Vegetation | CL expression (partial derivative of species richness equation) | CL (kg N⋅ha^{−1}⋅y^{−1}) | CL error^{§} | ||

Mean^{†} | Range^{†} | Range of 95% CI^{‡} | |||

Open canopy vegetation | [4.690 + (0.475 · (soil pH)) + (0.0018 · (mm of precip.)) + (−0.073 · (temp. (°C)))]/(−2 · −0.494) | 8.7 | 7.4–10.3 | 6.4–11.3 | −4.5%, 4.8% |

Closed canopy vegetation | [0.449 + (0.543 · (soil pH))]/(−2 · −0.125) | 13.4 | 7.9–19.6 | 6.8–22.2 | −6.2%, 7.7% |

The critical load (CL) expression is derived using the partial derivative with respect to nitrogen of the species richness equation in Table 1, and then evaluated locally with site-specific soil pH, precipitation, and temperature values.

↵

^{†}Mean and range of CLs across sites, reflecting variation in soil pH, precipitation, and temperature variables across sites but not uncertainty in coefficient estimates.↵

^{‡}Range of CL 95% confidence interval endpoints across sites (Fig. S3), reflecting both ecological variability (soil pH and climate variables) and uncertainty in coefficient estimates, with the latter calculated from the 2.5th and 97.5th percentiles of 10,000 Monte Carlo simulations of coefficient uncertainty.↵

^{§}Average of the site-specific CL % errors, calculated from the lower and upper endpoints of the 95% confidence interval of Monte Carlo simulations of coefficient uncertainty repeated at each site.