Climate‐driven elevational variation in range sizes of vascular plants in the central Himalayas: A supporting case for Rapoport's rule

Abstract A fundamental yet controversial topic in biogeography is how and why species range sizes vary along spatial gradients. To advance our understanding of these questions and to provide insights into biological conservation, we assessed elevational variations in the range sizes of vascular plants with different life forms and biogeographical affinities and explored the main drivers underlying these variations in the longest valley in China's Himalayas, the Gyirong Valley. Elevational range sizes of vascular plants were documented in 96 sampling plots along an elevational gradient ranging from 1,800 to 5,400 m above sea level. We assessed the elevational variations in range size by averaging the range sizes of all recorded species within each sampling plot. We then related the range size to climate, disturbance, and the mid‐domain effect and explored the relative importance of these factors in explaining the range size variations using the Random Forest model. A total of 545 vascular plants were recorded in the sampling plots along the elevational gradient. Of these, 158, 387, 337, and 112 were woody, herbaceous, temperate, and tropical species, respectively. The range size of each group of vascular plants exhibited uniform increasing trends along the elevational gradient, which was consistent with the prediction of Rapoport's rule. Climate was the main driver of the increasing trends of vascular plant range sizes in the Gyirong Valley. The climate variability hypothesis and mean climate condition hypothesis could both explain the elevation–range size relationships. Our results reinforce the previous notion that Rapoport's rule applies to regions where the influence of climate is the most pronounced, and call for close attention to the impact of climate change to prevent species range contraction and even extinction due to global warming.


| INTRODUC TI ON
Species range size is a fundamental unit in macroecology (Böhm et al., 2017). Understanding variation in species range size along spatial gradients is of primary importance in the study of climate change, biodiversity patterns, gene flow, and extinction mechanisms. A well-known theory about spatial variation in species range size is Rapoport's rule, which states that species range size is positively correlated with latitude and elevation, that is, species at higher latitude or elevation have larger range size than those at lower latitude or elevation (Stevens, 1989). However, despite early evidence from the Northern Hemisphere (e.g., Arita et al., 2005;Blackburn & Gaston, 1996;Gaston et al., 1998;Letcher & Harvey, 1994), further studies from other regions yielded complex and partial support for this rule (e.g., Feng et al., 2016;Hawkins & Diniz-Filho, 2006;Whitton et al., 2012), suggesting that this rule might be a regional phenomenon dependent on the local environment (Whitton et al., 2012). Therefore, recent attention has shifted from simply documenting variation in range size to exploring the drivers of variation.
Various studies have been conducted to understand the association between variation in range size and environmental factors such as climate (e.g., Sheldon & Tewksbury, 2014;Whitton et al., 2012), disturbance (e.g., Borkowski et al., 2016;Lozada et al., 2008), and the mid-domain effect (MDE; e.g., Luo et al., 2011). Climate appears to be most important driver of both latitudinal and elevational variations in range size. Several hypotheses have been proposed to explain the climate-range size relationship, among which the climate variability hypothesis is the most commonly accepted (Pintor et al., 2015;Whitton et al., 2012). This hypothesis was first proposed by Stevens in 1989 and was believed to be the underlying mechanism of Rapoport's rule (Stevens, 1989(Stevens, , 1992. Stevens (1989) stated that climate, specifically temperature, is more variable at higher latitudes and elevations. Greater climatic variability favors species with wider tolerance and larger range size, thus leading to a positive relationship between range size and latitude and elevation. The mean climate condition hypothesis is another prominent explanation for the climate-range size relationships, which is supposed to cooperate with climate variability hypothesis to generate increasing trends of range size (Luo et al., 2011). The mean climate condition hypothesis proposes that species living at higher latitudes or elevations are not only subjected to greater climatic variation but also to lower mean climate conditions; thus, they tend to be geographically widely distributed (Jiang & Ma, 2014;Luo et al., 2011). In addition to contemporary climate, historical climate, such as the Quaternary climate, has also been proposed as an explanation for range size variations based on the premise that historical climate oscillations select for species with greater physiological tolerance and adaptability (Jansson, 2003;Araújo et al., 2008).
Apart from climatic factors, disturbance and MDE are also believed to influence species range size. The disturbance hypothesis proposes that anthropogenic threats might lead to population declines and extinctions, thus constraining species range size (Whitton et al., 2012). The MDE postulates that the range of species who live near the edge of the domain will be truncated by the domain boundaries, leading to smaller mean range size near the boundaries and larger mean range size at the domain center. Therefore, it predicts a mid-peak pattern in species range size, regardless of the ecological factors (Feng et al., 2016;Luo et al., 2011;Sandel & McKone, 2006).
In addition to environmental factors, variations in species range size might also be associated with life form and biogeographical affinities, as these reflect species ecophysiological traits and evolutionary history, and may thus affect their response to environmental variation. For example, compared with herbaceous plants, woody plants tend to have a lower adaptability due to their longer reproductive cycles and slower accumulation rate of genetic changes (Smith & Beaulieu, 2009) and might thus be more sensitive to environmental gradients. Similarly, tropical taxa, which have experienced a more stable climatic environment in their evolutionary history, may be more susceptible to climatic variation and thus be more supportive of increasing trend in species range size with latitude and elevation (Feng et al., 2016;McCain, 2009 reinforce the previous notion that Rapoport's rule applies to regions where the influence of climate is the most pronounced, and call for close attention to the impact of climate change to prevent species range contraction and even extinction due to global warming.

