The species richness pattern of vascular plants along a tropical elevational gradient and the test of elevational Rapoport's rule depend on different life‐forms and phytogeographic affinities

Abstract The research about species richness pattern and elevational Rapoport's rule (ERR) have been carried out mostly in the temperate regions in the recent years and scarcely in the tropical mountains; meanwhile, it is unclear whether the ERR is consistent among different life‐forms and phytogeographic affinities. Here, we compiled a database of plant species of Mount Kenya, a tropical mountain of East Africa, and divided these species into twelve groups depending on the life‐form and phytogeographic affinity of each species. We inspected the species richness pattern of each group along the elevation gradient and also tested ERR of each group using Stevens' method. Our results showed that species richness of the total species showed a positively skewed (hump‐shaped) pattern along the elevation gradient and different life‐forms and phytogeographic affinities showed similar hump‐shaped patterns as the total species. The average elevation range size of the total species and herbaceous species showed increasing patterns along the elevation gradient, while lycophytes and ferns, and woody species showed an obvious downward trend after peaking in the high elevation regions. We concluded that the widely distributed herbaceous species which also have broad elevation range sizes are more applicable to ERR, while the narrowly distributed woody species with small elevation range sizes occurring in the higher elevations could reverse ERR. Therefore, we concluded that the ERR is not consistent among different organisms in the same region.

Mountains are the ideal natural experimental environments for the study of species richness variety along the elevation gradients, because they not only harbor vast biodiversity and encompass several protected areas (Khan, Page, Ahmad, & Harper, 2014;Kluge et al., 2017;Körner, 2000Körner, , 2007Smith, Oca, Reeder, & Wiens, 2007), but also because they contain diverse elevation gradients along their slopes (McCain, 2009;Rahbek, 2005;Stevens, 1992) which directly or indirectly impact the variations in availability of essential resources such as heat energy and moisture (Körner, 2000), affecting the physiological and ecological adaptation of plants thus influencing their species richness and patterns of distribution along the elevation gradients (Kessler, 2000;Kluge & Kessler, 2011;Lomolino, 2001).
The core prediction of elevational Rapoport's rule (ERR) is a positive and linear relationship between average elevation range size of species within increasing bands of elevation, which has subsequently been named as Stevens' method (Stevens, 1992); however, the range size-elevation patterns of different taxonomic groups may be different (Feng et al., 2016;McCain & Knight, 2013). The life-forms of plants are the response of plants to adapt to the eco-physiological traits to climatic or environmental factors. Herbaceous and woody taxa are believed to be differentially influenced by environmental factors such as precipitation and temperature (Whittaker, 1965 (Kluge et al., 2017). Nevertheless, that is not to imply that the range-elevation relationships of different life-forms will be consistent. In addition, phytogeographic affinities may be linked with elevational range sizes and their elevational trends (Feng et al., 2016;Wang, Tang, & Fang, 2007), that is, compared with narrowly distributed species, widely distributed ones always have broader tolerance ranges and stronger adaptability (Donohue, Rubio, Burghardt, Kovach, & Willis, 2010;Gaston & Spicer, 2001;Santamaría, 2002). However, in recent studies, little attention has been paid to compare the difference of ERR with regard to lifeforms and the influence of phytogeographic affinities.
Compared to the tropics, numerous studies about ERR have been carried out in the temperate regions in the recent years (Acharya, Vetaas, & Birks, 2011;Bhattarai & Vetaas, 2003;Kessler, Herzog, Fjeldså, & Bach, 2001;Kluge et al., 2017); furthermore, the support of the rule is scarce in the tropics (Gaston, Blackburn, & Spicer, 1998;Rohde, 1996). Evaluating and determining the patterns of species richness along the elevation gradients in the tropics is crucial as threats to the tropical biodiversity,   Following Zhou et al. (2018), life-form of each species was classified as woody plants (trees, shrubs, lianas) and herbaceous plants (climbers and herbs) and lycophytes and ferns based on the species description on monographs and field guides (Agnew, 2013;Beentje, 1994;Blundell, 1987;F.T.E.A. editors, 1952-2012.

| Phytogeographic affinities
According to the distribution range of each species, we set up three groups of phytogeographic affinities: worldwide species which are distributed not just in Africa, African species which are endemic in Africa, and tropical East African species which are endemic in Kenya, Uganda, Tanzania, and their vicinities. We also recorded the endemic species of Mount Kenya.

