Table 3 Significant results of generalized linear models (GLM) for the effects of alien pollinators on native species

	Estimate	Std. error	t Value
Alien effect on pollinators’ persistence (AIC: -5153.8)
Alien foraging efficiency (A. For. Eff.)	0.04	0.02	2.46	*
Alien mean Jaccardian index (A. Jacc.)	1.52	0.45	3.37	***
Connectivity of the most-generalist plant sp (Conn. Gen. P)	0.014	0.003	4.56	***
*A. For. Eff. A. Jacc.**	−1.14	0.25	−4.63	*******
A. For. Eff. * Conn. Gen. P	−0.007	0.002	−4.31	***
A. For. Eff. * Fr. plant sp visited by alien	0.20	0.03	6.56	***
A. Jacc.* Conn. Gen. P	−0.14	0.05	−2.64	**
Conn. Gen. P * Fr. plant sp visited by alien	−0.036	0.006	−6.27	***
*A. For. Eff. A. Jacc. * Conn. Gen. P**	0.10	0.03	3.43	*******
Alien effect on native pollinator density (AIC: -11619)
Fr. of plant sp visited by alien	−9.5e−3	4.7e−3	−2.03	*
*A. For. Eff. Fr. of plant sp visited by alien**	2.6e−2	0.2e−2	12.9	*******
Conn. Gen. P * Fr. of plant sp visited by alien	−2e−3	0.4e−3	−5.2	***
Alien effect on native plant density (AIC: -14201)
A. For. Eff.	3e−3	3e−4	8.20	***
Fr. specialist native pollinator sp (Fr. Spec Nat. Pol.)	2e−3	7e−4	3.42	***
*A. For. Eff. Fr. Spec Nat. Pol.**	−2e−3	5e−4	−4.65	*******

Predictors of the models were chosen based on CART results and the best models were chosen using AIC. Evaluated predictors for the alien effects on native pollinators’ persistence and density were (1) alien foraging efficiency, (2) alien mean Jaccardian index, (3) connectivity of the most-generalist plant species, and (4) fraction of plant sp visited by the alien. Evaluated predictors for the alien effects on plant density were (1) alien foraging efficiency, (2) fraction of plant species visited by the alien, and (3) fraction of specialist pollinator species. Full models are described in Table S4, Supplementary Information. Data used include independent species introduction in 1200 network structures, 600 each for average and efficient alien foragers (see Methods and Supplementary Table 4). The underlined terms are mentioned in the main text. Bold entries are mentioned in the main text. Significance codes for P values: 0 “***”, 0.001 “**”, and 0.01 “*”

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