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Global Ecology and Biogeography, (Global Ecol. Biogeogr.) (2015) 24, 1170–1180 bs_bs_banner RESEARCH PA P E R S Latitudinal differences in species abundance distributions, rather than spatial aggregation, explain beta-diversity along latitudinal gradients Wubing Xu1,2, Guoke Chen1, Canran Liu3 and Keping Ma1* 1 State Key Laboratory of Vegetation and Environmental Change, Institute of Botany, Chinese Academy of Sciences, Beijing 100093, China, 2University of Chinese Academy of Sciences, Beijing 100049, China, 3Department of Environment, Land, Water and Planning, Arthur Rylah Institute for Environmental Research, Heidelberg, Victoria 3084, Australia ABSTRACT Aim Variation in species composition among sites (β-diversity) generally decreases with increasing latitude, but the underlying mechanisms are ambiguous. Although both local and large-scale processes may drive this pattern, they act all through influencing species abundance distribution (SAD) and spatial pattern of species. A null model incorporating SAD is often used to calculate expected β-diversity, which accounts for most variation in β-diversity. However, a recent study has shown that the deviation of observed β-diversity from expected values (β-deviation) increases with latitude. The latitudinal gradients in β-deviation may be related to both latitudinal differences in SADs and the degrees of spatial aggregation. Our study aims to (1) investigate how β-deviation varies with SAD and spatial aggregation, and (2) separate the contributions of SAD and aggregation in explaining latitudinal gradients in β-deviation. Location Global. Methods 197 forest plots (each containing 10 subplots) distributed along latitudinal gradients were used. Two β-diversity models were derived for communities with randomly and nonrandomly distributed species. The two models were used to simulate relationships of β-deviation with SAD and aggregation, and to separate the contributions of these two factors in explaining latitudinal gradients in β-deviation. Results β-deviation increased with the degree of aggregation and peaked at intermediate species abundance. The fraction of β-deviation linked to SAD increased with latitude in global and regional analyses, whereas the fraction of β-deviation linked to aggregation was only significantly correlated with latitude in New World south. The degree of aggregation increased with latitude in New World south, but not in global extent and New World north. *Correspondence: Keping Ma, State Key Laboratory of Vegetation and Environmental Change, Institute of Botany, Chinese Academy of Sciences, Beijing 100093, China. E-mail: [email protected] 1170 Main conclusions The latitudinal gradients in β-deviation are primarily explained by latitudinal differences in SADs. Additionally, the expected β-diversity is determined solely by SAD. Therefore, we conclude that latitude-β-diversity gradients at local spatial scales appear to be explained by latitudinal differences in SADs. Keywords aggregation, beta-diversity, latitude, occupancy, random placement, spatial distribution, species abundance distribution, species diversity. DOI: 10.1111/geb.12331 © 2015 John Wiley & Sons Ltd http://wileyonlinelibrary.com/journal/geb Latitudinal gradients of β-diversity INTRODUCTION One of the most striking and frequently documented patterns in biogeography and macroecology is increasing species richness from the poles to the equator (Rosenzweig, 1995; Gaston, 2000) and a number of hypotheses have been proposed to explain this pattern (Hawkins et al., 2003; Willig et al., 2003; Mittelbach et al., 2007). By comparison, the patterns and mechanisms related to dissimilarity in species composition among sites (β-diversity) across biogeographic gradients have been poorly documented (Buckley & Jetz, 2008; De Cáceres et al., 2012; Tang et al., 2012). However, β-diversity not only links α-diversity and γ-diversity, but it also provides fundamental insights into mechanisms of community assembly (Condit et al., 2002; Legendre et al., 2009; Anderson et al., 2011). Several recent studies have shown that β-diversity generally increases with decreasing latitude (Qian & Ricklefs, 2007; Buckley & Jetz, 2008; De Cáceres et al., 2012; Tang et al., 2012). Many local processes such as dispersal limitation (Condit et al., 2002), habitat filtering (Legendre et al., 2009), density dependence (Johnson et al., 2012) and stochastic ecological drift (Chase, 2010) may contribute to latitudinal patterns of β-diversity. Alternatively, biogeographic and evolutionary processes that operate at large-scales, such as speciation, extinction, and biogeographic dispersal, may drive β-diversity patterns by influencing the size of species pool (Kraft et al., 2011; De Cáceres et al., 2012; Myers et al., 2013). To account for the influence of regional species pool, a null model approach is used to disentangle the ecological processes from random sampling effect when comparing β-diversity across biogeographic regions (Crist et al., 2003; Kraft et al., 2011; De Cáceres et al., 2012; Mori et al., 2013; Myers et al., 2013; Qian et al., 2013). For example, Kraft et al. (2011) used the null model approach to examine the latitudinal variation in β-diversity in 197 forest inventory plots that have been distributed in different continents (Phillips & Miller, 2002). They first determined expected β-diversity by a randomization procedure. Then, they calculated standardized β-deviation as the difference between observed and expected β-diversity divided by the standard deviation of expected values. While the expected β-diversity was interpreted as the effects of regional species