Climate-growth model comparisons
To test the influence of seasonal climate on growth, linear
mixed-effects model analyses were performed. In these, climate–growth
models were compared with a null model. Before the analyses, both the
climate and standardized individual shoot length series were normalized.
This was done by subtraction of the mean of the series, followed by a
division with the standard deviation. Annual shoot lengths of the
individual branches were included in the models as the response
variable. A total of 20 climate-growth models were compared with the
null model. Mean temperatures or precipitation sums of the previous
summer (June-August of the previous year), previous autumn
(September-October of the previous year), early winter
(November-December of the previous year), mid-winter (January-February),
late winter (March-April), winter (previous November-April), spring
(May), early summer (June-July), late summer (July-August), or summer
(June-August) sums were included as fixed effect. Furthermore, an
autocorrelation structure (AR1, autoregressive process of order one) was
included in each model to account for possible autocorrelation in the
shoot length series. Random intercepts were included in the models foryear to account for spatially correlated environmental conditions
not captured by the fixed effects. The null model was identical to the
climate models with a mean of one instead of a climate variable as fixed
effect. The linear mixed-effect model analyses were performed with the
R-package nlme v.3.1-152 . Maximum likelihood estimation was used for
model comparison and restricted maximum likelihood estimation was used
to calculate slope estimates . Coefficients of determination values for
each model were calculated using the r.squaredGLMM function of the MuMIn
package v.1.43.17 . The year 2014 was excluded from the analyses, as
growth may not have been completed at the time of sampling in early
August. The model comparison was done both at the site and shrub level.
To test the stability of the climate-growth relationships over time, the
model comparison was done for three different periods: the complete
period (1893-2013), the most recent 50 years (1964-2013) as there was a
clear increase in sample depth after 1964 (cf. Fig. 2) and the last
complete climate period (1984-2013).