How beta diversity and the underlying causes vary with sampling scales in the Changbai mountain forests

Abstract This study aims to establish a relationship between the sampling scale and tree species beta diversity temperate forests and to identify the underlying causes of beta diversity at different sampling scales. The data were obtained from three large observational study areas in the Changbai mountain region in northeastern China. All trees with a dbh ≥1 cm were stem‐mapped and measured. The beta diversity was calculated for four different grain sizes, and the associated variances were partitioned into components explained by environmental and spatial variables to determine the contributions of environmental filtering and dispersal limitation to beta diversity. The results showed that both beta diversity and the causes of beta diversity were dependent on the sampling scale. Beta diversity decreased with increasing scales. The best‐explained beta diversity variation was up to about 60% which was discovered in the secondary conifer and broad‐leaved mixed forest (CBF) study area at the 40 × 40 m scale. The variation partitioning result indicated that environmental filtering showed greater effects at bigger grain sizes, while dispersal limitation was found to be more important at smaller grain sizes. What is more, the result showed an increasing explanatory ability of environmental effects with increasing sampling grains but no clearly trend of spatial effects. The study emphasized that the underlying causes of beta diversity variation may be quite different within the same region depending on varying sampling scales. Therefore, scale effects should be taken into account in future studies on beta diversity, which is critical in identifying different relative importance of spatial and environmental drivers on species composition variation.

dbh ≥1 cm were stem-mapped and measured. The beta diversity was calculated for four different grain sizes, and the associated variances were partitioned into components explained by environmental and spatial variables to determine the contributions of environmental filtering and dispersal limitation to beta diversity. The results showed that both beta diversity and the causes of beta diversity were dependent on the sampling scale. Beta diversity decreased with increasing scales. The best-explained beta diversity variation was up to about 60% which was discovered in the secondary conifer and broad-leaved mixed forest (CBF) study area at the 40 × 40 m scale. The variation partitioning result indicated that environmental filtering showed greater effects at bigger grain sizes, while dispersal limitation was found to be more important at smaller grain sizes. What is more, the result showed an increasing explanatory ability of environmental effects with increasing sampling grains but no clearly trend of spatial effects. The study emphasized that the underlying causes of beta diversity variation may be quite different within the same region depending on varying sampling scales. Therefore, scale effects should be taken into account in future studies on beta diversity, which is critical in identifying different relative importance of spatial and environmental drivers on species composition variation.

K E Y W O R D S
beta diversity, dispersal limitation, environmental filtering, scale effects, variation partitioning

