Neutral models can provide reasonable descriptions of static biodiversity patterns, but they severely overestimate species’ geological ages. This suggests that in nature there may be “Red Queen” mechanisms that accelerate both the extinction of old species and the ascension of new species. But can Red Queen models make static predictions that are as good as those of neutral theory? We showed mathematically that a Red Queen model can indeed generate more realistic species ages while simultaneously predicting a species abundance distribution that is not radically different to the log-series predicted by the neutral model. This establishes the general plausibility of Red Queen dynamics as a mechanism structuring biodiversity in nature.