The greater area of tropical forest biomes has been proposed as a factor that drives the latitudinal gradient in species diversity by modulating speciation and extinction rates. But speciation and extinction are processes that operate over millions of years, so an adequate test of area's contribution to diversity patterns must take into consideration that biome areas have changed through time in response to climate. Here we correlate estimates of current tree species diversity with a composite parameter integrating area over geological time for each continent's tropical, temperate, and boreal biomes. We find significant positive correlations between current tree diversity and area-time for periods since the Eocene, Oligocene, and Miocene, which we take as evidence for a time-integrated species-area effect on current patterns of species richness across biomes. These results contribute to explanations for why most lineages have tropical origins and why tropical forests are more diverse than extratropical forests.