A set of explanatory spatial variables was generated from the geographic coordinates of the sampling plots, using a principal coordinate of neighbor matrices (PCNM) analysis (Borcard et al. 2004). This set of variables (called PCNM vectors) represents a spectral decomposition of the spatial relationships among the sampling plots and provide a better representation of the spatial structure present in the sampling data than simple geographic coordinates (Borcard et al. 2004). PCNM vectors are also uncorrelated variables that can be used as predictors in a canonical correspondence analysis (CCA) because they are not subject to multicollinearity errors (Borcard and Legendre 2002). We obtained 60 PCNM vectors, among which 36 had positive values and a significant autocorrelation (P < 0.05, tested by Moran’s 7.)
11.2.3 Data Analysis
We calculated species richness for all feeding guilds jointly and for bark insectivores alone, and in both cases we used the number of species-by-point data. To compare observed species richness among forest classes, we computed sample-based rarefaction (MaoTau) using EstimateS V8.2 (Colwell 2005) and individual-based rarefaction for a comparable number of individuals (1,169 for all feeding guilds jointly and 64 for bark insectivores) using EcoSim700 (Gotelli and Entsminger 2001).
For the species guild composition analysis, we examined the strength of species- environment relationships, whereby we tested for significant effects of three sets of variables: (1) vegetation structure (including stand age), (2) landscape pattern metrics (composition and configuration), and (3) spatial structure of sampling plots (for detailed description, see Table 11.1). To test for significant effects we used constrained analysis (i. e., CCA).
Two different data sets were tested: (1) the number of individuals per feeding guild, and (2) the number of species per feeding guild. For the CCA we used a biplot scaling with interspecies distances, no data transformation, and a Monte Carlo permutation test with 9,999 permutations under the reduced model (to minimize type I error). We tested for the significance of the first axis and of all canonical axes. Finally, to separate the marginal (independent) and conditional (partial) effects of each set of variables we used a variance partitioning method (Borcard et al. 1992)
We also estimated the predictive capacity of stand age for explaining abundance and species richness for all feeding guilds using forward simple linear regressions (SPSS ver. 11.5); when needed, the dependent variable was log-transformed to fulfil the assumption of linearity.