2.5.2 Multivariate analysis of BAI and tree synchrony: tree size, community and geographic effects
Following bivariate analyses, we fit a more comprehensive set of multivariate models to better assess the relative importance of geographic and structural/compositional factors as determinants of tree growth patterns. Tree-level models were fit separately for Piceaand Fagus . Both tree-level interseries correlations and mean BAI over the 1980-2010 interval were modeled as a function of canopy status, species diversity, altitude and latitude. For BAI models, growth synchrony was included as an additional explanatory factor. Tree synchrony was additionally integrated into models explaining variation in log(BAI). Effect sizes for altitude, latitude, diversity and synchrony were allowed to vary with competition class. All variables were standardized to a mean of zero and a standard deviation of 1. The fact that trees co-occurring within close proximity cannot be considered independent samples complicated the interpretation of this analysis. Mixed effect models allowed us to simultaneously estimate the effects of several explanatory factors while simultaneously fitting random effects to control for the potential autocorrelation among co-occurring trees. Using mixed effects models allowed us to fit a random intercept for each plot and nest our effect size estimates within tree competition classes:
Synchrony = β0i + β1j * Elevation + β2j * Latitude + β2j * Diversity + εk
log(BAI) = β0i + β1j * Elevation + β2j * Latitude + β2j * Diversity + β3j * Synchrony + εk,
where, β0i are random intercepts for each of iplots, and βnj are effect size estimates, nested within the j =2 canopy classes, and εk is a randomly distributed error term for each of k trees.
2.5.3 Multiple regression on regional variation in\(\overset{\overline{}}{r}\) and mean BAI
Multiple regressions were conducted to test the relative importance of abiotic vs. biotic factors in driving regional growth patterns that integrated all local variability in tree growth (averaging over species and competition classes). All variables were standardized to a mean of zero and a standard deviation of one prior to analysis. Response variables included \(\overset{\overline{}}{r}\) and mean BAI over 1980-2010. Importantly, \(\overset{\overline{}}{r}\) was also used as an explanatory factor in the model predicting BAI.
Abiotic factors included altitude and latitude. Structural factors included stem densities and plot-level basal area. The effect of species composition was incorporated, again using Shannon’s diversity index. Disturbance variables were also included. The time since the most recent disturbance and the severity of the most recent disturbance was included in the model of mean BAI, and the time since and severity of each plot’s most severe disturbance was incorporated into our model of\(\overset{\overline{}}{r}\).