Table 1. Hypothesis testing framework and consensus approach (see methods) to verify differences in α and β microbial diversity (detailed results in S2 Table).

Location effects	α diversity–ANOVA (ASVs frequencies)				β diversity–PERMANOVA (CLR-CoDa)		β diversity–PERMANOVA (ASVs frequencies)
	ACE	PD	H	IS	CLR ASVs	CLR aggregated genera	untransformed	4rt root	– log(X+1)	presence/absence
Management Practice: Ma	*	**
Altitude: Al
Crop: Cr										*
Ma x Al	*	**			*	*	*	*	*	*
Al x Cr
Ma x Cr
Site: Si (Ma x Al)					***	***	***	***	***	***
Al x Ma x Cr
Cr x Si (Ma x Al)	**	***			***	***	***	***	***	***
posthoc test Ma x Al
high altitude	conv. > agroec.	Conv. > agroec.			Conv. ≠ agroec.	Conv. ≠ agroec.
Low altitude	conv. = agroec.	Conv. = agroec.			Conv. = agroec.	Conv. = agroec.
Dispersion effects (Anna Karenina)					β diversity–PERMDISP (CLR-CoDa)
					CLR ASVs	CLR aggregated genera
Management Practice, High					conv. > agroec.	Conv. > agroec.
Management Practice, Low					conv. = agroec.	Conv. = agroec.

ANOVAs (on ASVs frequencies) and PERMANOVAs (on either ASVs frequencies or centered log-ratio transformed, compositional data, CLR-CoDa) were used to test univariate and multivariate location effects of management practice (Ma: conventional vs agroecological), altitude (Al: high altitude vs low altitude), crop (Cr: watermelon vs cucumber), and site (list and coordinates in S1 File). PERMDISP, based on CLR-CoDa, was used to test dispersion effects on β diversity (Anna Karenina principle) promoted by different management practices either at high or low altitudes. FDR: p value corrected via False Discovery Rate. Tests on α microbial diversity considered Abundance Coverage Estimator (ACE), Faith’s Phylogenetic Diversity (PD), Shannon-Weiner (H) and the Inverse Simpson indexes (IS). The results of the post hoc tests implemented for Ma x Al are indicated.

*: P = <0.05

**: P = <0.001

***: P = <0.0001.