The usefulness of species distribution models (SDMs) in predicting impacts of climate change on biodiversity is difficult to assess because changes in species ranges may take decades or centuries to occur. One alternative way to evaluate the predictive ability of SDMs across time is to compare their predictions with data on past species distributions. We use data on plant distributions, fossil pollen and current and mid-Holocene climate to test the ability of SDMs to predict past climate-change impacts. We find that species showing little change in the estimated position of their realized niche, with resulting good model performance, tend to be dominant competitors for light. Different mechanisms appear to be responsible for among-species differences in model performance. Confidence in predictions of the impacts of climate change could be improved by selecting species with characteristics that suggest little change is expected in the relationships between species occurrence and climate patterns.