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We study the evolution of transcription factor-binding sites in prokaryotes, using an empirically grounded model with point mutations and genetic drift. Selection acts on the site sequence via its binding affinity to the corresponding transcription factor. Calibrating the model with populations of functional binding sites, we verify this form of selection and show that typical sites are under substantial selection pressure for functionality: for cAMP response protein sites in Escherichia coli, the product of fitness difference and effective population size takes values 2NΔF of order 10. We apply this model to cross-species comparisons of binding sites in bacteria and obtain a prediction method for binding sites that uses evolutionary information in a quantitative way. At the same time, this method predicts the functional histories of orthologous sites in a phylogeny, evaluating the likelihood for conservation or loss or gain of function …