Well-known theoretical predictions are that the risk of extinction should decrease with maximum population size (K) and should increase with the temporal coefficient of variation in population size (CV). In an unvarying environment, where extinction is caused solely by demographic accidents, the risk of extinction should decrease steeply with K; the greater the contribution of environmental variability to the risk of extinction, the less steep should be the dependence on K. Large-bodied species tend to have long lifetimes but low rates of increase, which have opposite effects on the risk of extinction per year. We show that in comparisons of a large- and small-bodied species at the same average population size (N), the large-bodied species should be at less risk at low N but at greater risk at high N. We test these predictions using a data base of short-term survivals (up to a few decades) of 355 populations belonging to 100 species of British land birds on 16 islands. The mean N and risk of extinction ar...