies have yielded conflicting conclusions about the relative importance of positive selection and neutral drift in clonal evolution. Here, we sequenced larger areas of skin than previously, focusing on cancer-prone skin spanning five decades of life. The mutant clones identified were too large to be accounted for solely by neutral drift. Rather, using mathematical modelling and computational lattice-based simulations, we show that observed clone size distributions can be explained by a combination of neutral drift and stochastic nucleation of mutations at the boundary of expanding mutant clones that have a competitive advantage. These findings demonstrate that spatial context and cell competition cooperate to determine the fate of a mutant stem cell.