Abstract
The contributions of species to ecosystem functions or services depend not only on their presence but also on their local abundance. Progress in predictive spatial modelling has largely focused on species occurrence rather than abundance. As such, limited guidance exists on the most reliable methods to explain and predict spatial variation in abundance. We analysed the performance of 68 abundance-based species distribution models fitted to 800 000 standardised abundance records for more than 800 terrestrial bird and reef fish species. We found a large amount of variation in the performance of abundance-based models. While many models performed poorly, a subset of models consistently reconstructed range-wide abundance patterns. The best predictions were obtained using random forests for frequently encountered and abundant species and for predictions within the same environmental domain as model calibration. Extending predictions of species abundance outside of the environmental conditions used in model training generated poor predictions. Thus, interpolation of abundances between observations can help improve understanding of spatial abundance patterns, but our results indicate extrapolated predictions of abundance under changing climate have a much greater uncertainty. Our synthesis provides a road map for modelling abundance patterns, a key property of species distributions that underpins theoretical and applied questions in ecology and conservation.