(a) The raw number of functions greater than a threshold against richness, for thresholds ranging from 1% of the maximum (purple lines) to 99% of the maximum (red lines). Lines are predicted fits from GLMMs that fixed the covariate number of functions at 12. (b) The biodiversity effect (expected change in the number of functions exceeding a threshold with addition of one species) against threshold. Each point corresponds to the slope of a single regression of the number of functions greater than a given threshold against richness, from 2 (blue) to 12 (red) numbers of functions. The red line corresponding to 12 functions summarizes the slopes of each line from a. Shaded regions represent 95% confidence intervals. The circle represents the threshold of the maximum biodiversity effect observed for two functions (56%), and the square the threshold of maximum biodiversity effect for 12 functions (81%). The diamond represents the threshold at which the biodiversity effect was still significantly positive for two functions (87%), and the triangle the threshold for 12 functions (94%).