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\(\overset{\overline{}}{r}\).