2. Methods

2.1 Study area

The Gyirong Valley (28°16′-29° 00′ N, 84°56′-85°24′ E) is located in the southern part of the Tibetan Plateau of China, and border with northern part of Nepal (Fig. 1). The valley is expanded over 90 km, and spans an elevational range from 1,840 to 7,341 m above sea level (a.s.l.). Due to the influence of the Indian Ocean monsoon, the valley contain steep environmental gradients and distinct elevational vegetation zones which can be divided into evergreen broadleaf forest (1,800-2,500 m a.s.l.), coniferous and broadleaf mixed forest (2,500-3,300 m a.s.l.), subalpine coniferous forest (3,300-3,900 m a.s.l.), alpine bush and coryphilum (3,900-4,700 m a.s.l.) and alpine tundra with sparse herbs (4,700-5,400 m a.s.l.). Above 5,400 m a.s.l. there is the scree and nival zone where very few creatures can survive.
Our study was conducted along an elevation gradient from Resuo village at 1,800 m a.s.l. to Mt. Kongtanglamu and Mt. Mala at 5,400 m a.s.l.. We divided the gradient into 12 elevational bands of 300-m. Elevation lower than 1800 m a.s.l. and high than 5400 m a.s.l. were excluded from the study due to the geopolitical restrictions and scree and nival zone where very few creatures can survive.

2.2 Species sampling

Field study was carried out by 96 sampling plots along the 12 elevational bands from 1800 to 5400 m a.s.l. in July and August 2018. For each band, 8 sampling plots were placed depending upon the most common physiognomic vegetation and the topographic accessibility. In each plot, the vascular plant inventories were conducted exhaustively (2-4 hours by 5 persons) with a quadrat of 400 m2following Fang et al. (2009). Species that could not be identified in the field were taken to the Museum of Beijing Forestry University for identification.

2.3 Species grouping

To assess the influence of life form and biogeographical affinities on range size variation, we classified the vascular plants into four groups: (1) woody species, including trees and shrubs, (2) herbaceous species, including herbs and climber, (3) temperate species, whose distribution centers located in north temperate regions, and (4) tropical species, whose distribution centers located in pantropic regions. Life form and biogeographical affinities were determined referring to Flora of China (www.efloras.org), Flora of Pan-Himalayas (www.flph.org), Flora Xizangica (Wu, 1983) and Floristics of Seed Plants from China (Wu et al., 2010).

2.4 Species range size

For each species, elevational range size was estimated as the difference between maximum and minimum elevational band that it occurred. Following Steven’s method (Steven, 1992), we average species range size for all groups of vascular plants within each elevational band.

2.5 Environmental variables

Ten environmental variables which were divide into six groups were used to examine the role of mean climate condition, climate variability, historical climate change, disturbance, competition and the mid-domain effect on the elevational variation in vascular plants range size.
The mean climate condition variables include annual temperature (MAT) and mean annual precipitation (MAP). The climate variability variables include temperature seasonality (TS) and annual temperature range (MATR). MAT, MAP, TS, and MATR were derived from six mini weather stations establishing along the Gyirong Valley from 2016 to 2018 (2,457, 2,792, 3,368, 3,740, 4,140, and 5,230 m a.s.l., Fig. 1). We averaged three years’ data of the four variables for each station and extrapolated them for the entire study area using Kriging interpolation in a GIS environment (Hu et al., 2018), and then used the average of 8 grid cells corresponding to the sampling plots at each elevational band.
The variables of historical climate change included change in mean annual temperature (TC) and precipitation (PC) between present and the Last Glacial Maximum (LGM, about 22,000 years ago). The annual temperature and precipitation of the LGM were derived from the average of three Global Climate Models (GCMs), namely, CCSM4, MIROC‐ESM, and MPI‐ESM‐P, which were obtained from the WorldClim dataset (www.worldclim.org).
Variables related disturbance factors included the population (POP) and area of anthropogenic land use (AALU). The POP data was provided by the authority of Mount Qomolangma National Nature Reserve. The AALU was calculated as the area of artificial surfaces and cultivated land (Zhang et al., 2013) extracted from the GlobeLand30 land cover data (http://www.globallandcover.com).
Since the direct measurement of competition is difficult to achieve, we used the interpolated species richness as an indirect reflection (Stevens, 1996). The MDE were tested using the predicted average range size under geometric constraints, which were computed by randomizing the empirical species range size within the bounded domain using 1000 Monte Carlo simulations in the modules Mid-Domain Null (MaCain, 2004; Luo et al., 2011).

2.6 Statistical analysis

For each elevational band, we calculated the species accumulation curve to assess the sampling adequacy. Sampling in a band was considered adequate when the species accumulation curve reaches a plateau (Magurran and McGill, 2011). Additionally, we computed non-parametric estimated species richness (Chao2 and Jackknife2) for each band, and then performed regression of the observed species richness against the non-parametric estimated species richness (Colwell & Coddington, 1994; Rowe, 2009).
Linear regressions were calculated to assess the relationship between elevation and range size for all groups of vascular plants. Rapoport’s rule is supported where the relationship is positive (Moreno et al., 2008).
Relationships between species range size and elevation and each environmental variable were assessed using ordinary least squares (OLS) models. Simultaneous autoregressive (SAR) model was also performed in supplement to take account for the spatial autocorrelation in variables. All variables were standardized (mean = 0 and standard deviation = 1) to make the regression coefficients comparable in OLS and SAR.
Random Forests model was used to explore the relative importance of each environmental variable in explaining the range size variations for each species group. We chose the Random Forests model because it does not require strict assumptions in data and can better handle multicollinearity and non-linear relationships which perplexed most traditional methods like GLMs (Breiman, 2001; Feng et al., 2016). We run the Random Forests model 1000 times, and assessed the relative importance of each environmental variable based on the average of the percentage increase in mean squared error (%IncMSE) from the models. The %IncMSE was calculated by repeated permutation of each regression variable, which represents the increase in prediction error caused by each individual variable.
Species accumulation curve and estimated species richness were calculated by EstimateS 9.10 (Colwell, 2013). linear regression, OLS, SAR, and the Random Forest models as well as the bivariate model were conducted in R 3.5.1 using vegan, spdep, and randomForest package.