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We study a simple model of DNA evolution in a growing population of cells.Each cell contains a nucleotide sequence which randomly mutates at celldivision. Cells divide according to a branching process. Following typicalparameter values in bacteria and cancer cell populations, we take the mutationrate to zero and the final number of cells to infinity. We prove that almostevery site (entry of the nucleotide sequence) is mutated in only a finitenumber of cells, and these numbers are independent across sites. Howeverindependence breaks down for the rare sites which are mutated in a positivefraction of the population. The model is free from the popular but disputedinfinite sites assumption. Violations of the infinite sites assumption arewidespread while their impact on mutation frequencies is negligible at thescale of population fractions. Some results are generalised to allow for celldeath, selection, and site-specific mutation rates. For illustration weestimate mutation rates in a lung adenocarcinoma.

Genetic composition of an exponentially growing cell population