Figure 1: Percentage of variation in individual EFs that was explained
by year, season, species richness (SR), plot identity (plotID), and the
interaction among these variables. The influence of the explanatory
terms is plotted in % of total sum of squares, corresponding to
increments in multiple R2 * 100. Explanatory terms are
plotted for individual effects > 5%. All effects less
<5% are summarized as ”other”, e.g. various
interaction-effects. Hatched barplots represent a simpler model,
including only year, SR, plotID and their interactions for EF, which
were measured in only one season. Non-hatched barplots represent full
models including all terms. The graph corresponds to a hierarchical
partitioning of type one (Groemping 2006), but because explanatory terms
were not correlated, there was no need to average across different
fitting sequences.
Variation in EF
correlations
Positive correlations (indicating synergies) and negative correlations
(indicating trade-offs) were observed across all measures (Fig. 2, upper
triangle). For instance, plant height and shoot biomass showed a
synergy, while soil dissolved carbon and plant height showed a trade-off
in their mean correlations. The strength of these correlations differed
among pairs of EFs, with some EF pairs showed no correlation, while
others showed weak, moderate, or strong correlations. We observed no
strong negative correlations. All EFs showed positive correlations to
some and negative correlations to other EFs (according to their mean
correlation) (Fig. 2, upper triangle), with EFs in some classes showing
predominantly positive correlations (plant productivity and invasion
resistance) and others mostly negative correlations (plant productivity
and plant nutrients). The EF correlations were robust against the method
of calculating correlations, i.e. whether we used mean correlations
(correlation coefficient averaged across time points), grand-total
correlations (one correlation coefficient using all data from all time
points), or between-group correlations (one correlation coefficient
calculated with datapoints averaged across time points) (Supporting
information D, Fig. S4). As expected, EF correlations tended to be
stronger when the variation of individual measurements across time
points was removed, i.e. for the between-group correlations (Supporting
information D, Fig. S4).
The variation per EF pair was quantified by the standard deviation of
correlation coefficients, which were calculated for every time point
when the two EFs were measured in the same year and season. Overall,
there was considerable variation in EF correlations (mean standard
deviation = 0.16, mean correlation coefficient = 0.14) (Fig. 2, lower
triangle). We tested if the variation in the EF correlations depended on
the correlation’s average strength. EF pairs generally showed a higher
variation in their correlation when they show a stronger correlation
irrespective of this correlation being positive or negative
(F5,281=9.4, p<0.001, Supporting information
E, Fig. S5). Additionally, we
tested if the variation in the EF correlations depended on the number of
times the EF-pair was measured (number of years * number of seasons). EF
pairs generally showed an increasing variation in their correlations
with a higher number of times the EF-pair was measured
(F1,572=120.91, p<0.001) (Supporting
information E, Fig. S6). Lastly, we checked whether the variation in
correlations among EFs depend on the identity of time points they were
measured. These ranges of temporal variation were rather small, on
average showing a standard deviation ± 0.08 (Supporting information D,
Fig S7). Furthermore, the range of temporal variation of correlations,
are different for the individual EF-pairs, some EF-pairs show a strong
identity effect of time points (e.g.
SoilNH4__SoilNmin, PlantCover__WeedCover) and some a
weak identity effect of time points (e.g. ShootBM__SoilN,
PlantC__SoilCorg) (Supporting information E, Fig S7).