Stacking species distribution models and adjusting bias by linking them to macroecological models

AIM: Species distribution models (SDMs) are common tools in biogeography and conservation ecology. It has been repeatedly claimed that aggregated (stacked) SDMs (S‐SDMs) will overestimate species richness. One recently suggested solution to this problem is to use macroecological models of species richness to constrain S‐SDMs. Here, we examine current practice in the development of S‐SDMs to identify methodological problems, provide tools to overcome these issues, and quantify the performance of correctly stacked S‐SDMs alongside macroecological models. LOCATIONS: Barents Sea, Europe and Dutch Wadden Sea. METHODS: We present formal mathematical arguments demonstrating how S‐SDMs should and should not be stacked. We then compare the performance of macroecological models and correctly stacked S‐SDMs on the same data to determine if the former can be used to constrain the latter. Next, we develop a maximum‐likelihood approach to adjusting S‐SDMs and discuss how it could potentially be used in combination with macroecological models. Finally, we use this tool to quantify how S‐SDMs deviate from observed richness in four very different case studies. RESULTS: We demonstrate that stacking methods based on thresholding site‐level occurrence probabilities will almost always be biased, and that these biases will tend toward systematic overprediction of richness. Next, we show that correctly stacked S‐SDMs perform very similarly to macroecological models in that they both have a tendency to overpredict richness in species‐poor sites and underpredict it in species‐rich sites. MAIN CONCLUSIONS: Our results suggest that the perception that S‐SDMs consistently overpredict richness is driven largely by incorrect stacking methods. With these biases removed, S‐SDMs perform similarly to macroecological models, suggesting that combining the two model classes will not offer much improvement. However, if situations where coupling S‐SDMs and macroecological models would be beneficial are subsequently identified, the tools we develop would facilitate such a synthesis.