Colonization, speciation and extinction are dynamic processes that influence global patterns of species richness1-6. Island biogeography theory predicts that the contribution of these processes to the accumulation of species diversity depends on the area and isolation of the island7,8. Notably, there has been no robust global test of this prediction for islands where speciation cannot be ignored9, because neither the appropriate data nor the analytical tools have been available. Here we address both deficiencies to reveal, for island birds, the empirical shape of the general relationships that determine how colonization, extinction and speciation rates co-vary with the area and isolation of islands. We compiled a global molecular phylogenetic dataset of birds on islands, based on the terrestrial avifaunas of 41 oceanic archipelagos worldwide (including 596 avian taxa), and applied a new analysis method to estimate the sensitivity of island-specific rates of colonization, speciation and extinction to island features (area and isolation). Our model predicts-with high explanatory power-several global relationships. We found a decline in colonization with isolation, a decline in extinction with area and an increase in speciation with area and isolation. Combining the theoretical foundations of island biogeography7,8 with the temporal information contained in molecular phylogenies10 proves a powerful approach to reveal the fundamental relationships that govern variation in biodiversity across the planet.