pool on β-diversity, the standardized β-deviation was interpreted as the effects of mechanisms of community assembly on β-diversity. They found that the standardized β-deviation did not vary systematically along latitudinal gradients, and they thus concluded that differences in the mechanisms of community assembly might contribute little to latitudinal patterns of β-diversity. However, Qian et al. (2013) found that the β-deviation increased with latitude when they examined different continents separately and altered the measure of β-deviation as the difference between observed and expected β-diversity. Additionally, because the individual-based null model incorporates the species abundance distribution (SAD) which is affected by mechanisms of community assembly, they concluded that latitudinal patterns of β-diversity are largely driven by mechanisms of community assembly. The contradicting results of the above two studies are mainly due to the standard deviation of expected β-diversity decreasing with increasing γ-diversity (Qian et al., 2013). The raw β-deviation approach may be more appropriate for analyzing variation in β-diversity across biogeographic regions with different sizes of species pool. Although both local community assembly processes and large-scale processes could affect β-diversity, they act all through influencing the SAD and spatial pattern of species, which are considered to be the two most important factors in interpreting species-area relationships (Crawley & Harral, 2001; He & Legendre, 2002). Both the SAD and spatial pattern are affected by mechanisms of community assembly (Condit et al., 2000; McGill et al., 2007; Cheng et al., 2012). Large-scale processes also affect the SAD by influencing the number of species within communities because a SAD not only describes the abundance of each species, but also the number of species (McGill et al., 2007). Rather than disentangling the local and large-scale processes driving latitudinal patterns of β-diversity, our study aims to understand the relative contribution of SAD and spatial pattern of species in explaining latitudinal patterns of β-diversity (Fig. 1). In the null model mentioned above, observed β-diversity was decomposed to expected β-diversity and β-deviation (Kraft et al., 2011; De Cáceres et al., 2012; Qian et al., 2013). Expected β-diversity is calculated based on random sampling from the empirical SAD (Qian et al., 2013). Consequently, the variation of expected β-diversity along latitudinal gradients is determined solely by latitudinal differences in SADs. The magnitude of β-deviation reflects the level at which spatial patterns of species deviate from a random distribution (Myers et al., 2013). That is, more aggregated spatial patterns lead to higher values of β-deviation. Therefore, latitudinal gradients in β-deviation may be related to latitudinal aggregation patterns. Although the β-deviation was previously considered as the fraction of β-diversity after filtering out the sampling effects of SADs, the variation of β-deviation may also be associated with SADs because aggregation cannot affect β-diversity alone and it functions only through affecting spatial distributions of individuals and the outcome of same aggregation level on different abundance may be different. Therefore, latitudinal gradients in β-deviation may also be related to latitudinal differences in SADs. However, the relationship between β-deviation and the SAD is still not clear. Distinguishing the contributions of the SAD and spatial aggregation in explaining the variation of β-deviation will promote a better understanding of mechanisms governing the biogeographic patterns of β-diversity. In this study, β-deviation was measured as the difference between observed and expected β-diversity, as in Qian et al. (2013) and De Cáceres et al. (2012). Our specific aims are: (1) to investigate how β-deviation varies with the SAD and spatial aggregation; and (2) to separate the contributions of the SAD and spatial aggregation in explaining latitudinal gradients in β-deviation. This study is organized as follows. First, based on the occupancy abundance relationship (He & Gaston, 2000), we derived two β-diversity models, one for random distribution of individuals and the other for nonrandom distribution. Using these two models, the β-diversity for random and nonrandom Global Ecology and Biogeography, 24, 1170–1180, © 2015 John Wiley & Sons Ltd 1171 W. Xu et al. (a) (c) Plot i Plot i β-diversity Observed β Aggregationlinked fraction β-deviation Observed Expected Low β-deviation SADi + Predicted β High Latitude (b) SADs Spatial aggregation SADlinked fraction Expected β β-deviation SADi Observed β Expected β Figure 1 Conceptual figure illustrating how to disentangle the relative contributions of the species abundance distribution (SAD) and aggregation in explaining latitudinal gradients in β-diversity. (a) The latitudinal gradients in observed and expected β-diversity. The expected β-diversity is the expected value of β-diversity when all species in a plot are randomly distributed. The difference between observed and expected β-diversity is β-deviation, which probably increases with latitude. (b) The factors explaining the latitudinal differences in expected β-diversity and β-deviation, the two components of observed β-diversity. The latitudinal differences in expected β-diversity can be explained solely by latitudinal differences in SADs, whereas the latitudinal differences in β-deviation may be related to the latitudinal differences in both SADs and spatial aggregation. (c) Separating the fractions of β-deviation linked to the SAD and aggregation. Because the SAD and aggregation