Individual level
First we diagnose if duration and growth are different between treatment and environmental contexts.
Using sugar maple as example.
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: value ~ model + (1 | heat_name)
## Data: df
##
## REML criterion at convergence: 6497.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.0857 -0.6922 -0.1028 0.5607 2.9699
##
## Random effects:
## Groups Name Variance Std.Dev.
## heat_name (Intercept) 2.219 1.489
## Residual 142.071 11.919
## Number of obs: 834, groups: heat_name, 3
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 32.9332 1.1688 4.5159 28.177
## modelclosed canopy, ambient rainfall -6.6558 1.0022 829.2760 -6.641
## modelopen canopy, reduced rainfall -0.5412 1.1148 829.5223 -0.485
## Pr(>|t|)
## (Intercept) 3.00e-06 ***
## modelclosed canopy, ambient rainfall 5.63e-11 ***
## modelopen canopy, reduced rainfall 0.627
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) mcn,ar
## mdlccnpy,ar -0.535
## mdlpcnpy,rr -0.481 0.561Using white spruce as example.
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: value ~ model + (1 | heat_name)
## Data: df
##
## REML criterion at convergence: 4700.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.99929 -0.79442 -0.09612 0.64256 2.94494
##
## Random effects:
## Groups Name Variance Std.Dev.
## heat_name (Intercept) 6.008 2.451
## Residual 282.388 16.804
## Number of obs: 555, groups: heat_name, 3
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 42.228 1.868 3.888 22.604
## modelclosed canopy, ambient rainfall -2.699 1.749 550.286 -1.544
## modelopen canopy, reduced rainfall 4.833 1.737 550.377 2.783
## Pr(>|t|)
## (Intercept) 2.86e-05 ***
## modelclosed canopy, ambient rainfall 0.12326
## modelopen canopy, reduced rainfall 0.00557 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) mcn,ar
## mdlccnpy,ar -0.455
## mdlpcnpy,rr -0.459 0.489In both species, duration tends to be shorter in closed canopy, in addition to the effects of warming. This means we need to control for both warming treatment and environmental context when we look at the individual-level covariation of growth parameters.
Site-year level
