Table 1.

Model calculation of pairwise interaction weights (x_ij). (Letters composing the model name indicate the factors that it considers: A, abundance; B, bark texture of woody species; D, plant size (DBH); S, spatial overlap of species; W, wood density of woody species.)

models	xij calculation	variables
null	xij = 1/IJ	I—total number of woody species
		J—total number of epiphyte species
A	xij = aiaj	ai—number of individuals of species i
		aj—number of individuals of species j
B	xij = P(presence of epiphytesi | bark texturei)	P(presence of epiphytes) = ez/(1+ez)a,b
S	xij = s	s—number of sites in which species i and j co-occur
W	xij = wi	wi—woody species specific gravity
ADc, ABD		M—total number of individuals of species i
		P(presence of epiphytes) = ez/(1+ez)a
		nm = 100.777log(v1), expected number of epiphytes for individual md; v1—DBH category of m
AS, ADS, ABDS	xij is calculated as for A, AD and ABD, respectively, but calculated for each of the three sites separately, and summing the three weights of xij obtained for each site.
AB, BS, ABS	The respective probability matrices are calculated as the element-wise multiplication of the probability matrices P of models A and B, B and S, AS and B, respectively. The resulting matrices are normalized again to obtain P.
AW, BW, SW, ADW, ABW, ASW, BSW, ABSW, ABDW, ADSW, ABDSW	The respective probability matrices are calculated as the element-wise multiplication of each of the probability matrices P of all models above (except W), and the probability matrix of model W. The resulting matrices are normalized again to obtain P.

^ae is the Napier's constant; z is calculated from a logistic regression equation that describes the log odds of presence of epiphytes on a tree, z = ln(odds(presence of epiphyes)), in which bark category and DBH are the explaining variables. z = b₀ + b₁ v₁ + b₂ v₂, where b₀ is the intercept, v₁ is the DBH category of the tree, v₂ is the bark category of the species to which the tree belongs, and b₁ and b₂ are the regression coefficients (see the electronic supplementary material, appendix S2).

^bIn this model v₁ is held constant to five, the minimum DBH category size of the individuals considered.

^cIn this model v₂ is held constant to the intermediate category (two), the bark category to which most tree species belong (see the electronic supplementary material, appendix S1).

^dn_m is the back-transformation of the log (expected number of epiphytes on a woody individual), calculated from the regression equation that describes the linear relation between log(DBH of phorophytes) and log(epiphyte abundance) (see the electronic supplementary material, appendix S2).