K E Y W O R D S
climate variability, elevational gradient, Himalayas, Rapoport's rule, species range size, vascular plants variation in species richness and its drivers in the Himalayas (e.g., Acharya et al., 2011;Kluge et al., 2017;Manish et al., 2017;Sun et al., 2020;Yang et al., 2018), corresponding studies on species range size are limited. As understanding range size variations is a prelude to effective biodiversity conservation (Luo et al., 2011), bridging this research gap will not only help address the theoretical issue, but also contribute to conservation practices in this high-profile region.
Vascular plants have long been considered an excellent subject for studying spatial variations in range size because of their wide distribution and ease of observation. In this study, we aimed to examine the elevational variations in range sizes of vascular plants with different life forms and biogeographical affinities, and to explore the role of climate, disturbance, and MDE on such variations, based on a detailed field survey in the Gyirong Valley, which is the longest valley in China's central Himalayas. As species range size is considered to be closely associated with species richness (Stevens, 1992), and as climate has been reported as the primary determinant of species richness in the Himalayas (Bhattarai & Vetaas, 2003;Liang et al., 2020;Manish et al., 2017;Sun et al., 2020), we hypothesized that climatic factors would better explain the elevational variation in range sizes of vascular plants in the Gyirong Valley than other factors. In this case, considering that Rapoport's rule is supported in regions with the most pronounced influence of climate (Pintor et al., 2015), we further speculated that the range size of vascular plants would increase with elevation as the rule predicts, particularly for woody and tropical species, which are more sensitive to climatic variation.

| Study area and field sampling
The alpine tundra with sparse herbs (4,700-5,400 m a.s.l.), and a scree and nival zone above 5,400 m a.s.l.
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. Elevations lower than 1,800 m a.s.l. and higher than 5,400 m a.s.l. were excluded from the study due to geopolitical restrictions and the scree and nival zone, where very few creatures can survive. Field surveys were carried out in July and August 2018 using 96 sampling plots along this elevation gradient. The sampling plots were established based on the most common physiognomic vegetation and topographic accessibility. In each plot, the vascular plants were exhaustively inventoried (for 2-4 hr by 5 individuals) within a quadrat of 400 m 2 , following Fang et al. (2009). Species that could not be identified in the field were taken to the Museum of Beijing Forestry University for identification.

| Species grouping
Life form of each species was divided into woody species (i.e., trees and shrubs) and herbaceous species (i.e., herbs and climbers) based on the field survey and species description on monographs (e.g., Flora of China, www.eflor as.org; Flora of Pan-Himalayas, www.flph.org).
Following Feng et al. (2016), biogeographical affinity of each species was classified as temperate species, tropical species, and cosmopolitan species, based on a classification system of biogeographical affinities proposed by Wu (1991). Species with distribution centers in northern temperate regions (i.e., East and North Asia, America, old world temperate regions, temperate Asia, Mediterranean, west to central Asia, Central Asia, and East Asia) were considered as temperate species, while species with distribution centers in pantropic regions (i.e., tropical Asia and tropical America, old world tropic regions, tropical Asia to tropical Australia, tropical Asia to tropical Africa, and tropical Asia) were considered as tropical species. Species that span from tropics to temperate regions and have no obvious distribution centers were considered as cosmopolitan species. Only temperate and tropical species were considered when assess the influence of biogeographical affinities on range size variation (Feng et al., 2016).

