Model selection for the LMEs was done via multi-model averaging
(Burnham and Anderson, 2002) based on minimization of corrected
Akaike's Information Criterion (AICc), using the dredge function in the MuMIn package in R. This involves creating a global model with all possible models and combinations of factors. In this method, the smallest AICc value indicates the model of best fit, or the model supported most by the data, given the models considered. Relative support for one model is determined by calculating the differences between AICc and the smallest AICc (A AICc). These differences are then scaled into model weights (wAicc). which are used to calculate model-averaged coefficients with associated standard error values and P-values for each predictor variable. Selection of a subset of candidate models to be used in model averaging included all models with AAICc values of s2. As suggested by Burnham and Anderson (2004). Analyses were performed in R (R Development Core Team, 2012) using the moments, nlme. mcgv, and MuMin packages for distribution parameters, LMEs, GAMMs, and multi-model inference, respectively.