Aim Species distribution models (SDMs) use the locations of collection records to map the distributions of species, making them a powerful tool in conservation biology, ecology and biogeography. However, the accuracy of range predictions may be reduced by temporally autocorrelated biases in the data. We assess the accuracy of SDMs in predicting the ranges of tropical plant species on the basis of different sample sizes while incorporating real-world collection patterns and biases. Location Tropical South American moist forests. Methods We use dated herbarium records to model the distributions of 65 Amazonian and Andean plant species. For each species, we use the first 25, 50, 100, 125 and 150 records collected and available for each species to analyse changes in spatial aggregation and climatic representativeness through time. We compare the accuracy of SDM range estimates produced using the time-ordered data subsets to the accuracy of range estimates generated using the same number of collections but randomly subsampled from all available records. Results We find that collections become increasingly aggregated through time but that additional collecting sites are added resulting in progressively better representations of the species’ full climatic niches. The range predictions produced using time-ordered data subsets are less accurate than predictions from random subsets of equal sample sizes. Range predictions produced using time-ordered data subsets consistently underestimate the extent of ranges while no such tendency exists for range predictions produced using random data subsets. Main conclusions These results suggest that larger sample sizes are required to accurately map species ranges. Additional attention should be given to increasing the number of records available per species through continued collecting, better distributed collecting, and/or increasing access to existing collections. The fact that SDMs generally under-predict the extent of species ranges means that extinction risks of species because of future habitat loss may be lower than previously estimated.