Table 1. Effect of ecosystem services providers (pollinators and biocontrol agents) and nitrogen application on productivity per flower (g) and overall land productivity (kg ha-1) of common bean (P. vulgaris) farms.

Response variable (Y)	Explanatory terms				Weight	AICc	∆AICc
Productivity per flower	DN	DE	N	DN*N
Model1	-	-	X	-	0.269	63.9	0.00
Model2	-	X	X	-	0.134	65.3	1.39
Model3	X	-	-		0.113	65.7	1.74
Model4	X	-	X	X	0.111	65.7	1.78
Average model: log(Y/(2-Y))=-1.32+(638.5-6.8*N)*DN+0.016*N-45.1*DE
Overall land productivity	DN	DE	N	DN*N
Model 1	-	-	-	-	0.287	110.3	0.00
Model 2	X		-	-	0.135	111.8	1.51
Model 3	-	X	-	-	0.124	112.0	1.68
Average model: log(Y/(5300-Y))= -014 + 54.25*DN –86.2*DE

Models were selected based on the Akaike information criterion corrected to small sample size (AICc), and all models with a variation of AICc (ΔAICc) lower than 2 units were considered in the average model, the contribution being proportional to the model weight. As productivity models typically follow a sigmoid relationship (i.e. have established maximum and minimum values) we applied a logit transformation, using the maximum value of productivity per flower rounded to units (2 g) and productivity per ha rounded to hundreds (5300 kg.ha^-1) as the top asymptote.

DN = Density of native pollinators

DE = Density of exotic pollinators (A. mellifera)

N = Nitrogen input

X = terms that were included in the models (Gaussian distribution for productivity per flower, and log transformed for overall land productivity to normalize residuals)

* = two-way interaction between explanatory variables or multiplication in the equation