Large islands typically have more species than comparable smaller islands. Ecological theories, the most influential being the equilibrium theory of island biogeography, explain the species-area relationship as the outcome of the effect of area on immigration and extinction rates. However, these theories do not apply to taxa on land masses, including continents and large islands, that generate most of their species in situ. In this case, species-area relationships should be driven by higher speciation rates in larger areas, a theory that has never been quantitatively tested. Here we show that Anolis lizards on Caribbean islands meet several expectations of the evolutionary theory. Within-island speciation exceeds immigration as a source of new species on all islands larger than 3,000km2, whereas speciation is rare on smaller islands. Above this threshold island size, the rate of species proliferation increases with island area, a process that results principally from the positive effects of area on speciation rate. Also as expected, the slope of the species-area relationship jumps sharply above the threshold. Although Anolis lizards have been present on large Caribbean islands for over 30 million years, there are indications that the current number of species still falls below the speciation-extinction equilibrium.