affect β-deviation simultaneously, one way to separate these two factors is to compare one of them when keeping the other constant among regions. Here, the degrees of aggregation of all plots along latitude are set to be the same and equal to the global average degree of aggregation ( k ). Then, a predicted value of β-diversity of each plot at the average degree of aggregation can be calculated with its SAD and k using a nonrandom β-diversity model (plot i in figure a used as an example here). The difference between predicted and expected β-diversity is the fraction of β-deviation linked to the SAD because variation in the departure among regions can only result from the variation in SADs. The difference between observed and predicted β-diversity is the fraction of β-deviation linked to aggregation. Note that predicted β-diversity may be less than, equal to or greater than observed β-diversity, corresponding to the degree of aggregation of plot i being more, equivalent or less aggregated relative to the average degree of aggregation. communities can be calculated, respectively. Second, we conducted a simulation, using the two β-diversity models, to explore how β-deviation varies with the SAD and aggregation. In the simulation, β-deviation was the difference between the results of nonrandom and random β-diversity models. Third, we separated the contributions of the SAD and aggregation in explaining latitudinal gradients in β-deviation, using a dataset of 197 forest plots (Gentry’s data set) (Fig. 1). Because the SAD and aggregation may affect β-deviation simultaneously, one way to separate these two factors is to compare one of them when keeping the other constant. We thus set the degree of aggregation of each plot to the global average degree of aggregation over all plots. We then calculated the value of β-diversity of each plot at the average aggregation level as predicted β-diversity (Fig. 1c). The difference between predicted and expected β-diversity is the fraction of β-deviation linked to the SAD because the predicted β-diversity of each plot was calculated with the same aggregation level and variation in the departure can only result from variation in SADs. The difference between observed and predicted β-diversity is the fraction of β-deviation linked to aggregation. 1172 M AT E R I A L S A N D M E T H O D S Data sets We used Gentry’s data set of 197 forest plots distributed along latitudinal gradients (http://www.mobot.org/MOBOT/ research/gentry/transect.shtml). These 197 plots were also used in Kraft et al. (2011) and Qian et al. (2013). Each plot has ten 2 × 50 m subplots. These subplots were randomly spatially oriented with respect to one another (Phillips & Miller, 2002), and thus no latitudinal trends in spatial orientation exist. All woody stems with diameter at breast height (DBH) ≥ 2.5 cm were recorded to species or morphospecies (Phillips & Miller, 2002). Latitude, longitude and elevation for each plot were obtained from Phillips & Miller (2002). Among the 197 plots, 157 were located in the New World and the other 40 were scattered in the Old world. Following the suggestion of Qian et al. (2013), we assembled two subsets from the New World plots. One included all the 71 plots located south of the equator and the other included 79 plots located north of the equator and east of 100° W longitude. Global Ecology and Biogeography, 24, 1170–1180, © 2015 John Wiley & Sons Ltd Latitudinal gradients of β-diversity β-diversity and occupancy abundance relationship We used the same definition of α-, β- and γ-diversity as in Kraft et al. (2011) and Qian et al. (2013). The α-diversity was defined as the species richness of each 0.01-ha subplot, γ-diversity as the total species richness of a plot, and β-diversity as the heterogeneity of species composition among subplots: β = 1− α γ (1) The value of α and β can also be calculated from the occupancy of species (Arita & Rodríguez, 2004). The occupancy is the proportion of subplots that are occupied by a species or the probability that a species occurs in each subplot (He & Gaston, 2003). If species richness of a plot is γ and the number of subplots in that plot is m, the presence or absence of γ species over m subplots can be expressed as a species by subplot (γ × m) matrix with elements d(i, j). If the species i is present in the subplot j, then d(i, j) = 1, otherwise d(i, j) = 0. The sum of elements in column j is the α-diversity of subplot j (aj), and the sum of elements in row i is the occurrence of species i (oi). The sum of all columns is equal to the sum of all rows. Thus, α is related to occurrence as α = ∑ mj =1 α j m = ∑ iγ=1 oi m . The occurrence oi divided by m equals the occupancy pi, i.e. the proportion of subplots that are actually occupied by species i. Then, α is γ related to occupancy of all species in a plot as α = expression of β with occupancy is: β = 1− ∑ γ i =1 pi ∑ pi . The i =1 (2) γ Although many biotic and abiotic factors may influence the occupancy of species, species abundance and their spatial distribution are the two most immediate factors (Gaston & He, 2011). The proportion of subplots occupied by a species increases with its abundance, and more aggregated species tend to be more narrowly distributed. The positive relationship between occupancy and species abundance is a general pattern in ecology (He & Gaston, 2003; Karlson et al., 2011). There are many models developed to describe this pattern (He & Gaston, 2000; He et al., 2002). For species i with ni individuals randomly distributed in m subplots, the presence or absence of the species at a subplot is a Bernoulli trial, and the occupancy abundance relationship is derived as (He & Gaston, 2000): ( m1 ) ni pi = 1 − 1 − (3) Therefore, by substituting model (3) to equation (2), the β-diversity model for a community where all species are distributed randomly is: β= ∑ γ i =1 (1 − m1 ) γ ni (4) where γ is the species richness of the community, ni is the abundance of species i, and m is the number of subplots in the community. However, most species in nature have an aggregated distribution (Condit et al., 2000) and are often described with negative binomial distribution (NBD; Krebs, 1999). Although the NBD is a spatially implicit model of aggregation as it does not account for spatial autocorrelation between cells, it performed equally accurately with a spatially explicit model in predicting occupancy (Hui et al., 2006). By the NBD, the occupancy abundance relationship follows (He & Gaston, 2000): ( pi = 1 − 1 + ni mk ) −k (5) where k is a spatial aggregation parameter. Although k of the NBD is defined to be positive, He & Gaston (2000) have shown that k in model (5) could take negative values to describe regular spatial distributions of species. When k takes positive values, a smaller k represents a stronger spatial aggregation of species. Thus, the corresponding β-diversity model for a nonrandom community where all species are assumed to have the same degree of aggregation is: β= ∑ γ i =1 (1 + mkn ) −k i (6) γ In this study, we use model (4) to calculate expected β-diversity when species are randomly distributed, and use model (6) to calculate the β-diversity when species exhibit a certain degree of aggregation. Simulating the relationship of β-deviation with the SAD and spatial aggregation To investigate how β-deviation varies with the SAD and spatial aggregation, we conducted a simulation, where we calculated the β-diversity in two scenarios that spatial distributions of species were random and aggregated, respectively. We used average abundance per species to summarize the SAD, as in Qian et al. (2013). This is because a SAD is a vector of abundance which cannot illustrate the relationship between β-deviation and SAD on a two-dimensional plot, because the SAD can be accurately predicted by total species richness (γ-diversity) and total abundance (Harte et al., 2008, 2009; White et al., 2012; Locey & White, 2013; McGlinn et al., 2013), because average abundance characterizes the relationship between γ-diversity and total abundance, and because β-diversity and β-deviation are nearly independent from γ-diversity after controlling for average abundance (Figs S1b, c, S2c, d & S3c, d in Supporting Information). For the random scenarios, the expected β-diversity was calculated using model (4) given the average abundance, γ-diversity, and number of subplots. We changed the average abundance from 2 to 100 individuals per species, and held γ-diversity as 106 (the average γ-diversity in Gentry’s 197 plots). Global Ecology and Biogeography, 24, 1170–1180, © 2015 John Wiley & Sons Ltd 1173 W. Xu et al. Multiplying the average abundance by γ-diversity gave the total abundance. We then assigned all individuals in the species pool using the log-series, log-normal and uniform species abundance distribution models. The number of subplots was set to be 10 in accord with 10 subplots per plot in Gentry’s data set. For the aggregated scenarios, we applied model (6) to calculate β-diversity using the same set of parameters as in the random scenarios as well as an additional aggregation parameter k. The parameter k was set to have four levels: 2.0, 1.5, 1.0, and 0.7. Smaller values of k indicated higher degrees of aggregation. We calculated the β-deviation as the difference between β-diversity in aggregated scenarios and that in random scenarios. Disentangling the contributions of the SAD and spatial aggregation in explaining latitudinal gradients in β-deviation We calculated expected β-diversity for each plot in Gentry’s data set using model (4). However, an individual-based null model approach is often used to calculate expected β-diversity in previous studies (Kraft et al., 2011; Mori et al., 2013; Qian et al., 2013; Stegen et al., 2013). In the null model, all individuals within a plot are randomly shuffled among subplots while preserving the SAD of the plot and the number of individuals in each subplot. Compared to the null model approach, model (4) does not maintain the number of individuals in each subplot but it does maintain the observed site-specific SAD. To investigate whether these two methods differ significantly in measuring the expected β-diversity, we also calculated a value of expected β-diversity for each plot using the null model. We ran 999 randomizations for each plot and calculated expected β-diversity as the mean of 999 values. The two values of expected β-diversity for each plot were compared. Theoretically every species has its own value of the aggregation parameter k. Since model (6) assumes all the species in a plot have the same value of k, it is necessary to investigate how well this model can predict β-diversity for real data. We therefore applied this model to estimate the β-diversity in Gentry’s 197 plots. The maximum likelihood method was used to estimate parameter k in model (6) by fitting model (5) to occupancy-abundance data (He et al., 2002; He & Gaston, 2003). For each plot, the parameter k was estimated by maximizing the log-likelihood function γ l= ∑ [o log ( p ) + (m − o ) log (1 − p )], where o is the number of i i =1 i i i i occupied subplots for species i, m is the total number of subplots (equals 10 in our case), and pi is the predicted occupancy from model (5) given the abundance ni for species i. Based on the estimated parameter k and SAD for each plot, the value of