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Evolution is typically thought to proceed through divergence of genes, proteins and ultimately phenotypes^,,. However, similar traits might also evolve convergently in unrelated taxa owing to similar selection pressures^,. Adaptive phenotypic convergence is widespread in nature, and recent results from several genes have suggested that this phenomenon is powerful enough to also drive recurrent evolution at the sequence level^,,,. Where homoplasious substitutions do occur these have long been considered the result of neutral processes. However, recent studies have demonstrated that adaptive convergent sequence evolution can be detected in vertebrates using statistical methods that model parallel evolution^,, although the extent to which sequence convergence between genera occurs across genomes is unknown. Here we analyse genomic sequence data in mammals that have independently evolved …