| Species range size
For each species, the range size was estimated as the difference between the maximum and minimum elevation of the sampling plot where it was recorded. Following Steven's method (Stevens, 1992), we averaged the range size for each group of vascular plants within each sampling plot for the subsequent analyses.

| Environmental variables
Eight environmental variables were used to examine the effect of mean climate condition, climate variability, historical climate change, disturbance, and MDE on the elevational variation in vascular plant range sizes.
The mean climate condition variables included mean annual temperature (MAT) and mean annual precipitation (MAP). The climate variability variables included temperature seasonality (TS) and mean annual temperature range (MATR). MAT, MAP, TS, and MATR were obtained from six mini weather stations established along the Gyirong Valley, from 2016 to 2018 (at 2,457, 2,792, 3,368, 3,740, 4,140, and5,230 m a.s.l.; Figure 1). We averaged the 3-year data of the four variables for each station and extrapolated this data for the entire study area using Kriging interpolation in a GIS environment (Hu et al., 2018). For each of the four variables, we used the grid value corresponding to the location of the 96 sampling plots. The disturbance was quantified using the inverse distance weighted interpolation of human population (POP), based on the assumption that the larger the population, the greater its disturbance to surrounding environment, and such disturbance decreases with increasing distance. The POP data were derived from the demographics of villages and towns in the Gyirong Valley, which were provided by the authority of the Mount Qomolangma National Nature Reserve. We extracted POP from the interpolation for each of the sampling plots.
The MDE was tested using the predicted mean range size under boundary constraints, which was calculated by reshuffling the species ranges within the elevational gradient (1,800-5,400 m a.s.l.).
The calculation was performed using the Monte Carlo simulation and implemented in Range Model 5 software (Colwell, 2008). We ran 1,000 Monte Carlo simulations of empirical range sizes sampled without replacement to ensure that all species were reshuffled, and used average of the simulations as the predicted mean range size (Luo et al., 2011).

| Statistical analysis
Linear regressions were calculated to assess the relationship between the elevation and average species range size of sampling plots. Rapoport's rule was considered to be supported for regressions with a positive relationship (Moreno et al., 2010).
Relationships between species range size and each environmental variable were assessed using ordinary least squares (OLS) models.
The simultaneous autoregressive (SAR) model was further used to account for spatial autocorrelation in variables. All variables were standardized (mean = 0 and standard deviation = 1) to yield comparable regression coefficients for OLS and SAR models. The Random Forest model was used to explore the relative importance of each environmental variable in explaining the elevational variations in species range size. We selected this model as it does not require any assumptions in the data (e.g., normality in errors and homoscedasticity) and can better manage multicollinearity and nonlinear relationships among variables, unlike most traditional methods, such as GLMs (Breiman, 2001;Feng et al., 2017). We ran the Random Forests model 1,000 times and assessed the relative importance of each environmental variable using the average of the percentage increase in mean squared error (%IncMSE) of the models. The %IncMSE was calculated by repeated permutation of each environmental variable, which represents the increase in prediction error caused by each individual variable.

| Elevational trends of species range size
The species range size was positively correlated with elevation for all groups of vascular plants and presented uniform increasing trends along the elevational gradient as predicted by Rapoport's rule (Figure 3). Woody and tropical species were found to have a relatively stronger range size-elevation relationship with a higher regression coefficient.

| Relationships between species range size and environmental variables
The OLS and SAR models yielded similar results regarding the relationship between species range size and environmental variables, although the correlation decreased when spatial autocorrelation was taken into account (Tables 1 and 2

| D ISCUSS I ON
The range size of all groups of vascular plants exhibited uniform increasing trends along the elevational gradient of the Gyirong Valley.
As predicted, climatic factors played a greater role in shaping these trends than did other factors. Both the climate variability hypothesis and mean climate condition hypothesis could explain the elevationrange size relationships. Therefore, as expected, Rapoport's rule was supported regardless of the life form and biogeographical affinities.

