Table S1.

Effects of biodiversity (S and S_plants) on proxies of productivity (EVI_GS), the stability of productivity ($\mathbf{C}{\mathbf{V}}_{\mathbf{E}\mathbf{V}{\mathbf{I}}_{\mathbf{G}\mathbf{S}}}^{-1}$), and GSL lengthening (d·y⁻¹) when fitted after covariates related to climate, land cover, and topography

Model terms		S						Splants
		EVIGS		${\text{CV}}_{{\text{EVI}}_{\text{GS}}}^{-1}$		GSL lengthening, d·y−1		EVIGS		${\text{CV}}_{{\text{EVI}}_{\text{GS}}}^{-1}$		GSL lengthening, d·y−1
BGR	Covariate	Effect size	Significance	Effect size	Significance	Effect size	Significance	Effect size*	Significance	Effect size*	Significance	Effect size*	Significance
—	—	0.25 ± 0.02	F1,379 = 240***	9.2 ± 1.4	F1,445 = 45***	1.1 ± 0.3	F1,444 = 18***	0.053 ± 0.004	F1,378 = 172***	2.1 ± 0.3	F1,444 = 43***	0.27 ± 0.06	F1,442 = 19***
	Alt.	0.15 ± 0.02	F1,437 = 64***	9.3 ± 1.6	F1,438 = 35***	1.6 ± 0.3	F1,437 = 31***	0.027 ± 0.005	F1,437 = 32***	2.2 ± 0.4	F1,443 = 33***	0.40 ± 0.07	F1,441 = 34***
	Slope	0.27 ± 0.02	F1,402 = 278***	9.1 ± 1.4	F1,443 = 45***	1.1 ± 0.3	F1,443 = 17***	0.059 ± 0.004	F1,407 = 206***	2.1 ± 0.3	F1,443 = 43***	0.26 ± 0.06	F1,443 = 19***
	N-Aspect	0.24 ± 0.02	F1,375 = 220***	11.0 ± 1.3	F1,443 = 70***	0.9 ± 0.3	F1,443 = 13***	0.050 ± 0.004	F1,374 = 157***	2.5 ± 0.3	F1,442 = 65***	0.24 ± 0.06	F1,441 = 15***
	Irrad.	0.23 ± 0.02	F1,415 = 158***	9.6 ± 1.5	F1,443 = 41***	1.2 ± 0.3	F1,444 = 18***	0.046 ± 0.005	F1,410 = 103***	2.2 ± 0.4	F1,444 = 39***	0.30 ± 0.07	F1,442 = 20***
	Precip.	0.25 ± 0.02	F1,399 = 212***	9.0 ± 1.4	F1,443 = 42***	1.2 ± 0.3	F1,443 = 22***	0.051 ± 0.004	F1,395 = 151***	2.0 ± 0.3	F1,444 = 40***	0.29 ± 0.06	F1,443 = 23***
	Temp.	0.18 ± 0.02	F1,410 = 95***	10.4 ± 1.5	F1,442 = 45***	1.4 ± 0.3	F1,444 = 24***	0.034 ± 0.005	F1,409 = 55***	2.4 ± 0.4	F1,442 = 43***	0.35 ± 0.7	F1,444 = 26***
	Grass	0.23 ± 0.02	F1,376 = 237***	8.7 ± 1.4	F1,443 = 39***	1.1 ± 0.3	F1,442 = 17***	0.050 ± 0.004	F1,376 = 185***	2.0 ± 0.3	F1,443 = 39***	0.26 ± 0.06	F1,441 = 18***
	Forest	0.29 ± 0.02	F1,379 = 232***	5.0 ± 1.5	F1,441 = 11**	0.8 ± 0.3	F1,444 = 7**	0.058 ± 0.005	F1,381 = 157***	1.2 ± 0.4	F1,440 = 10**	0.20 ± 0.07	F1,443 = 9**
	LCrichness	0.24 ± 0.02	F1,380 = 178***	10.4 ± 1.5	F1,444 = 50***	1.3 ± 0.3	F1,442 = 22***	0.048 ± 0.004	F1,376 = 124***	2.4 ± 0.3	F1,443 = 47***	0.31 ± 0.06	F1,440 = 23***
	Arable	0.26 ± 0.02	F1,382 = 268***	9.1 ± 1.4	F1,443 = 45***	1.1 ± 0.3	F1,443 = 17***	0.055 ± 0.004	F1,383 = 195***	2.1 ± 0.3	F1,443 = 43***	0.26 ± 0.06	F1,442 = 19***
	Urban	0.25 ± 0.02	F1,376 = 241***	9.5 ± 1.4	F1,443 = 47***	1.2 ± 0.3	F1,443 = 21***	0.054 ± 0.004	F1,374 = 174***	2.2 ± 0.3	F1,441 = 47***	0.30 ± 0.06	F1,441 = 24***
Yes	—	0.25 ± 0.02	F1,387 = 236***	9.5 ± 1.4	F1,438 = 46***	0.9 ± 0.3	F1,438 = 13***	0.053 ± 0.004	F1,382 = 164***	2.2 ± 0.3	F1,434 = 45***	0.24 ± 0.06	F1,435 = 15***
