## 5 Results  
Automated soil respiration measurements in the control plot were consistent with those of long-term point measurements [49]. Findings from the present study demonstrate that the treatment site had lower \(R_{s}\) than the control site for all years (Figure 3). Bivariate and conditional G-causalities on _GPP_ and \(T_{s}\) over \(R_{s}\) showed a large effect of temperature and a much smaller effect of _GPP_, especially at low frequencies (Figure 4). At daily frequency, and in minor extent at the corresponding half day sub-harmonic, the effect of _GPP_ on \(R_{s}\) appears to be important, although it is largely reduced when \(T_{s}\) is included in the analysis. There are no apparent differences between the two sites in response to temperature and/or _GPP_. This hypothesis was tested computing the difference \(G(\omega)_{GPP\to R_{s}|T_{s}}^{Control}-G(\omega)_{GPP\to R_{s}|T_{s}}^{Treatment}\). Confidence intervals obtained upon bootstrapping showed that the differences were not significant (Figure 5). The analyses were more complicated when other variables were progressively included. To synthetize the results we aggregated the G-causalities in either long time scales (\(0.2<\text{frequency}<0.7625\text{ day}^{-1}\)) and short time scales (\(0.7625<\text{frequency}<1.7\text{ day}^{-1}\)). Given the fact that the results in both sites were very similar, we also aggregated the data without differentiating among sites. The connectivity graphs (Figure 5) depict only significant direct interactions, _i.e.,_ not mediated by other variables. Figure 4: Bivariate (dashed lines) and conditional (thick lines) G-causalities of \(GPP\) and \(T_{s}\) over \(R_{s}\). Top panels represent control (AmeriFlux) and bottom panels, treatment (FASET). The thick lines represent the desired goal of the analysis because they isolate direct effects, while the dashed lines indicate the apparent connections which are due to a combination of direct and indirect effects. Figure 5: Difference of conditional G-causalities of \(GPP\) given \(T_{s}\) over \(R_{s}\) between control (AmeriFlux) and treatment (FASET). Dashed lines are the 95 th quantiles obtained boostrapping the 60 days blocks of the pulled dataset and divide them in two random groups. We consider three cases. In the first case only _GPP_, \(R_{s}\) and \(T_{s}\) are included. This diagram supports the hypothesis of _GPP_ control over \(R_{s}\) at long time scales, though at short time scales a significant interaction cannot be detected (Figure 6A). Note the biologically improbable interaction of _GPP_ over \(T_{s}\) especially at short time scales. In the second case \(RAD_{n}\) also is included in the analysis (Figure 6B). Introducing this variable changes the causality pattern slightly. The causal effect of _GPP_ over \(R_{s}\) can still be detected at long scales, although considerably reduced. The causality of _GPP_ over \(T_{s}\), however, disappears and \(RAD_{n}\) influences all variables at all time-scales, except for _GPP_ at short scale. This makes sense, as \(RAD_{n}\) controls all energy processes and is closely coupled with biological processes such as _GPP_. The disappearance of the influence of _GPP_ on \(T_{s}\), which was previously detected, indicated that _GPP_ influences \(T_{s}\) indirectly through an unmeasured variable not included in the 3-variable analysis, and  
Figure 6: Connectivity diagram based on the significant direct G-causalities using (**A**) three, (**B**) four or (**C**) five multivariate systems. The widths and values on the arrows indicate average G-causalities for long time scale (0.2 \(<\) frequency \(<\) 0.7625 day\({}^{-1}\)) and short time scales (0.7625 \(<\) frequency \(<\) 1.7 day\({}^{-1}\)). most probably \(RAD_{n}\). The lack of G-causality of \(RAD_{n}\) over \(GPP\) at short scales can be explained by the fact that radiation influences \(GPP\) almost instantaneously, while G-causality only detects lagged responses at the time-scale of the measurements, here--one hour.