Table 1. Intercept-only and most parsimonious mixed-effects meta-regression models.

Model	Model statistics			Parameters	Mean	Se	z-value	p-value
Grand mean all
(= damage, abundance and	τ2 = 0.11			Intercept	0.01	0.03	0.31	0.76
incidence rate pooled)	Q = 395.35	df = 144	p < 0.001
Damage
Grand mean	τ2 = 0.07	AICc = 67.03		Intercept	0.06	0.06	1.12	0.26
	Q = 92.24	df = 52	p < 0.001
Most parsimonious model	τ2 = 0.07	AICc = 65.63		Intercept	0.14	0.1	1.33	0.18
				(observational at zero MAT)
	QE = 77.99	df = 50	p = 0.01	MAT	- 0.02	0.01	- 2.3	0.02
	QM = 8.22	df = 2	p = 0.02	Experimental vs.	0.23	0.1	2.24	0.03
				observational
Abundance
Grand mean	τ2 = 0.19	AICc = 93		Intercept	0.08	0.04	2.13	0.03
	Q = 220.33	df = 51	p < 0.001
Most parsimonious model	τ2 = 0.15	AICc = 92.17		Intercept	0.15	0.08	1.94	0.05
	QE = 210.51	df = 50	p < 0.001	(generalist)
	QM = 3.64	df = 1	p = 0.06	Specialists vs	- 0.26	0.14	- 1.91	0.06
				generalists
Incidence rate
Grand mean	τ2 = 0.06	AICc = 56.44		Intercept	- 0.08	0.07	- 1.08	0.28
	Q = 73.18	df = 39	p < 0.001
Most parsimonious model	τ2 = 0.04	AICc = 43.54		Intercept	- 0.42	0.07	- 5.67	< 0.001
	QE = 57.75	df = 38	p = 0.02	MAT	0.03	0.01	4.9	< 0.001
	QM = 23.97	df = 1	p < 0.001
Species richness
Grand mean	τ2 = 0.34	AICc = 57		Intercept	0.36	0.15	2.35	0.02
(= most parsimonious model)	Q = 99.23	df = 27	p < 0.001

Mixed-effects models tested the effect of mean annual temperature (MAT), study design (tree plantations or semi-natural forests) and herbivore specialization on the transformed correlation coefficient (Fisher’s z-scores) between the diversity of tree species and the four different aspects of herbivory. In each model the intercept denotes the reference level of coefficient estimates, τ² denotes the variance between study cases, Q/Q_E relate to Cochran's Q-test for residual heterogeneity and Q_M denotes to the omnibus test of model coefficients. Significant parameter estimates are in bold.