β-diversity in model (6) was obtained. We compared the estimated β-diversity with observed β-diversity. The latitudinal variation of β-deviation may be related to latitudinal differences in SADs and spatial aggregation simultaneously. One way to separate these two factors is to compare one of them when keeping the other constant. For disentangling the explanatory factors of β-deviation in Gentry’s data set, we assumed that the aggregation parameter k in each of Gentry’s 197 1174 plots was the same by fitting model (5) to all the 20,816 observations of occupancy and abundance from all 197 plots. The estimated parameter k was the global average degree of aggregation over all plots. With the estimated k, we calculated a value of β-diversity for each plot using model (6) given the site-specific SAD. We called this predicted β-diversity which held the information of SAD in each plot (Fig. 1c). By comparing among the observed, predicted and expected β-diversity, we disentangled the contributions of the SAD and spatial aggregation. We first calculated the β-deviation as the difference between observed and expected β-diversity. Next we calculated the departure between predicted and expected β-diversity. Because both predicted and expected β-diversity were calculated with the observed SAD, the departure is the increment of β-diversity owing to the increase of aggregation level from random placement to the global average degree of aggregation. But the increments from expected to predicted β-diversity among different plots were different. The variation in the departure among plots can only come from the differences in SADs because the predicted β-diversity of each plot was calculated with the same aggregation level. Therefore, the departure indicates the fraction of β-deviation linked to the SAD. Then, we calculated the departure between observed and predicted β-diversity. The departure is the change of β-diversity relative to predicted β-diversity owing to the deviation of site-specific aggregation level from the global average degree of aggregation. This departure indicates the fraction of β-deviation linked to the spatial aggregation. Positive departure values imply that species are more aggregated in space than the average degree of aggregation; negative values imply less aggregated. However, we noted that the SAD was also different among plots and the shared influence between the SAD and aggregation was also possible. But it only affected the magnitude of absolute values of the departure, and did not change the sign of values. That is to say, the departures of those more aggregated plots were greater than those of less aggregated plots regardless of the differences in SADs. Further, to explore the latitudinal variation in the fraction of β-deviation linked to aggregation, we compared the degree of aggregation among plots with an aggregation index 1/k. The k is the aggregation parameter in model (6). Because the variation of k among plots was too large, we did not directly use the parameter. The linear relationships of β-deviation, the fractions of β-deviation linked to the SAD and aggregation, and 1/k with latitude were examined. We also applied the same analyses described above to two subsets of Gentry’s 197 plots. There were 9757 observations of abundance and occupancy for 71 plots in New World south and 6439 observations for 79 plots in New World north. R E S U LT S The results of simulation confirmed that β-deviation varies with both the SAD and the degree of aggregation (Figs 2, S2b & S3b). The β-deviation increased with the increasing degree of aggre- Global Ecology and Biogeography, 24, 1170–1180, © 2015 John Wiley & Sons Ltd 40 60 80 100 Average abundance Figure 2 The relationship between β-deviation and average abundance at four spatial aggregation levels, using log-series species abundance distribution model. Smaller k represents stronger spatial aggregation of species. The β-deviation was calculated from the difference between the result of model (6) and that of model (4). Model (4) and (6) are two β-diversity models derived based on the occupancy abundance relationships for random and nonrandom distribution of individuals, respectively. gation. At each aggregation level, β-deviation had a humpshaped distribution peaking at intermediate abundance. The null model approach and model (4) made very similar estimates of expected β-diversity (R2 = 0.999; Fig. 3a). This suggested that whether maintaining the number of individuals in each subplot as raw data did not influence expected β-diversity, and model (4) was an appropriate substitute for the null model in estimating expected β-diversity. Model (6) also made excellent estimates of observed β-diversity for natural aggregated communities (R2 = 0.989; Fig. 3b). This indicated that model (6) was robust in estimating β-diversity for the empirical data, even though it assumes all the species in a plot have the same aggregation parameter value. For Gentry’s data set, there were consistent and positive relationships between β-deviation and latitude in the global extent, New World south and New World north (Fig. 4a–c; all were significant, P < 0.01). When the fractions of β-deviation linked to the SAD and aggregation were separated, they presented different patterns along latitudinal gradients. The SAD-linked fraction was positively and significantly correlated with latitude in all the three data sets (Fig. 4d–f). However, the similar pattern for the aggregation-linked fraction was detected only in New World south (Fig. 4h). There were no significant relationships between aggregation-linked fraction and latitude in the global extent (Fig. 4g) as well as New World north (Fig. 