Analysis
To assess the relationships between precipitation, temperature, and forest structure, we calculated Spearman rank correlation coefficients in R (R Core Team, 2021) for each pair of variables. We considered pairwise comparisons above a 0.6 to have a strong correlation. All pairwise comparisons with a p-value < 0.05 were considered significantly correlated.
To assess whether each forest ecosystem between the 12 forest domains has a distinct three-dimensional structure we tested the variations in structure, topography, and climate across forest ecosystems using a non-parametric Kruskal-Wallis one-way ANOVA test. We also used Kruskal-Wallis tests to assess whether the species richness and functional diversity in each forest ecosystem was distinct with a pairwise Dunn test to identify significant differences between forest ecosystems. Analyses were carried out using the functionggbetweenstats from the ‘ggstatsplot’ package in R, with violin plots to illustrate differences (Patil, 2021).
To assess the relative strength of temperature, precipitation, and forest structure in explaining the differences in species richness and functional diversity, we modeled the relationship of each functional diversity metric as a function of structure, climate, and topography. To model these relationships, we applied boosted generalized additive models (GAMs) to all data using the function gamboost in the package ‘mboost’ in R (Hothorn et al., 2021). These models are particularly suited for disentangling the effects of collinearity among variables and modelling non-linear relationships common to ecological systems (Hothorn et al., 2010), which is especially important for this study as structural metrics of forests can be highly correlated, in that structurally complex forests are also more productive (Fortis et al., 2018; Hardiman et al., 2011). Component-wise boosting optimized parameter estimates and prediction accuracy, including variable selection. Overfitting was mitigated with 25-fold bootstrap estimates of the empirical risk to determine the appropriate number of boosting iterations for each model using the function cvrisk. Finally, the selection frequencies of the 25 bootstraps were averaged to compare the effect size and importance of each structure, topographic, and climactic variable as a predictor for each functional diversity metric using NEON’s domain classification as a random intercept.
Three-dimensional surfaces were generated to visualize how the relationships between temperature, precipitation, and structure predict species richness and functional diversity across North American forests. A smoothed surface was created with a GAM framework to model forest structure metrics across temperature and precipitation gradients. Both Shannon’s Diversity of LAD and maximum canopy height resulted in two of the highest selection frequencies for our models of avian richness and functional diversity. However, maximum canopy height was selected in every model of avian richness and functional diversity. Thus, maximum canopy height was our third structural axis in the 3D modeled surface with precipitation and temperature. The predictive surface includes boreal and temperate forests, temperate rainforests, and woodlands. Using this modeled surface and fitted models, we predicted functional diversity and species richness across temperate forest biomes as defined by Whittaker (1975).