• Boosted regression trees;
  • Kumaraswamy distribution;
  • macroecological models;
  • maximum likelihood;
  • poisson binomial distribution;
  • richness regression models;
  • species richness;
  • stacked species distribution models



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.


Barents Sea, Europe and Dutch Wadden Sea.


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.


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.