4i). Similarly, aggregation index 1/k was significantly correlated with latitude in New World south, but not in the global extent and New World north (Fig. 5). These results indicated that latitudinal gradients in β-deviation were explained mainly by lati- 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Expected β−diversity using model (4) 0.9 20 (b) 0.8 0 R 2 = 0.999 0.7 k =2 0.6 k = 1.5 (a) R 2 = 0.989 0.5 k =1 Expected β−diversity using null model k = 0.7 Observed β−diveristy 0.00 0.02 0.04 0.06 0.08 0.10 0.12 β−deviation Latitudinal gradients of β-diversity 0.5 0.6 0.7 0.8 0.9 Estimated β−diveristy using model (6) Figure 3 (a) The relationship between the values of expected β-diversity calculated from null model approach and model (4), respectively. (b) The relationship between observed β-diversity and estimated β-diversity calculated with model (6). The diagonal line is the one-to-one line. The similarity of two values of expected β-diversity or between observed and estimated β-diversity was evaluated using coefficient of determination with respect to the 2 2 one-to-one line: R 2 = 1 − ∑i (obsi − predi ) ∑i (obsi − obs i ) , where obsi and predi are the values of β-diversity of point i at y-axis and x-axis, respectively. tudinal differences in SADs and only partly explained by variation of spatial aggregation in New World south. The predicted β-diversity calculated with the site-specific SAD and the global average degree of aggregation thus explained a large proportion of the variation in observed β-diversity (92.7, 93.5 and 93.3% for global extent, New World south and New World north, respectively; Fig. 6). DISCUSSION Our results demonstrate that the departure of β-diversity from the null expectation not only increases with the degree of aggre- Global Ecology and Biogeography, 24, 1170–1180, © 2015 John Wiley & Sons Ltd 1175 60 10 (e) 20 30 40 0.18 50 r = 0.59, P < 0.001 0.04 50 60 10 (h) 20 30 40 50 r = 0.56, P < 0.001 10 20 30 40 50 60 10 20 (i) 30 40 50 Figure 4 The relationship of β-deviation (a–c), the fractions linked to the SAD (d–f) and aggregation (g–i) with latitude for global extent (a, d, g), New World south (b, e, h) and New World north (c, f, i). Note that similar plots of the first row (a–c) have been shown in Qian et al. (2013). r = −0.11, P = 0.338 10 20 30 40 50 0 10 2.0 Absolute latitude (°) r = −0.04, P = 0.555 50 0.00 0 Absolute latitude (°) r = 0.27, P = 0.023 (b) 20 30 40 50 Absolute latitude (°) Figure 5 The relationship between aggregation index 1/k and latitude for global extent (a), New World south (b) and New World north (c). Larger 1/k represents stronger spatial aggregation. The values of k were estimated by fitting model (5) to occupancy and abundance data. r = −0.21, P = 0.062 (c) 1 1.0 0.5 20 30 40 50 60 0 Observed β−diversity 10 20 30 40 50 0 Absolute latitude (°) 0.4 0.5 0.6 0.7 0.8 0.9 Absolute latitude (°) (a) R 2 = 0.927 0.4 0.5 0.6 0.7 0.8 Predicted β−diversity 0.9 10 20 30 40 50 Absolute latitude (°) 0.4 0.5 0.6 0.7 0.8 0.9 10 0 0.0 0 0 0.4 0.5 0.6 0.7 0.8 0.9 2 1 1/k 2 3 1.5 (a) 40 r = 0.63, P < 0.001 0 3 0 30 −0.07 −0.07 −0.07 0.00 0.00 0.07 0.07 r = −0.01, P = 0.910 0 0.14 40 20 0.07 30 10 (f) 0.00 0.00 20 0.14 10 (g) 0 0.04 0.08 0.08 r = 0.67, P < 0.001 0.00 0 0.12 50 r = 0.28, P = 0.011 0.08 40 (c) 0.12 0.06 0.00 30 0.12 20 0.04 0.14 0 4 r = 0.61, P < 0.001 0.06 0.12 0.06 0.12 10 (d) 0.00 SAD−linked fraction 0 Aggregation−linked fraction (b) 0.12 r = 0.34, P < 0.001 0.18 (a) 0.00 β−deviation 0.18 W. Xu et al. (b) R 2 = 0.935 0.4 0.5 0.6 0.7 0.8 Predicted β−diversity 0.9 (c) R 2 = 0.933 0.4 0.5 0.6 0.7 0.8 0.9 Predicted β−diversity Figure 6 The relationship between observed and predicted β-diversity for global extent (a), New World south (b) and New World north (c). The predicted β-diversity was calculated with model (6) based on the site-specific SAD and the global average degree of aggregation in three respective regional extents. The diagonal line is the one-to-one line. The similarity between observed and predicted β-diversity was evaluated using coefficient of determination with respect to the one-to-one line: R 2 = 1 − ∑i (obsi − predi )2 ∑i (obsi − obs i ) , where obsi and predi are the ith observed and predicted β-diversity, respectively. Note that the difference between observed and predicted β-diversity is the fraction of β-deviation linked to aggregation. 2 gation of species but also varies with the SAD (Figs 2, S2b & S3b). Because the relationship between β-deviation and average abundance is hump-shaped, caution is needed when analyzing the empirical relationships that may be positive, such as in 1176 Gentry’s data set, negative or hump-shaped, which depends on the range of average species abundance. In previous studies, variation of β-deviation was considered to be related to differences in spatial aggregation which was caused by many Global Ecology and Biogeography, 24, 1170–1180, © 2015 John Wiley & Sons Ltd Latitudinal gradients of β-diversity ecological processes, and the patterns of β-deviation along environmental gradients were used to infer whether the patterns of β-diversity were affected by mechanisms of community assembly (Kraft et al., 2011; De Cáceres et al., 2012; Mori et al., 2013; Myers et al., 2013). Our study provides some of the first evidence that variation of β-deviation among regions could also be explained by differences in SADs. Therefore, the contributions of the SAD and aggregation in explaining the variation of β-deviation should be separated to better understand the mechanisms shaping the patterns of β-diversity along environmental gradients. One striking finding in this study is that the latitudinal pattern of β-deviation