| INTRODUCTION
Beta (β) diversity, a subject of interest to community ecologists, which is introduced by Whittaker (1960) as the ratio between regional (γ) and local species diversity (α), has also been developed as the variation in species composition among sites within a geographical area of interest (Anderson et al., 2011;Gorelick, 2011), or to describe the species turnover from site to site (Anderson et al., 2011). Beta diversity reflects the spatial organization of species diversity. As a consequence, it provides fundamental insights into community assembly.
Ecologists typically measure the scale in terms of extent and grain (Nekola & White, 1999;Whittaker, Willis, & Field, 2001). A framework has summarized priori expectations for how beta diversity might vary among sampling grains drawn at the spatial extent ranging from local, regional to global scales (Barton et al., 2013). Generally, if the sampling grain is fixed and spatial extent is allowed to increase, beta diversity will naturally increase monotonically. Because when new sampling grains are incorporated, variation in stochastic occupancy patterns among sites and deterministic variation in species responses to habitat heterogeneity would result in increasing compositional dissimilarities between sampling grains. However, if spatial extent is fixed and sampling grain is allowed to vary, beta diversity might decrease monotonically. Because larger sampling grains can capture a larger portion of the community, and similarity between sampling units would therefore increase (Barton et al., 2013).
Theoretically, the variation of beta diversity across different sampling grains may be the result of different processes operating at various spatial scales (De Cáceres et al., 2012;Laliberté, Paquette, Legendre, & Bouchard, 2009). At local scales (<10 6 m 2 ), environmental filtering and dispersal limitation have been suggested to the main deterministic processes that contribute to beta diversity. Environmental filtering assumes that environmental conditions and species niche preferences control species composition. Sampling units with similar habitats are more likely to have similar species compositions (Kraft et al., 2011;Kristiansen et al., 2012). Dispersal limitation suggests that species composition may be determined by spatial process, which emphasizes the effects of spatial dispersal history. Under dispersal limitation, sampling units that are located in close proximity to each other should have a more similar species composition than units that are distant from each other (Chisholm & Lichstein, 2009;Qiao et al., 2015). Biotic interactions and stochastic process also contribute to beta diversity, but those processes are difficult to be quantified as far as now. At regional and global scale, ecological and evolutionary processes will also affect species composition of local communities. Those processes, including speciation, extinction, or biogeographic dispersal, should be taken into account when comparing beta diversity across regional or global scales (Whittaker et al., 2001).
At present, beta diversity has been studied in a great variety of forest ecosystems, including temperate and tropical forests (Myers et al., 2013), Amazonian palm communities (Kristiansen et al., 2012), Southern African dry woodlands (De Cauwer, Geldenhuys, Aerts, Kabajani, & Muys, 2016), and subtropical broad-leaved forests in China Qiao et al., 2015). While unfortunately, even though some studies have reported the variation of beta diversity across large spatial extent (Kraft et al., 2011;Lenoir et al., 2010;Qian & Ricklefs, 2007), limited studies have specifically investigated the scale dependence of beta diversity and how the processes driving beta diversity variation vary across different spatial scales of sampling grains (Barton et al., 2013). The establishment of large permanent forest plots makes it possible to compare beta diversity values and the underlying local ecological processes at different sampling grains.
However, to our knowledge, only few studies investigated how the causes of beta diversity variation depend on sampling grains (De Cáceres et al., 2012;Laliberté et al., 2009). The patterns and causes of scaling beta diversity need more evidence to be thoroughly explored.
In this study, beta diversity was calculated as the total variance of community data. To identify the causes of beta diversity variation, variation partitioning analysis was used to determine the contribution of environmental variables and spatial variables. To test the scale effects, beta diversity and the relative importance of environmental and spatial processes were assessed for four different sampling grains, ranging from 20 × 20 m to 50 × 50 m. The objective is to understand the underlying causes of beta diversity variations across sampling grains, based on two hypotheses: • The beta diversity values of tree species decreases with increasing sampling grains when the spatial extent of sampling area is fixed; • The causes underlying beta diversity are varying across different spatial grains.

| Study area
This study was conducted at three observational study plots in the Changbaishan Nature Reserve, located in northeastern China  The plots represent three distinct forest communities at different altitudes and varying in species richness.
The Changbai mountains are situated in a temperate monsoon montane climate, characterized by both continental weather conditions and a temperate monsoon. The observational study was established at the Changbaishan Forest Ecosystems Research Station, which has an annual mean temperature of 3.6°C. The average coldest monthly temperature is −15.4°C in January, and the average hottest one is 19.6°C in July. The mean annual precipitation is about 695 mm, concentrated during the period from June to September. The mean relative air humidity is around 72% (Zhang et al., 2005). The soil properties at the Changbaishan Nature Reserve differ along an elevational gradient. Montane tundra soils dominate at the highest elevations, changing to montane forest sward soils and montane brown coniferous forest soils at midelevations, and finally, dark brown forest soils at the lowest elevations. The rootable depths range from 10 to 130 cm.

| Sampling design
To examine the scale effects on beta diversity and the underlying causes, we divided the surface of each 5.2-ha plot, based on four grain designs with grain sizes ranging from 20 × 20 m (0.04 ha) up to 50 × 50 m (0.25 ha) by increments of 10 × 10 m. Table 2 shows the number of grains, decreasing with increasing grain size, and the total area for each sampling design.

