Fig. 4: Experimentally increased heterogeneity weakened the diversity-spatial variability relationships.

a Alpha-diversity (diversity*heterogeneity interaction slopes and 95% confidence intervals: 0.0046 (0.0077 to 0.0108)). b Gamma-diversity (0.0029 (0.0015 to 0.0043)). c Beta-diversity (−0.309 (−0.617 to −0.002)). Different colors represent different sites (see Fig. 2 for site color key assignment), major lines represent the fixed-effect linear regression slopes among sites and small colored lines show patterns within sites. Comparison of SEM models with d ambient and e experimentally increased spatial heterogeneity, using the subset of 42 sites that implemented the experimental protocol, identified two major changes (red numbers; P ≤ 0.05 in multigroup analysis; see Supplementary Table 7 for exact P values) in the pathways whereby increased heterogeneity weakened the three diversity–variability relationships: (1) the negative relationship between alpha-diversity and species covariation under ambient conditions was neutral under increased spatial heterogeneity; (2) the neutral relationship between beta-diversity and species covariation under ambient conditions became negative under increased heterogeneity. Model fit was assessed using Shipley’s test of d-separation (ambient heterogeneity: Fisher’s C = 1.108, df = 6, P = 0.981; experimentally increased spatial heterogeneity: Fisher’s C = 3.108, df = 4, P = 0.54). Solid blue arrows and solid orange arrows represent significant (P ≤ 0.05, no multiple comparison adjustments made) positive and negative paths, respectively (see Supplementary Table 8 for non-standardized coefficient values and exact P values of individual paths), and light-gray arrows represent non-significant paths that were included in the initial model. Tests of significance of path coefficients are two-sided for a difference from 0. Bidirectional arrows represent paths that were modeled as correlated errors (i.e., bidirectional relations instead of causal and unidirectional relations). Numbers next to the arrows are averaged effect sizes as standardized path coefficients. Path coefficients that have been constrained (multigroup analysis; P > 0.05; see Supplementary Table 7 for exact P values) are the same between the two models and are followed by a (C) (path coefficients are globally estimated, but standardized coefficients differ because the variance differs between groups, and thus the standardization). Numbers within brackets show bidirectional path coefficients estimated for the global model (i.e., as if they were conditional). Width of arrows reflects standardized effect sizes. The marginal (i.e., explained by the fixed factors alone) and conditional (i.e., explained by both the fixed and the random factors) percent variance of endogenous variables (R²) are shown next to them (marginal between brackets).