SummaryHistorical demography, surname concordance (isonymy), migration, and genealogy give a consistent description of population structure. The census size has averaged about 1400 over the last five centuries. Conjoined with an effective migration rate of 0.05 per generation as estimated by three different methods, this gives an evolutionary size of638, random kinship of 0–008 and inbreeding of 0.007 relative to the rest of Britain. The population structure of Barra is similar to other British isolates in the recent past, but an order of magnitude less inbred than slash‐and‐burn agriculturalists and Pacific Islanders. Some consequences for rare genes and polymorphisms are disc