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Understanding why some species are at high risk of extinction, while others remain relatively safe, is central to the development of a predictive conservation science. Recent studies have shown that a species' extinction risk may be determined by two types of factors: intrinsic biological traits and exposure to external anthropogenic threats. However, little is known about the relative and interacting effects of intrinsic and external variables on extinction risk. Using phylogenetic comparative methods, we show that extinction risk in the mammal order Carnivora is predicted more strongly by biology than exposure to high-density human populations. However, biology interacts with human population density to determine extinction risk: biological traits explain 80% of variation in risk for carnivore species with high levels of exposure to human populations, compared to 45% for carnivores generally. The results suggest that biology will become a more critical determinant of risk as human populations expand. We demonstrate how a model predicting extinction risk from biology can be combined with projected human population density to identify species likely to move most rapidly towards extinction by the year 2030. African viverrid species are particularly likely to become threatened, even though most are currently considered relatively safe. We suggest that a preemptive approach to species conservation is needed to identify and protect species that may not be threatened at present but may become so in the near future.