| Species richness
The number of species present in each band was estimated by the interpolation method, that is, a species was defined as being present in every 100-m elevation band between its upper and lower elevation limits (Bhattarai & Vetaas, 2006;Rahbek, 1997;Vetaas & Grytnes, 2002). The species richness was defined as the total number of species found in each 100-m elevation band, referred to as γ-diversity (Bhattarai & Vetaas, 2006;Lomolino, 2001). We calculated the species richness-elevation patterns of the total plants, each life-form and each group of phytogeographic affinities.

| Elevation range size
The elevation range of each species was estimated as the difference between the maximum and minimum elevations, whose data were from literatures, specimens, and our own field observations. Actually, several methods have been frequently used in the recent decades to evaluate ERR, such as Stevens' method (Stevens, 1989), the midpoint method (Rohde, 1992), Pagel's method (Pagel, May, & Collie, 1991), and the cross-species method (Letcher & Harvey, 1994), and often provide information that complements different perceptions of the patterns. In order to compare the results of different components under the same standard, we exclusively used Stevens' method to investigate the average range size-elevation patterns of each group (including total, lycophytes and ferns, woody, herbaceous, trees, shrubs, lianas, climbers, herbs, worldwide, African and Tropical East African species) along the elevation gradient of Mount Kenya. We used generalized additive models (GAM) with a Gaussian function of variance to determine the trends of the response curve of species richness and range size along the elevation gradient, instead of using linear correlation analysis (Bhattarai & Vetaas, 2006;Feng et al., 2016). In this method, a cubic smooth spline was used to evaluate the significance of a specific trend for species richness-elevation and range size-elevation relationships (Hastie & Tibshirani, 1990). These analyses were carried out using R 3.3.3 software (R Core Team, 2017).

| Species richness along the elevation gradient
Species richness of the total species showed a positively skewed (hump-shaped) pattern along the elevation gradient, with a pronounced mid-elevational peak at 2027 m a.s.l. containing over 1,000 taxa in each band of this range; meanwhile, there were species in less than 100 taxa above 4,300 m a.s.l. in each band, and only 11 species were found around 5,000 m a.s.l (Figure 2a).

| Elevation range size
Regardless of the elevation gradient, we first compared the elevation range of life-forms (including lycophytes and ferns, woody, and herbaceous species) and phytogeographic affinities (worldwide, African, and tropical East African species) (Figure 4). The elevation range of herbaceous species was significantly higher than that of lycophytes and ferns and woody species, while there was no significant difference between the latter two groups (Figure 4a). Meanwhile, the elevation range of the tropical East African species was significantly lower than the worldwide and African species, while there was no significant difference between the latter two groups (Figure 4b).

| Mean elevation range size along the elevation gradient
Calculated herein are the mean elevation range size of 12 groups of species including total species, lycophytes and ferns, woody species, herbaceous species, trees, shrubs, lianas, climbers, herbs, worldwide species, African species, and tropical East African species. In

