Theory predicts that small populations may be driven to extinction by random fluctuations in demography and loss of genetic diversity through drift. However, population size is a poor predictor of extinction in large carnivores inhabiting protected areas. Conflict with people on reserve borders is the major cause of mortality in such populations, so that border areas represent population sinks. The species most likely to disappear from small reserves are those that range widely-and are therefore most exposed to threats on reserve borders-irrespective of population size. Conservation efforts that combat only stochastic processes are therefore unlikely to avert extinction.