Accurate predictions of future shifts in species diversity in response to global change are critical if useful conservation strategies are to be developed. The most widely used prediction method is to model individual species niches from point observations and project these models forward using future climate scenarios. The resulting changes in individual ranges are then summed to predict diversity changes; multiple models can be combined to produce ensemble forecasts. Predictions based on environment-richness regressions are rarer. However, richness regression models, based on macroecological diversity theory, have a long track record of making reliable spatial predictions of diversity patterns. If these empirical theories capture true functional relationships between environment and diversity, then they should make consistent predictions through time as well as space and could complement individual species-based predictions. Here, we use climate change throughout the 20th century to directly test the ability of these different approaches to predict shifts of Canadian butterfly diversity. We found that all approaches performed reasonably well, but the most accurate predictions were made using the single best richness-environment regression model, after accounting for the effects of spatial autocorrelation. Spatially trained regression models based on macroecological theory accurately predict diversity shifts for large species assemblages. Global changes provide pseudo-experimental tests of those macroecological theories that can then generate robust predictions of future conditions.