To resolve a panselectionist paradox, the population geneticist Kimura invented a neutral theory, where each gene is equally likely to enter the next generation whatever its allelic type. To learn what could be explained without invoking Darwinian adaptive divergence, Hubbell devised a similar neutral theory for forest ecology, assuming each tree is equally likely to reproduce whatever its species. In both theories, some predictions worked; neither theory proved universally true. Simple assumptions allow neutral theorists to treat many subjects still immune to more realistic theory. Ecologists exploit far fewer of these possibilities than population geneticists, focussing instead on species abundance distributions, where their predictions work best, but most closely match non-neutral predictions. Neutral theory cannot explain adaptive divergence or ecosystem function, which ecologists must understand. By addressing new topics and predicting changes in time, however, ecological neutral theory can provide probing null hypotheses and stimulate more realistic theory.