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).