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Although predator effects on the number of locally coexisting species are well understood, there are few formal predictions of how these local predator effects influence patterns of prey diversity at larger spatial scales. Building on the theory of island biogeography, we develop a simple model that describes how predators can alter the scaling of diversity in prey metacommunities and compares the effects of generalist and specialist predators on regional prey diversity. Generalist predators, which consume prey randomly with respect to species identity, are predicted to reduce α‐diversity and increase β‐diversity thereby maintaining regional diversity (γ‐diversity). Alternatively, specialist predators, which filter out prey species intolerant of predators, are predicted to reduce bothα‐diversity andβ‐diversity by causing the same prey species to be extirpated in each locality, resulting in regional prey species extinctions and …