## 3 Results
### Trends in the Cumulative Root Surface and Root Count
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(\mathbf{Y_{i}}\)} & \multirow{2}{*}{**Model Equation**} & \multicolumn{2}{c}{**Family**} & \multirow{2}{*}{**Link Function**} & \multirow{2}{*}{**Adjusted \(\mathbf{R^{2}}\)**} & \multirow{2}{*}{**Site**} & \multirow{2}{*}{**Smooth Term**} & \multirow{2}{*}{**Speces**} & \multirow{2}{*}{**Eff**} & \multirow{2}{*}{**For Chi.sq**} & \multirow{2}{*}{**\(p\)-Value**} \\  & & **Distribution** & & & & & & & & & & & \\ \hline New root count & g(\(\mathrm{Z}[y_{i}]\)) = \(f_{1}\)(Day) + \(\mathrm{z_{D}}\) + \(\mathrm{z_{i}}\) & Negative & Logarithmic & 0.28 & PB & Day & _Fegus splitting_ L & 6 & 18 & \textless{}0.05 \\ New root count & g(\(\mathrm{Z}[y_{i}]\)) = \(\mathrm{\beta_{i}}\)Speces + & Negative & & Negative & & & & & & \\ \(f_{1}\)Speces(Day) + \(\mathrm{z_{D}}\) + \(\mathrm{z_{i}}\) & binomial & Logarithmic & 0.11 & KS & Day & _Fegus splitting_ L & 1 & 30 & \textless{}0.001 \\  & \(f_{1}\)Speces(Day) + \(\mathrm{z_{D}}\) + \(\mathrm{z_{i}}\) & binomial & & PB & & & & _Quercus number_ L & 2.6 & 59 & \textless{}0.001 \\  & & & & KS & & & & & & & \\ Cumulative root & g(\(\mathrm{Z}[y_{i}]\)) = \(f_{1}\)(Day) + \(\mathrm{z_{D}}\) + \(\mathrm{z_{i}}\) & Gamma & Inverse & 0.2 & PB & Day & _Fegus splitting_ L & 5.3 & 3.6 & \textless{}0.01 \\ Cumulative root & g(\(\mathrm{Z}[y_{i}]\)) = \(\mathrm{\beta_{i}}\)Speces + & Gamma & Inverse & 0.25 & KS & Day & _Fegus splitting_ L & 4 & 4.2 & \textless{}0.001 \\  & \(f_{1}\)Speces(Day) + \(\mathrm{z_{D}}\) + \(\mathrm{z_{i}}\) & & & PB & & & & & & \\  & & & KS & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Adjusted \(R^{2}\), effective degrees of freedom (e/d), and F-test values of the GAM smooth terms (Day counted from the first of January). \(\mathrm{Z}[y_{i}]\) are the expected values of the response variable \(y_{i}/R(\mathrm{z_{i}})\) is the smooth function of the covariate \(\mathrm{z_{i}}\), \(\mathrm{z_{i}}\) is the intercept of the covariate \(\mathrm{z_{i}}\), \(\mathrm{z_{i}}\) is the random effect; and \(\mathrm{z_{i}}\) are the errors. All smooth functions were fitted using P-splines. In oak, the mean cumulative root surface increased until a plateau was reached around the beginning of summer 2019. This plateau remained until the end of autumn 2019 and was followed by a relatively fast subsequent decline in the early spring of 2020. The pattern in the mean new root count per tube in oak was similar to the pattern found in the beech trees of the KS, with very few roots produced in 2020. However, the initial number of new root counts in oak was approximately fivefold higher than those of beech. Birch presented a stable cumulative root surface for the whole measurement period. Like beech and oak, the mean new root count per tube in birch decreased from the beginning of the measurements until approximately December 2019. However, unlike in beech and oak, the mean new root count per tube in birch increased again in the spring of 2020. In late August 2020, a peak was reached in the mean new root count per tube in birch. This peak was followed by a decrease until the beginning of December 2020 when seemingly no new fine-roots were produced. Linking the Above- and Belowground Phenology of Fagus sylvatica L., Quercus robur L., and Betula pendula Roth  
In 2019 and 2020, the bud burst occurred during the first week of April in birch and during the second to third week in beech and oak (Figure 5A). The mean phenological transition date suggests that the onset of the re-organization phase of leaf senescence in 2019 took place somewhere around the second week of September in oak, the second week of October in birch and the fourth week of October in beech (Figure 5B,C). In 2020, the mean phenological transition date suggests a similar timing for beech but a slightly earlier and later onset of the re-organization phase of senescence for birch and oak, respectively. This would be around the fourth week of September for birch and the fourth week of October for oak.