The Red Queen hypothesis posits that sex has evolved in response to the shifting adaptive landscape generated by the evolution of interacting species. Previous studies supporting the Red Queen hypothesis have considered a narrow region of parameter space and only a subset of ecological and genetic interactions. Here, we develop a population genetics model that circumscribes a broad array of ecological and genetic interactions among species and derive the first general analytical conditions for the impact of species interactions on the evolution of sex. Our results show that species interactions typically select against sex. We conclude that, although the Red Queen favors sex under certain circumstances, it alone does not account for the ubiquity of sex.