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Forecasts of species range shifts under climate change most often rely on ecological niche models, in which characterizations of climate suitability are highly contingent on the species range data used. If ranges are far from equilibrium under current environmental conditions, for instance owing to local extinctions in otherwise suitable areas, modelled environmental suitability can be truncated, leading to biased estimates of the effects of climate change. Here we examine the impact of such biases on estimated risks from climate change by comparing models of the distribution of North American mammals based on current ranges with ranges accounting for historical information on species ranges. We find that estimated future diversity, almost everywhere, except in coastal Alaska, is drastically underestimated unless the full historical distribution of the species is included in the models. Consequently forecasts of climate change impacts on biodiversity for many clades are unlikely to be reliable without acknowledging anthropogenic influences on contemporary ranges.