Appendix B. Additional methods for spatial and phylogenetic analysis.
Model residuals may be spatially non-independent. In a second step we repeat our analyses and account for spatial autocorrelation using maximum-likelihood spatial autoregressive (SAR) models (R package spdep, Bivand 2005). Longitude and latitude were used to develop neighborhoods with threshold distances of 400, 800, and 1500 km. Threshold distances were selected by examining correlograms. Neighbors were weighted a priori using row standardization, such that the weights of all neighbors within the threshold distance sum to one (Haining 2003). We used Moranís I Tests to evaluate the spatial autocorrelation of the model residuals, with larger absolute values indicating higher spatial autocorrelation. The three model types considered account for spatial-autocorrelation in the response variable (spatial lag), error term (error dependence), and both predictor and response variables (mixed) (Anselin 1988). Model fits and coefficients as well as performance in reducing spatial autocorrelation were similar between the three types of models. We report error dependence models as correlated unobserved variables are the most likely source of spatial autocorrelation in the analysis. Approximate Global Moranís I tests were used to assess the performance of the spatial autoregressions in reducing spatial autocorrelation (Haining 2003).
Phylogenetic relatedness is an additional source of data non-independence. We account for phylogenetic covariation using generalized-least squares regressions (GLS), in which expected variances of and correlations between error terms are derived from phylogenetic topology and branch lengths (R packages ape and PHYLOGR, Garland et al. 2005). We built a phylogeny based on Pough et al. (2001) to the familial level. As sub-familial phylogenies are not well resolved across the analyzed species, we subsequently incorporated taxonomic classifications (genus and species). Branchings for genera within families and species within genera were incorporated as star phylogenies (termed mini-stars in Garland et al. 2005). We assumed equal branch lengths. The GLS method required restricting the analysis to one randomly selected observation for each of the databaseís 246 species. We indicate the degree of phylogenetic correlation with Pagelís λ , which ranges between 0 (phylogenetic independence) and 1 (species traits covary in direct proportion to their shared evolutionary history).LITERATURE CITED
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