| Environmental and spatial variables
In 2010, two soil samples were taken from the top 20-cm layer in each 20 × 20 m grain. These samples were used to quantify the following five variables: organic matter (%), soil pH, total nitrogen, phosphorus, and potassium (p.p.m.). The average value of these two samples was used to represent the soil nutrients of each 20 × 20 m grain. The soil rootable depth was also measured in each grain.
In the summer of 2017, we measured the elevation of four vertexes for each 20 × 20 m grain. On this basis, four topographical variables were calculated for each grain including mean elevation, aspect, slope, and convexity. The corresponding six soil variables for the other three grain sizes were estimated by Kriging interpolation (Journel & Huijbregts, 1978), and a trend surface analysis was performed before interpolation. We also interpolated elevation values of four vertexes for each 30 × 30 m, 40 × 40 m, and 50 × 50 m grain, which were used to estimate the four topographical variables.
The analysis was conducted in software ArcGIS (version 10.3), and interpolation process was explained in Appendix S1. The spatial variables were modeled using principal coordinates of neighbor matrices (PCNM; Borcard & Legendre, 2002;Borcard, Legendre, Avois-Jacquet, & Tuomisto, 2008). The PCNM variables were generated for each grain design from the spectral decomposition of the spatial relationships among grains. Moran's eigenvectors were computed for each grain design, and eigen functions with positive Moran indices were then generated (Dray, Legendre, & Peres-Neto, 2006). Following Blanchet, Legendre, and Borcard (2008), forward selection by permutations of residuals at the 5% level of significance was applied to obtain the significant environmental parameters and PCNM vectors to serve as explanatory variables. The analysis was performed using R (version 3.1.1) with the packages "spacemakeR" (Dray et  2006) for spatial analyses and "packfor" (Dray, 2005) for the forward selection.

| Calculating beta diversity
At each sampling grain, we obtained an n × p (grains-by-species) data table X by counting the number of living individuals in every grain of each species. The element x ij in table X represents the abundance of species j in grain i.
The Hellinger distance, as proposed by Legendre and Gallagher (2001), was used to measure the dissimilarity in the species composition between plot grains. The species abundance data transformed by the Hellinger distance can be analyzed directly by canonical redundancy analysis (RDA), which provided an easier and more informative way for beta diversity assessment. Each observed x ij value was transformed using the following transformation : where k is the species index, and p refers to the number of species in a given grain with row and column indices i and j. This transformation was applied to each of the three study areas and each grid design to convert the observed community where SS Total is the total sum of all the squares, representing the total variance of the community composition. The index BD Total is the unbiased form of the total variance, that is, beta diversity, which also expresses the average dissimilarity among grains.

we incorporated fraction [a] and [b] (fraction [a + b]) as the variation explained by environmental variables and in-
terpreted fraction [c] as variation explained by a spatial process. The explanatory ability of each factor is expressed using the adjusted coefficients of determinations (R 2 adj ). The calculations of beta diversity were carried out in R (version 3.1.1) using the "beta.div" function (Legendre & De Cáceres, 2013).

| Beta diversity and local contributions to beta diversity
As expected, beta diversity decreased with increasing grain size, as shown in Figure

| Variation partitioning of beta diversity
The results of the variation partitioning for the three study areas are presented in Figure 4.

| DISCUSSION
The decrease in beta diversity with increasing grain size reflected decrease in the compositional dissimilarity between sampling units ( Figure 2). This result was consistent with the expectation that if spatial extent is fixed and sampling grain is allowed to vary, then beta diversity will decrease monotonically (Barton et al., 2013). In this study, the spatial extent was limited by 5. in some previous studies, the sampling grain size was fixed, but the total study area varied (see for example Gering, Crist, & Veech, 2003;Lira-Noriega, Soberón, Nakazawa, & Peterson, 2007). As expected, the beta diversity increased with increasing spatial extent of the study areas. These results show much variation of the relationship between beta diversity and spatial scale. Studies with different sampling design revealed different patterns and ecological mechanisms. A limitation of our study is that we only present the beta scaling relationship at local scales. Further researches are required to assess the effects of grain size on beta diversity at regional and even continental scales.

