## 2 Materials and Methods
### Model Improvements
#### 2.3.3 Evergreen Phenology  
Evergreen canopy turnover was modified from [37]. 3D-CMCCFEM v.5.1 assumes that evergreen leaf turnover is constant throughout the year, and that annual leaf turnover is equal to leaf biomass produced the year before [37; 48]. However, leaf turnover seems to be concentrated in specific seasonal windows: (1) consistently to leaf emergence (spring); and (2) approaching of photosynthetic inefficient season (fall) [51]. For this reason, this approach may affect the ability in estimating leaf biomass and GPP intra-annual variability. To better represent leaf turnover dynamics, we developed a new framework where competition for light dynamically affected leaf turnover. We assumed the canopy to be a population of leaves optimized to intercept the highest amount of light. Since leaves cannot move from their position in the canopy, they get partially shaded by new emergent leaves when aging. Conceptually, leaves can be assumed to be in competition for one resource, light, and their turnover can be predicted by using a competition for one resource scheme as in [52]:  
\[\left\{ \begin{array}{c}\frac{\partial B_{i}(t)}{\partial t}B_{i}(t)^{-1}=f_{ i}(R)-f_{i}(m_{i})\\ f_{i}(R)=\frac{r_{i}\cdot R}{(R+K_{i})}\\ {R_{i}}^{*}=\frac{m_{i}\cdot Y_{i}}{(r_{i}-m_{i})}\end{array} \right., \tag{9}\]  
In this model, \(R\) and \({R_{i}}^{*}\) are respectively the concentration of available light in J m\({}^{-2}\) day\({}^{-1}\) (i.e., resource that leaves are competing for), and the light needed to survive in a progressively more shaded canopy. \(r_{i}\) is the max photosynthetic rate (gC m\({}^{-2}\) day\({}^{-1}\)), \(m_{i}\) is the maintenance respiration in gC m\({}^{-2}\) day\({}^{-1}\), \(Y_{i}\) carbon yield. We assumed for hypothesis that:1. Older leaves live in the shaded portions of the canopy, where light transmitted is reduced following [PERSON]'s exponential decay equation. For this reason, we expect an exponential reduction in absorbed photosynthetically active radiation (APAR);
2. An age dependent quasi-exponential decay in leaf quantum yield efficiency [53]. These decays impact on the reduction of \(r_{i}\);
3. Nitrogen content in older leaves is often lower than in young ones, because of its transfer from portions of the crown with low productivity to portions more exposed to light [53]. Since maintenance respiration is proportional to nitrogen content, we expect an exponential reduction in \(m_{i}\);
4. \(Y_{i}\) was assumed to be constant as in [17] because of the joint effect of reduction in respiration rate and quantum yield efficiency. We assumed that the three components of the Equation (9) may have the following shapes: \[\left\{ \begin{array}{c}m_{i}=m_{0}\cdot e^{-k_{\eta}\cdot t}+m_{m}\\ r_{i}=\left(\alpha_{0}\cdot e^{-k_{\lambda}\cdot t}+\alpha_{m}\right)\cdot\left( \lambda_{0}\cdot e^{-k_{\lambda}\cdot t}+\lambda_{m}\right)\\ k_{i=const}\end{array} \right.,\] (10) where \(t\) is time, the independent variable. \(m_{0},~{}\alpha_{0},~{}\lambda_{0}\) are MR, quantum yield and APAR at first day of budburst, the second year of life. \(m_{m},~{}\alpha_{m},~{}\lambda_{m}\) are the theoretical minimum values of MR, quantum yield and APAR to let a proportion of leaves survive in a non-shading context. \(k_{\eta},~{}k_{\alpha},~{}k_{\lambda}\) are the exponential parameters for the three functions. Based on these hypotheses Equation (10) becomes:  
\[{R_{i}}^{*}=\frac{\left(m_{0}\cdot e^{-k_{\eta}\cdot t}+m_{m}\right)\cdot k_{i }}{\left(\alpha_{0}\cdot e^{-k_{\lambda}\cdot t}+\alpha_{m}\right)\cdot\left( \lambda_{0}\cdot e^{-k_{\lambda}\cdot t}+\lambda_{m}\right)-\left(m_{0}\cdot e ^{-k_{\eta}\cdot t}+m_{m}\right)}, \tag{11}\]  
Assuming that \(k_{\eta}=k_{\alpha}=k_{\lambda}\), and that the denominator of Equation (9) has to be greater than zero for the leaves in the ith generation to survive, R* is a sigmoid positive function. Knowing R*, we can calculate the amount of live leaf biomass of the ith generation (\(\{i_{0}\}\)) as the inversion of R* (i.e., \(S_{i}^{*}(t)\)).