Barton was educated at Peterhouse, Cambridge where he graduated with a first-class degree in Natural Sciences in 1976 and gained his PhD supervised by Godfrey Hewitt at the University of East Anglia in 1979. Barton was made a professor in 1994. He had got many awards such as Erwin Schrödinger Prize and Darwin–Wallace Medal.

His research centres on the evolution of populations that are distributed through space, and that experience natural selection on many genes. These interests grew from field work on the narrow hybrid zones that separate divergent taxa, including grasshoppers, toads, butterflies and deer. The mathematical methods developed for analysing these have proven useful for a wide range of problems in evolutionary genetics and beyond: speciation theory, quantitative genetics, coalescence in structured populations, and evolutionary computation.