| D ISCUSS I ON
Mountains are usually more likely to display unimodal patterns for they invariably exhibit greater elevational extent and longer climatic gradients. In fact, most of the unimodal gradients were positively skewed (hump-shaped), that is, peak diversity below the elevational midpoint, and this pattern is a well-known finding for many tropical and subtropical mountains (Guo et al., 2013;Rahbek, 2005;Rahbek & Museum, 1995). Global data research showed that over 80% of species richness-elevation patterns occurring in the tropical mountains are unimodal (Guo et al., 2013). The species richness of vascular plants of Mount Kenya also showed a strong support for the positively skewed pattern along the elevation gradients, with the maximum diversity at about 2000 m a.s.l., below the middle of the elevation gradients. These results emanate from the empirical data, which have been compiled by us based on collections from numerous scientific expeditions since the 1900s, and also from the revision of previous results where land-snail faunas were observed to be decreasing in diversity along the elevation gradient of this mountain (Tattersfield, Warui, Seddon, & Kiringe, 2001).
Even if different groups of life-forms and phytogeographic affinities have similar but slightly modified richness-elevation patterns with total species, the proportion of each component varies very much along the elevation gradient (Figure 2). Taller life-forms like trees and shrubs are confined to the lower elevations, and similar patterns of lianas and ferns are coupled to that of trees (Carpenter, 2005;Kluge et al., 2017), leading to a significant decrease in the proportion of woody plants along the elevation gradient, and this reflects physiological adaptations to high elevation and alpine environments (Kluge et al., 2017;Körner, 2003). Analogous to most mountains of the world (Steinbauer et al., 2016), such as Andes (Kessler, 2000), Himalayas (Kluge et al., 2017;Vetaas & Grytnes, 2002), and Hengduan Mountains (Zhang, Zhang, Boufford, & Sun, 2009), endemic species are confined to high elevations in the tropical African mountains (Hedberg, 1969;Morton, 1972 (Coe, 1967;Niemelä & Pellikka, 2004;Zhou et al., 2018).
An increase in the elevation range of occurrence of species in an assemblage with increasing elevation is explainable as a consequence of individuals having to be able to withstand a broader range of climatic conditions at higher elevations (Fernández & Vrba, 2005;Gaston & Chown, 1999;Morin & Lechowicz, 2011).
Herbaceous species can always adapt to new climatic conditions 2 to 10 times faster than woody species for the latter have longer reproductive cycles and tend to accumulate genetic changes at slower rates (Smith & Beaulieu, 2009). Therefore, compared with woody species, herbaceous species have significantly higher elevation ranges (Figure 3a), which can be reflected in some exotic herbs with strong invasiveness (Giorgis et al., 2016;Molina-Montenegro & Naya, 2012;Yang et al., 2018). Some studies have tried to divide species in an assemblage into different components, such as tropical and temperate species to investigate their differences in elevation range (Feng et al., 2016), while, few studies have divided species into different groups depending on their dispersal regions. Janzen (1967) proposed the influential hypothesis, stating F I G U R E 3 The species richness-elevation pattern of endemic species of Mount Kenya F I G U R E 4 Comparison of elevation range between different groups regardless of the elevation gradient. (a) elevation range of lycophytes and ferns, woody, and herbaceous species; (b) elevation range of worldwide, African, and tropic East African species. The letters indicate significant differences (α = 0.05) between different groups that tropical mountains are physiologically higher than temperate mountains, namely, that elevational range sizes of organisms get smaller on mountains at decreasing latitudes (McCain, 2009).
That is to say, the plant species restricted to the tropical regions (such as tropical East African species or endemic species in Mount Kenya) have smaller elevation ranges than the widely distributed species in the world (Figure 3b).
A strong support for the range-elevation relationships predicted by elevation Rapoport's rules (ERR) was observed in total and herbaceous species (including climbers and herbs), as well as in different phytogeographic affinities (Figure 5a,d,h-l). However, the decreasing trend of the mean elevation ranges in high elevations has been detected in lycophytes and ferns and woody species (including trees, shrubs, and lianas) (Figure 5b,c,e-g). Bhattarai  Table 1 and Vetaas (2006) observed the similar decreasing trend of trees above 1,500 m a.s.l., with narrow elevational ranges at both ends of the gradient and a wider elevation range in the middle, and the explanation for this shift was boundary effects. Feng et al. (2016) came to a similar conclusion that boundary effects such as environmental or climatic conditions could cause a trend of decreasing of average range size at high elevation regions. Considering that total and herbaceous species showed support for the ERR with increasing trend of the range size-elevation relationship, we speculate that the boundary effect did not notably impact the patterns of lycophytes and ferns and woody species. Actually, the proportion of narrowly distributed and endemic species increasing along the elevation gradient might impact the average elevation range sizeelevation relationship of species assemblages (Vetaas & Grytnes, 2002

| CON CLUS IONS
This study firstly tested the elevational Rapoport's rule by dividing all plants into different components, after comprehensively mastering the plant diversity of a tropical African mountain. The elevation range of the herbaceous species was significantly higher than the woody species, and the elevation range of the narrowly distributed species was significantly lower than the widely distributed species.
These indicate that the widely distributed herbaceous species have broad elevation range size because they can probably withstand a broader range of climatic conditions, thus can possibly be more applicable to elevational Rapoport's rule. Therefore, we concluded that this rule is not consistent among different organisms (such as different life-forms) in the same region.

ACK N OWLED G M ENTS
We would like to thank Z. Zhong from Wuhan Botanical Garden, CAS, China and I. Malombe from National Museums of Kenya, for their help on the field work and our research work at the East African Herbarium. Thanks also given to J. Feng and X. Hu from Department of Life Science and Chemistry, Dali University, for their help on the generalized additive models analysis of this research. This study was supported by the fund of Sino-Africa Joint Research Center, CAS, China (Y323771W07 and SAJC201322) and National Natural Science Foundation of China (31800176).

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