was explained mainly by the latitudinal variation in SADs, rather than spatial aggregation (Fig. 4). Variation in aggregation contributed partly to the latitudinal variation of β-deviation in New World south, but not in global extent and New World north (Figs 4 & 5). Sampling bias might cause the significant relationship between the fraction of β-deviation linked to aggregation and latitude in New World south. Plots used in this study were not evenly distributed across latitudes. Among the 71 plots in New World south, 68 plots were below 27°, and the remaining three plots were at about 40° and were less than 113 km apart (Phillips & Miller, 2002; fig. S1 in Qian et al., 2013). Because there were no plots located in the regions between 27° and 40°, the three plots in high latitude could heavily affect the relationship between aggregation-linked fraction and latitude. When the three plots were excluded, the relationships of aggregation-linked fraction and aggregation index 1/k with latitude became non-significant (Fig. S4). In a recent study, Qiao et al. (2012) showed that the departure of empirical species-area relationships from simulated relationships, based on random distribution of individuals, decreased with temperature. They interpreted this latitudinal pattern as species are more spatially aggregated in the cold climates than warm ones. Our results suggest that this latitudinal pattern might be caused by the variation in SADs, which requires further investigation. Because latitudinal gradients in both expected β-diversity and β-deviation are explained by latitudinal differences in SADs, latitudinal patterns of β-diversity appear to be strongly associated with the variation in SADs and nearly independent from the variation in spatial aggregation. Thereby, the predicted β-diversity calculated with the site-specific SAD and the global average degree of aggregation is very closely related to observed β-diversity (Fig. 6). The close relationship between latitudinal variation in SADs and β-diversity, however, does not guarantee the causality between them. This relationship might be caused by the effect of SADs on β-diversity, or conversely by the effect of β-diversity on SADs. The β-diversity can be derived from the SAD (e.g. this study) and the SAD can also be derived on the basis of species spatial turnover (Šizling et al., 2009; Kůrka et al., 2010). Furthermore, the link between latitudinal variation in SADs and β-diversity may not be caused by the interaction between them, but rather the local and regional processes that simultaneously influence them. Despite the uncertainty in the causality, our results at least revealed a link between latitudinal variation in β-diversity and SADs, which does not exist between β-diversity and aggregation. Accordingly, the processes driving latitudinal differences in SADs are expected to be the same as those driving latitudinal gradients in β-diversity. Even though some previous studies directly or indirectly highlighted the importance of the SAD in explaining latitudinal gradients in β-diversity, they have not been able to clearly elucidate the importance of spatial aggregation. For example, based on the facts that expected β-diversity resulting from the null model was determined by the SAD, and average abundance explained a high fraction of variation in β-diversity, Qian et al. (2013) concluded that the SAD plays a key role in explaining latitudinal gradients in β-diversity. However, the β-deviation still increased with latitude, and they interpreted this latitudinal pattern as being driven by the processes beyond those driving the SAD. Compared to their results, our study clarifies the factors related to the latitudinal variation in β-deviation: the SAD also plays a dominant role and the effects of spatial aggregation are negligible. In another study, Harte et al. (2009) found that slope (z-value) of species-area relationship, a measure of β-diversity, can be predicted by a single parameter, the average abundance, a summary value of SAD. However, as Šizling et al. (2011) pointed out that the deviation of empirical value from prediction is biologically informative, revealing that species tend to be more aggregated or dispersed than predicted by Harte et al. (2009). Indeed, the joint influences of the SAD and spatial aggregation on β-diversity and specie-area relationship have been confirmed by numerous studies (He & Legendre, 2002; Crist et al., 2003; Morlon et al., 2008; Tjørve et al., 2008; Okuda et al., 2009; Chase & Knight, 2013). Our finding that latitudinal gradients in β-diversity are nearly independent from the latitudinal variation in spatial aggregation does not deny the effects of spatial aggregation on β-diversity, but means that the effects are consistent along latitudinal gradients. The SAD is one of the most intensively studied patterns in ecology and is potentially influenced by an array of community assembly processes, such as niche differentiation and dispersal limitation (Hubbell, 2001; McGill et al., 2007; Cheng et al., 2012). However, several recent studies have demonstrated that SADs can be accurately predicted by total species richness (γ-diversity) and total abundance, whose latitudinal variations are both likely driven by large-scale processes (Harte et al., 2008, 2009; White et al., 2012; Locey & White, 2013; McGlinn et al., 2013). For Gentry’s data set, the empirical SADs are remarkably similar to the predicted SADs calculated with γ-diversity and total abundance using a maximum entropy model (White et al., 2012). Using site-specific aggregation parameter k and the observed or predicted SADs, we estimated two values of β-diversity for each