Maps of a species’ potential range make an important contribution to conservation and invasive species risk analysis. Spatial predictions, however, should be accompanied by an assessment of their uncertainty. Here, we use multimodel inference to generate confidence intervals that incorporate both the uncertainty involved in model selection as well as the error associated with model fitting. In the case of the invasive Argentine ant, we found that it was most likely to occur where the mean daily temperature in mid-winter was 7–14 °C and maximum daily temperatures during the hottest month averaged 19–30 °C. Uninvaded regions vulnerable to future establishment include: southern China, Taiwan, Zimbabwe, central Madagascar, Morocco, high-elevation Ethiopia, Yemen and a number of oceanic islands. Greatest uncertainty exists over predictions for China, north-east India, Angola, Bolivia, Lord Howe Island and New Caledonia. Quantifying the costs of different errors (false negatives vs. false positives) was considered central for connecting modelling to decision-making and management processes.