## Materials and Methods
### Field Data  
A stratified random sampling approach was established in June and July 2012 to collect ground information describing the forest ecosystem (Figure 1). A total of 35 squared field plots with a size of 30 m \(\times\) 30 m were inventoried. During the field data collection, a slope correction factor depending on the slope angle was applied to convert the plot size into its equivalent on a horizontal plane [54]. The slope angle was measured by a SUUNTO clinometer device (Susunto, Vantaa, Finland) [55]. The identified plots represent most of the present tree species and their properties, i.e., canopy cover, density, and species composition. The geographical position of each field plot was recorded using a differential global positioning system (DGPS) with an accuracy of \(\pm\)30 cm (Trimble Geo XH, Sunnyvale, CA, USA). In each plot, all trees having a diameter at breast height (DBH) larger than 5 cm were counted, corresponding DBHs and species types were recorded as well [3]. The selection of the 5 cm DBH threshold is justified by common practice in forest inventory [56]. TD was calculated as the number of trees per hectare by summing up all measured trees in each field plot [5]. In total, 1598 trees were counted in all plots, while European larches compose 718 trees (45%), Swiss stone pine 602 trees (38%), and Norway spruce 278 trees (17%). Considering the basal area per plot, European larches account for 59% of the total, followed by Swiss stone pines (29%), and Norway spruce trees (12%). Descriptive statistics of TD obtained from all field plots for the Val Trupchun area can be found in Table 1. The mean TD amounts to up to 507 trees per ha. This is in line with findings by [PERSON] et al. [57] who reported a value of 473 \(\pm\) 90 trees per ha for this study area. We implemented various DBH thresholds to calculate the corresponding number of trees per ha. Due to different environmental factors for north-facing and south-facing slopes (i.e., solar radiation, water and soil nutrient availability) [12], we classified our field plots into north- and south-facing plots. Table 1 shows large differences of TD's for south- and north-facing field plots. Results of an independent sample \(t\)-test [58] prove that this difference is statistically significant (\(t(33)=3.269\), \(p=0.003\)). The reasons for these differences are primarily environmental factors, natural disturbances, and historical human activity before 1914 (i.e., charcoal production, timber harvesting) [53; 57; 59]; multiple-stemmed trees frequently exist on south-facing areas, while high self-thinning due to light competition among trees causes the smaller TD on north-facing areas. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & **DBH \textgreater{} 5 cm** & **DBH \textgreater{} 12 cm** & **DBH \textgreater{} 20 cm** & **DBH \textgreater{} 30 cm** & **South-Facing** & **North-Facing** \\ \hline Number of plots [-] & 35 & 35 & 35 & 25 & 10 \\ Number of trees [-] & 1598 & 1360 & 1103 & 691 & 1314 & 284 \\ \hline
**Tree density [N/ha]** & & & & & & \\ \hline Mean & 507 & 432 & 350 & 219 & 584 & 316 \\ Minimum & 122 & 122 & 89 & 56 & 122 & 122 \\ Maximum & 1067 & 755 & 600 & 456 & 1067 & 644 \\ Standard deviation & 249 & 189 & 141 & 96 & 238 & 161 \\ \hline \hline \end{tabular} DBH: diameter at breast height.  
\end{table} 
Table 1: Tree density (TD) statistics for field plots in Val Trupchun. Figure 1: Study area and location of field plots. (**a**) Location of the Swiss National Park (SNP) in Switzerland (red polygon) with a true color ortho image as background (source: Federal Office of Topography swissstopo: [[https://shop.swissstopo.admin.ch/en/products/images/ortho_images/SWISSIMAGE](https://shop.swissstopo.admin.ch/en/products/images/ortho_images/SWISSIMAGE)]([https://shop.swissstopo.admin.ch/en/products/images/ortho_images/SWISSIMAGE](https://shop.swissstopo.admin.ch/en/products/images/ortho_images/SWISSIMAGE))). (**b**) Location of field plots in Val Trupchun.