plot, respectively. The estimated β-diversity calculated with the predicted SADs accounts for 86.9% of the variation in the β-diversity calculated with the observed SADs (Fig. S5). Furthermore, because β-diversity is nearly independent from γ-diversity when controlling for the average abundance, the link of β-diversity to the SAD could be characterized approximately by the link to average abundance (Figs S1a, S2a & S3a). Both γ-diversity and total abundance have systematic vari- Global Ecology and Biogeography, 24, 1170–1180, © 2015 John Wiley & Sons Ltd 1177 W. Xu et al. ation along latitudinal gradients (Gaston, 2000; Fang et al., 2012; Qian et al., 2013), but since γ-diversity declines more rapidly with latitude than does total abundance, the average species abundance therefore increases with latitude (Qian et al., 2013), which may explain why β-diversity decreases with latitude. This fact also suggests that the latitudinal differences in γ-diversity and SADs are very closely tied together. Our results partly support the finding in Kraft et al. (2011) that latitudinal differences in γ-diversity have a crucial importance in explaining latitudinal gradients in β-diversity. A challenge in ecology is that most metrics of biodiversity, including β-diversity, are scale-dependent and are influenced by spatial extent and grain size (Loreau, 2000; Chase & Knight, 2013). Despite the small spatial scale of Gentry plots used in this study, it should capture the effects of fine-grained spatial aggregation on β-diversity, as reflected by the extensive positive β-deviation at nearly all plots (Fig. 4a). We recognize that, however, it does not capture the effects of coarse-grained spatial aggregation, which are structured by coarse-grained environmental heterogeneity and dispersal limitation. These processes may amplify the effects of aggregation on β-diversity at coarse scale. Indeed, the fraction of nonrandom β-diversity increases with the size of sampling unit across a global network of forest plots (De Cáceres et al., 2012). Nevertheless, the latitudinal gradients in β-diversity at broad scales may also be explained by latitudinal differences in SADs if the greater aggregation effects are consistent along latitudinal gradients. The relative contributions of the SAD and spatial aggregation in explaining latitudinal gradients in β-diversity at broader spatial scales needs to be evaluated in the future. In conclusion, because the β-deviation varies with both the SAD and the degree of aggregation, we cannot deduce whether the patterns of β-diversity along environmental gradients are driven by variations in spatial aggregation according to whether β-deviation varies systematically along these gradients. Our results show that the latitudinal gradients in β-deviation are explained mainly by the variation in SADs at the local spatial scale. Additionally, because the expected β-diversity is determined solely by the SAD, we suggest that the latitudinal patterns of β-diversity appear to be explained by latitudinal differences in SADs, whereas variation in spatial aggregation contributes little. The factors that cause latitudinal differences in SADs are likely the drivers of latitudinal patterns of β-diversity. ACKNOWLEDGEMENTS We are grateful to Associate Editor Dr. Andrés Baselga and two anonymous reviewers for their thoughtful comments, to Dr. Alwyn H. Gentry and his co-workers for collecting the plot data, to Drs. Xiangcheng Mi, Jens-Christian Svenning, Minggang Zhang, Yanjun Du and Haibao Ren for helpful discussions, to Drs. Hong Qian and Fangliang He for insightful comments on the earlier version of the manuscript, to Dr. Alison Beamish for her assistance with English language and grammar editing. 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(2012) Characterizing species abundance distributions across taxa and ecosystems using a simple maximum entropy model. Ecology, 93, 1772– 1778. Willig, M.R., Kaufman, D.M. & Stevens, R.D. (2003) Latitudinal gradients of biodiversity: pattern, process, scale, and synthesis. Annual Review of Ecology, Evolution, and Systematics, 34, 273– 309. S U P P O RT I N G I N F O R M AT I O N Additional supporting information may be found in the online version of this article at the publisher’s web-site. Figure S1 The relationship of β-diversity with average abundance, and of β-diversity and β-deviation with γ-diversity using log-series species abundance distribution. Figure S2 The relationship of β-diversity and β-deviation with average abundance and γ-diversity using log-normal species abundance distribution. Figure S3 The relationship of β-diversity and β-deviation with average abundance and γ-diversity using uniform species abundance distribution. 1180 Figure S4 The relationship of β-deviation, the fractions linked to the SAD and aggregation, and aggregation index 1/k with latitude in New World south when the three plots in high latitude were excluded. Figure S5 The relationship between two values of estimated β-diversity calculated with site specific aggregation parameter k and the observed or predicted SADs. Appendix S1 The R code for simulation. BIOSKETCHES Wubing Xu is a Ph.D. candidate at Institute of Botany, Chinese Academy of Sciences. He is interested in large-scale distribution of species diversity and the effects of species pool and mechanisms of community assembly. Keping Ma is a professor of ecology in Institute of Botany, Chinese Academy of Sciences. His research interests are mainly in species coexistence, biodiversity and ecosystem functioning, and large-scale species distribution patterns. Editor: Andres Baselga Global Ecology and Biogeography, 24, 1170–1180, © 2015 John Wiley & Sons Ltd