Fig. 5: Structural equation models (SEMs) accounting for the hypothesized direct and indirect relationships between aridity, soil properties (pH and clay content), biodiversity (plant species richness and the soil microbial diversity index), BNPP, and soil multifunctionality.

a, b SEMs are shown for sites with aridity <0.8 (a; N = 54) and >0.8 (b; N = 76). Note that we only present significant relationships (two-sided P < 0.05) and their coefficients (numbers adjacent to arrows) for graphical simplicity. Latitude, longitude, and elevation of the field sites are included to account for the spatial structure of our dataset, and thus their coefficients are not included. A priori model including all hypothesized causal relationships is available in Supplementary Fig. 17a, and all the rest of coefficients and their significance levels are available in Supplementary Table 5. For the SEM of sites with aridity >0.8, we remove the relationship between soil pH and BNPP with a coefficient close to zero to improve its overall goodness-of-fit. Continuous and dashed arrows indicate positive and negative relationships, respectively. The thickness of the arrow is proportional to the magnitude of standardized path coefficients and indicative of the strength of the relationship. Asterisks indicate the significance level of each coefficient: *P < 0.05; **P < 0.01; ***P < 0.001. R² is the proportion of variance explained by the model. Goodness-of-fit statistics for each SEM are given (d.o.f. degrees of freedom, RMSEA root mean squared error of approximation).