Table 2. GLMMs applied to data simulated under null models.

Null models 1 and 2 were generated under the ZSM distribution, with a single distribution for the whole dataset (Model 1) or one distribution per environment (Model 2). Model 3 is similar to Model 1, except with a single Poisson distribution for the whole dataset, and +DBD or +EC refer to adding these effects to all ASVs in each sample (see Materials and methods and Figure 2—figure supplement 17). Each row reports the effect of community diversity (Div) on focal lineage diversity, as well as its standard error, Wald z-statistic for its effect size and the corresponding P-value (Wald test) (left section), or standard deviation on the slope for the significant random effects (right section). SE = standard error, Env = environment type, Lin = lineage type, Sample = EMP Sample ID. n.s. = not significant (likelihood-ratio test), n.t. = not tested, because separate environments were not included in Models 1 or 3.

	Slope (fixed effects)				Stand dev on the slope (random effects)
	Div	SE	z	P	Env	Lin	Lin*Env	Sample
Model 1	−0.005	0.000	−9.807	<2 e −16	n.t.	0.639	n.t.	n.s.
Model 2	n.s.
Model 3	−0.012	0.002	−6.552	5.69e-11	n.t.	0.021	n.t.	n.s.
Model 3 + DBD	0.016	0.001	11.48	<2e-16	n.t.	0.008	n.t.	n.s.
Model 3 + EC	−0.011	0.002	−6.14	8.26e-10	n.t.	ns	n.t.	n.s.