## 2 Materials and Methods
### Measurements
#### 2.2.3 Net Primary Production  
Annual net primary production (NPP) was evaluated from biomass in the peak growth period (August through early September, as shown in the result). This study site, which is at the early secondary succession stage, has both herbaceous (non-woody plants including forb, grass, sedge, and rush) and woody plants. Therefore, the NPP was evaluated separately. For example, NPP of the herbaceous plants is estimated from the annual maximum biomass unless plants die more than one time per year [42]. In contrast, the NPP of the woody plants was estimated from the sum of the annual difference in all biomass and the total amount of loss, such as dead leaves, branches, and roots [43].  
Because most understory plants are perennial species, we assumed that the belowground coarse roots survive overwinter. Assuming that the carbon losses attributable to herbivory, volatiles, and exudation are negligibly small, the NPP of woody species is expressed as shown below.  
\[\text{understory woody species NPP}=\text{c}\left(\Delta\text{AGB}+\Delta\text{BGB}+ \text{BL}_{i}+\text{TRFR}\times\text{BFR}_{i}\right) \tag{4}\]  
\[\text{overstory woody species NPP}=\text{c}\left(\Delta\text{AGB}+\Delta\text{BGB}+ \text{BL}_{i}+\text{TRFR}\times\text{BFR}_{i}+\text{MT}_{i}\right) \tag{5}\]  
In the above equations, constant c stands for the carbon content of the biomass (0.5), \(\Delta\text{AGB}\) and \(\Delta\text{BGB}\) respectively denote annual increments of AGB and BGB, BL and BFR respectively represent the biomass of leaves and fine roots, and TRFR is a fine root turnover rate. MT is the mortality of overstory trees. Suffix \(i\) represents the value in the previous year. If \(\Delta\text{AGB}\) or \(\Delta\text{BGB}\) are negative, they are set to zero. This equals to adding mortality.  
For herbaceous species, annual NPP is the sum of AGB in the peak growth period (AGB), the increment of BGB (\(\Delta\text{BGB}\)), and fine root production (TRFR \(\times\) BFR) (Equation (6)).  
\[\text{herbaceous species NPP}=\text{c}\left(\text{AGB}_{j}+\Delta\text{BGB}+ \text{TRFR}\times\text{BFR}_{j}\right) \tag{6}\]  
Therein, suffix \(j\) denotes the current year. In 2008 and 2010, understory AGB was missing observations; for these years the AGB was estimated from the yearly interpolation. Understory and overstory \(\text{BL}_{i}\) were respectively estimated from the harvested and allometric-estimated litter biomass. In this study site, all overstory species are deciduous. There is only one evergreen woody species in the undergrowth (_Pachysandra terminalis_). We calculated the NPP assuming that the life of the leaves is one year. Similar to the calculation of woody species NPP, \(\Delta\)RGB are set to zero if it is negative.  
Understory and overstory TRFR were set at 0.25 (temperate shrubs) and 0.65 (temperate trees), respectively, which are the mean values of the fine-root turnover rates of each ecosystem in a meta-analysis (Table S4) [44]. Fine root biomass (BFR) of understory vegetation was estimated from BGB by multiplying the ratio of BFR and BGB (BFR/BGB). The ratio (BFR/BGB) of understory vegetation was obtained from root sampling in August 2014 (0.332, Table S4). The overstory BFR/BGB was set at 0.231 from data measured in an adjacent deciduous forest (Table S4).