Environmental change research is plagued by the curse of dimensionality: the number of environmental drivers and the number of communities potentially at risk are both large. This raises the pressing question if a general understanding of ecological impact is achievable. Here, we show evidence that this is indeed possible. Theoretical results for both small and very large bi- and tritrophic communities, and simulation results for communities of intermediate size, show that linear combinations of mean species responses to environmental change predict the resulting effects on coexistence, quantified as the feasibility domain size. We next show that the same mean responses also predict effects on site occupancy in simple metacommunities. We then benchmark our findings using two relevant cases of environmental change (temperature change and pollution), showing that means of temperature optima and of species sensitivities to pollution predict concomitant effects on coexistence. Finally, we apply the concept to field data, finding support for effects of land use on coexistence in natural invertebrate communities.