	Alt.	0.18 ± 0.02	F1,416 = 78***	7.2 ± 1.7	F1,439 = 17***	1.3 ± 0.3	F1,438 = 18***	0.031 ± 0.005	F1,415 = 39***	1.7 ± 0.4	F1,438 = 17***	0.33 ± 0.07	F1,436 = 20***
	Slope	0.27 ± 0.02	F1,402 = 261***	9.2 ± 1.4	F1,437 = 44***	0.9 ± 0.3	F1,438 = 12***	0.056 ± 0.004	F1,400 = 184***	2.2 ± 0.3	F1,434 = 42***	0.22 ± 0.06	F1,436 = 14***
	N-Aspect	0.24 ± 0.02	F1,381 = 218***	11.3 ± 1.3	F1,437 = 71***	0.8 ± 0.3	F1,437 = 10**	0.050 ± 0.004	F1,376 = 152***	2.6 ± 0.3	F1,434 = 67***	0.21 ± 0.06	F1,434 = 12***
	Irrad.	0.25 ± 0.02	F1,422 = 185***	8.6 ± 1.5	F1,436 = 33***	1.1 ± 0.3	F1,434 = 16***	0.050 ± 0.005	F1,417 = 120***	2.0 ± 0.4	F1,439 = 32***	0.28 ± 0.07	F1,437 = 18***
	Precip.	0.25 ± 0.02	F1,398 = 212***	8.8 ± 1.5	F1,439 = 37***	1.1 ± 0.3	F1,438 = 15***	0.052 ± 0.004	F1,389 = 144***	2.1 ± 0.3	F1,436 = 36***	0.26 ± 0.06	F1,435 = 17***
	Temp.	0.19 ± 0.02	F1,394 = 108***	9.8 ± 1.7	F1,433 = 35***	1.0 ± 0.3	F1,437 = 11***	0.037 ± 0.005	F1,392 = 62***	2.3 ± 0.4	F1,428 = 34***	0.26 ± 0.07	F1,434 = 13***
	Grass	0.23 ± 0.02	F1,392 = 226***	9.0 ± 1.4	F1,437 = 40***	1.0 ± 0.3	F1,437 = 14***	0.049 ± 0.004	F1,390 = 171***	2.2 ± 0.3	F1,435 = 41***	0.24 ± 0.06	F1,434 = 15***
	Forest	0.28 ± 0.02	F1,383 = 224***	5.3 ± 1.6	F1,431 = 11***	0.6 ± 0.3	F1,438 = 5*	0.057 ± 0.005	F1,381 = 144***	1.2 ± 0.4	F1,426 = 11***	0.17 ± 0.07	F1,434 = 6*
	LCrichness	0.24 ± 0.02	F1,387 = 176***	10.9 ± 1.5	F1,435 = 51***	1.1 ± 0.3	F1,434 = 16***	0.048 ± 0.005	F1,377 = 117***	2.5 ± 0.4	F1,428 = 49***	0.27 ± 0.07	F1,428 = 17***
	Arable	0.26 ± 0.02	F1,386 = 262***	9.3 ± 1.4	F1,435 = 45***	0.9 ± 0.3	F1,437 = 13***	0.054 ± 0.004	F1,381 = 184***	2.2 ± 0.3	F1,432 = 44***	0.23 ± 0.06	F1,434 = 14***
	Urban	0.26 ± 0.02	F1,383 = 240***	9.7 ± 1.4	F1,435 = 47***	1.0 ± 0.3	F1,436 = 15***	0.054 ± 0.004	F1,377 = 170***	2.3 ± 0.3	F1,429 = 47***	0.26 ± 0.06	F1,431 = 18***

Alt., mean plot altitude; BGR, the model does (yes) or does not (-) first account for effects of biogeographic region before the covariate; covariate, the specific covariate, which was included in the fixed-effects term before the biodiversity variables; effect size, coefficients (mean ± SE); Irrad., annual shortwave irradiation; LC_richness, number of land cover types in plot; N-aspect, North-south component of aspect; Precip., annual precipitation; S, the biodiversity index for all taxa combined; significance, F values with associated degrees of freedom and P values; Slope, average slope in degrees; S_plants, the biodiversity of plants; Temp., mean annual temperature; Forest, Grass, Urban, and Arable, fraction of plot covered by forest, grassland, urban, or arable land; for details see SI Materials and Methods and Table S2. (n = 447; ^*P < 0.05; **P < 0.01; ***P < 0.001; n.s. not significant).

^*Effect size is given for an increase of 100 species.