F I G U R E 3
The spatial distribution of local contribution to beta diversity for the three study areas. The shading from light to dark shows that local contributions to beta diversity values increases from low to high

CBF P BF TKF
The spatial distribution of the local contributions to beta diversity showed that there was more compositional variation in CBF and PBF than in TKF. This result probably indicated that beta diversity was affected by differences in species richness. The greater the number of species in a plot, the greater is the possibility that the species composition varies among sampling units. And differences in composition variation (i.e., beta diversity) often obviously found along great environmental gradients which mainly caused by changes in the size of species pools (Kraft et al., 2011).
By partitioning beta diversity into different components, an attempt was made to investigate the underlying causes of the dissimilarity between sampling units, expressed in terms of beta diversity. The amount of explained variation of beta diversity may indicate how the forest community is affected by two underlying ecological processes, usually referred to as environmental filtering and dispersal limitation.
Environmental filtering is related to specific resource require- The relative importance of environmental and spatial processes has been the subject of several previous studies. Myers et al. (2013) found that environmental variables have a greater impact on beta diversity variation in temperate forests, while spatial effects explain a larger proportion of that variation in tropical forests. Qiao et al. (2015) reported that, in Badagongshan (a subtropical forest), topography and soil together explained 27% of beta diversity. This value is slightly less than the 34% explained by the spatial variables.  Myers et al., 2013;Qian & Ricklefs, 2007;Wang, Fang, Tang, & Shi, 2012 The unexplained proportion of beta diversity variation may be related to unmeasured environmental variables, such as radiation and moisture. When the uncertainties are spatially structured but which is not explained by the measured environmental variables, studies would possibly overestimate the spatial effects and underestimate environmental effects (Qiao et al., 2015). Future studies should therefore collect as many environmental variables as possible. The unexplained portion of beta diversity variation may also relate to local stochastic processes (De Cáceres et al., 2012), such as death and recruitment. These processes create randomly different compositions of the sampling units (Alonso, Etienne, & McKane, 2006).
When the number of individuals in the sampling unit is small (i.e., at small sampling scales or in plots with few individuals per unit area), this difference is more evident. It may also be evident in plots with higher species richness, because more species can be excluded by local ecological drift (De Cáceres et al., 2012). Thus, beta diversity is a result of complex process. The greater portion of unexplained variation does not necessarily indicate a greater importance of death and recruitment. But it is useful to capture differences in local beta diversity caused by some stochastic factors and processes that are hard to be quantified.
Our study examined the scale dependence of beta diversity and its underlying causes. For future studies, we emphasize the importance of choosing proper scales. When sampling grains are too small, there is a problem of undersampling. Because if the average number of trees per sampling unit is clearly less than the total number of species, many species for which the environmental conditions within a unit would be suitable will be absent simply because too few individuals were sampled. While at large grain sizes, the number of trees per unit usually exceed the total number of species of the entire plot. So if a species is absent, there is a bigger chance that this is not only a sampling artifact but also reflects something of ecological relevance. This may, for example, indicate that the differences among grain sizes would be not only due to the differences in how ecological processes function, but also may be due to the effects of undersampling at small scales. What is more, when sampling grain is smaller than the grains at which the environmental variables are sampled, interpolation to a smaller scale would increase the uncertainty of environmental variations and may result in incorrect variation partitioning. Conversely, when sampling grains are too big, the number of samples may be too small which affects the accuracy. Additional research is therefore needed to assess the ecological properties and mechanical causes of beta diversity of local forest communities.

| CONCLUSION
Two hypotheses were presented in this study: (i) beta diversity of tree species decreases with increasing spatial scale within the same region and (ii) beta diversity is the result of different underlying causes at different sampling grains. It is shown that beta diversity variation is a complex response to environmental heterogeneity, species dispersal ability, and possibly some stochastic processes. Both beta diversity and its causes are affected by the sampling scales. The explained beta diversity variation across scales in all three plots showed that the effect of environmental filtering is more importance at greater grain sizes, whereas dispersal limitation is more important at small grain sizes especially effective at the 20 × 20 m scale. The effect of sampling scale on beta diversity and its underlying causes is considerable.
Therefore, we conclude that, in future studies on beta diversity, the sampling scale is critical to identifying the different spatial and environmental drivers of species composition.