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Tredennick et al. criticize one of our statistical analyses and emphasize the low explanatory power of models relating productivity to diversity. These criticisms do not detract from our key findings, including evidence consistent with the unimodal constraint relationship predicted by the humped-back model and evidence of scale sensitivities in the form and strength of the relationship., (Copyright © 2016, American Association for the Advancement of Science.)

The search for predictions of species diversity across environmental gradients has challenged ecologists for decades. The humped-back model (HBM) suggests that plant diversity peaks at intermediate productivity; at low productivity few species can tolerate the environmental stresses, and at high productivity a few highly competitive species dominate. Over time the HBM has become increasingly controversial, and recent studies claim to have refuted it. Here, by using data from coordinated surveys conducted throughout grasslands worldwide and comprising a wide range of site productivities, we provide evidence in support of the HBM pattern at both global and regional extents. The relationships described here provide a foundation for further research into the local, landscape, and historical factors that maintain biodiversity., (Copyright © 2015, American Association for the Advancement of Science.)