## 2 Materials and Methods
### Measurements
#### 2.2.1 Species and Biomass  
Hereinafter, we refer to ground vegetation of herbs, grasses, ferns, shrubs, and saplings shorter than 0.5 m as the \"understory\" or \"understory vegetation\" irrespective of the presence or absence of canopy-forming trees. Moreover, we designate trees taller than 0.5 m as the \"overstory\" as a sense of overlying understory vegetation.  
Aboveground biomass (AGB) of understory species was measured gravimetrically. In each year, a survey strip with 1 m \(\times\) 100 m was installed in the study site to avoid harvesting a plot sampled in the past. Ten rectangular plots (1 m \(\times\) 10 m) were located in the survey strip. Each plot was divided into 10 square subplots (1 m \(\times\) 1 m), and aboveground parts of all understory vegetation were harvested in the peak growth season (from August through early September) of 2006, 2007, 2009, 2011, 2012, 2013, and 2014. Except for 2012 and 2013, harvesting was implemented monthly or bimonthly during the snow-free season (May-December). The harvest plot during each sampling time within a year was at the neighboring subplot. The harvest was divided by species and subdivided into leaf, stem/branch, and flower/fruit parts, which were weighed after oven drying at 80 \({}^{\circ}\)C for more than 48 h.  
Belowground biomass (BGB) of understory species was calculated by multiplying the root/shoot ratio (RS ratio) to AGB. In late August of 2014, to determine the RS ratio, we collected all aboveground and belowground parts (including coarse and fine roots) of the plants from fifteen 0.3 m \(\times\) 0.3 m quadrats (ten from _Solidago gigantea_ Aiton subsp. _serotina_ (Kuntze) McNeill community, and five from the _Rubusidae_ L. subsp. _melanolasius_ Focke community); the RS ratio was calculated from their oven-dried weights.  
Some deciduous trees grew to a height of 1-2 m in 2010. Therefore, the overstory tree biomass was measured separately from 2010. The species, height (H), and stem diameters at the ground surface (DS\({}_{0}\)) and the breast height of 1.3 m (DBH) of overstory trees were recorded annually in three 20 m \(\times\) 20 m permanent plots. Overstory tree biomass was separated into leaf, stem/branch, and coarse root parts. To form allometric equations for their parts, trees of 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 5.5, and 7.3 m height (14 trees) were uprooted and separated into each part. Then, dry weights of stem/branch, leaf, and coarse root parts (BSB, BL, and BCR, respectively) were determined (Table S1). The allometric equations were as follows.  
\[\ln\left(\text{BSB}\right)=0.985\text{ln}\left(\text{DS}_{0}^{2}\times H\right)+11.7 \tag{1}\]  
\[\ln\left(\text{BL}\right)=0.708\text{ln}\left(\text{DS}_{0}^{2}\times H\right)+8.74 \tag{2}\]  
\[\ln\left(\text{BCR}\right)=0.816\text{ln}\left(\text{DS}_{0}^{2}\times H\right)+ 9.83 \tag{3}\]  
To correct the bias in log-transformed allometric equations [40], the biomass of each part was multiplied by the correction factor (CF). The CF was 1.04 for BSB, 1.10 for BL, and 1.14 for BCR. AGB was calculated as the sum of BSB, BL, and BCR.  
The mortality of overstory trees was evaluated based on population and AGB from the ratio of the numbers of dead trees to all living trees, and the ratio of dead AGB to all living AGB, respectively.