Electronic Supplementary Material I

Electronic Supplementary Material I

The three level random coefficient model generates at level 1 the following model:

plts = b0ts + b1lts h + elts

with plts representing the leaf parameters (measured at leaf “l”, within tree “t”, belonging to species “s”), b0ts the intercept term which is allowed to vary between individual trees and species, b1lts the coefficient term describing how plts varies with the sampling height h per tree and species and elts is the residual error term. At level two of the model, the intercept b0ts can be described as

b0ts = b00s + r0ts

with b00s being the tree-level effect per species on the random intercept, and r0ts the tree specific deviation, and b1lts is described as:

b1lts = b10s + r1ts

with b10s explaining the tree level effect on the random slope and r1ts being the tree specific deviation of the random slope. At level three of the model, b00s is described as:

b00s = y000 + u00s

with y000 giving the common value of the intercept for each leaf of each tree and for each species, and u00s the species specific variation around this value. b10s is described as:

b10s = y100 + u10s

With y100 being the common value for the random slope for all leaves from all trees and all species, and u10s describing the species-specific deviation from the slope. Combining the equations above, the model can be written as:

plts = y000 + r0ts + u00s + (y100 + r1ts+ u10s) h + elts

The ‘null model’ of this equation is therefore:

plts = b0ts + elts or

plts = y000 + r0ts + u00s + elts

The residual terms of the null model can be used to examine the inherent sources of variation in the untransformed dataset with:

Var(elts) = s2, var(r0ts)= t2 and var(u00s) = f2

The total variance in the data set is then s2 + t2 + f2. We can use the variance partition coefficient (e.g., s2/(s2 + t2 + f2)) to examine how much of the variance can be attributed to inter-tree differences, between-tree differences and in-between species differences. It has to be noted that when a large portion of the variance can be attributed to inter-tree differences, this does not necessarily mean a significant relationship of that leaf variable with height.

To test whether the random regression coefficient b1lts is significantly different from 0, we compared the difference of -2loglikelihood (-2LL) values of both models with a chi-squared distribution with three degrees of freedom (since three variables were added to the model). In a similar fashion, we tested whether adding level 2 (r1ts) and 3 (u10s) to the random slope model provided a better fitting model that a singular slope, by comparing the -2LL values of the fits of these models with a chi-squared distribution (df = 1 and df=2 respectively). Because of the heteroscedastic nature of the random coefficient model, we centred the model around the average height of the canopy (10.9 m) in our dataset (Snijders and Bosker 1999).

Electronic Supplementary Material II

We measured diurnal stomatal conductance on 9 different days between 18 July and 14 august on 4 leaves of 3-5 different individual trees of the species Clethra cuneata, Clusia cretosa and Schefflera allocotantha.

Figure 1 a) Average diurnal values of pressure deficit (VPD) and photosynthetically active radiation (PAR) ± SE White circles denote VPD and black circles denote PAR. b) Average diurnal and stomatal conductance (white circles, n=120) ± SE and their time of measurement ± SE for the species Clethra cuneata, Clusia cretosa and Schefflera allocotantha