For centuries, biogeographers have examined the factors that produce patterns of biodiversity across regions. The study of islands has proved particularly fruitful and has led to the theory that geographic area and isolation influence species colonization, extinction and speciation such that larger islands have more species and isolated islands have fewer species (that is, positive species-area and negative species-isolation relationships). However, experimental tests of this theory have been limited, owing to the difficulty in experimental manipulation of islands at the scales at which speciation and long-distance colonization are relevant. Here we have used the human-aided transport of exotic anole lizards among Caribbean islands as such a test at an appropriate scale. In accord with theory, as anole colonizations have increased, islands impoverished in native species have gained the most exotic species, the past influence of speciation on island biogeography has been obscured, and the species-area relationship has strengthened while the species-isolation relationship has weakened. Moreover, anole biogeography increasingly reflects anthropogenic rather than geographic processes. Unlike the island biogeography of the past that was determined by geographic area and isolation, in the Anthropocene--an epoch proposed for the present time interval--island biogeography is dominated by the economic isolation of human populations.