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Predator–prey interactions play an important role for species composition and community dynamics at local scales, but their importance in shaping large‐scale gradients of species richness remains unexplored. Here, we use global range maps, structural equation models (SEM), and comprehensive databases of dietary preferences and body masses of all terrestrial, non‐volant mammals worldwide, to test whether (1) prey bottom‐up or predator top‐down relationships are important drivers of broad‐scale species richness gradients once the environment and human influence have been accounted for, (2) predator–prey richness associations vary among biogeographic regions, and (3) body size influences large‐scale covariation between predators and prey. SEMs including only productivity, climate, and human factors explained a high proportion of variance in prey richness (R² = 0.56) but considerably less in …