Figure 2. The method of reflections illustrated with synthetic, stochastic datasets.

We use two datasets where the species distribution, respectively: (a,c) follows the precipitation gradient (dataset D1); (b,d) does not include any trend with precipitation (dataset D2). Site species richness (k_s,0, panels a,b) and generalised species richness (k_s,18, panels c,d) as a function of annual precipitation (mm y⁻¹). For dataset D1, a) species richness decreases as a quadratic function of annual precipitation (with small variance explained, R² = 0.07), while c) generalized species richness decreases linearly with annual precipitation (with large variance explained by the model, R² = 0.84). For dataset D2, no significant trend is observed neither in species richness (b) nor in generalized species richness (d)(all model fits have R² < 0.01). See Supplementary Note, Table S1 for details on model selection.