| The influence of life form and biogeographical affinities
Life form and biogeographical affinities are known to affect species response to environmental gradients; however, studies on how they Rapoport's rule, this rule was equivocally supported in Feng's study but was strongly supported in our study. Collectively, our results suggest that the influence of life form and biogeographical affinities on range size variation might be environment-dependent.

| The role of different environmental factors
Climate, particularly contemporary climate, played a greater role in shaping the increasing trends of vascular plant range sizes in the Gyirong Valley than other environmental factors. This result echoes the predominance of climate in determining the elevational gradient of plant richness in the Himalayas (Bhattarai & Vetaas, 2003;Liang et al., 2020;Manish et al., 2017;Sun et al., 2020). This could be attributed to the fact that the Himalayas have a more distinct   (Hewitt, 1996(Hewitt, , 2004Leprieur et al., 2011;Zhao et al., 2016),

| The applicability of Rapoport's rule
Since its formulation, the validity of Rapoport's rule has been controversial. The applicability of this rule varies greatly in different regions of the world. In general, the rule appears to be more well defined in the Northern Hemisphere and at higher latitudes than in the Southern Hemisphere and at lower latitudes (Böhm et al., 2017). It must be noted that when Stevens first introduced Rapoport's rule in 1989, he emphasized that the rule should apply to species inhabiting regions with conspicuous gradients of climate variability (Stevens, 1989).
Further studies also confirmed the necessity for climate variability to the validity of Rapoport's rule. For example, Whitton et al. (2012) suggested that the primary importance of climate variability may explain why Rapoport's rule is largely restricted to northern latitudes, as this is where temperature seasonality is the most pronounced.
Similarly, Pintor et al. (2015) attributed the absence of Rapoport's rule in Australia to the complex climate pattern across the entire continent, with minimum and maximum temperatures varying considerably at any given latitude. In our study, climate variability exhibited a monotonically increasing pattern along the elevational gradient in the Gyirong Valley and was the most influential factor affecting the elevational variation in range size of all groups of vascular plants.

| Conservation implication
As climate plays a significant role in determining species range, there is an urgent need to focus on the impact of climate change. It has been widely reported that climate change will force species to shift their range upward along the mountains (Feeley & Silman, 2010;Feeley et al., 2011;Rehm, 2014), leading to a shift in elevational biodiversity hotspots (Wu et al., 2016). On the other hand, climate change has been implicated in species range contractions on several F I G U R E 4 The average percentage increase in mean squared error of each environmental variable in 1,000 Random Forest models for (a) overall species, (b) woody species, (c) herbaceous species, (d) temperate species, and (e) tropical species mountains. For example, Engler et al. (2011) assessed the impacts of climate change on 2,632 plant species across all major European mountain ranges and predicted that 36%-55% of alpine species, 31%-51% of subalpine species, and 19%-46% of montane species will lose more than 80% of their suitable habitat by 2070-2100.
As the Himalayas are among the most sensitive regions to climate change (Xu et al., 2009) Considering that the response to climate change is species-specific, long-term monitoring is imperative for understanding the impact of climate change on local biodiversity.

| CON CLUS IONS
In the Gyirong Valley of the central Himalayas, the range size of vascular plants across different life forms and biogeographical affinities was found to increase uniformly along the elevational gradient, which was consistent with the prediction of Rapoport's rule.
Climate, particularly contemporary climate, was the main driver of the increasing trends of vascular plant range sizes. Both the climate variability hypothesis and mean climate condition hypothesis could explain the elevational variation in range size. Our results reinforce the previous notion that Rapoport's rule applies to regions where the influence of climate is the most pronounced. Such climate-driven variations in range size call for close attention to the impact of climate change, which has been implicated in range contractions and even extinction of several taxa.

ACK N OWLED G EM ENTS
This study was supported by the National Natural Science Foundation

CO N FLI C T O F I NTE R E S T
None declared.