Download - Wiley Online Library

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. This work was supported by the National
Nature Science Foundation (41471044).
1178
REFERENCES
Anderson, M.J., Crist, T.O., Chase, J.M., Vellend, M., Inouye,
B.D., Freestone, A.L., Sanders, N.J., Cornell, H.V., Comita,
L.S., Davies, K.F., Harrison, S.P., Kraft, N.J.B., Stegen, J.C. &
Swenson, N.G. (2011) Navigating the multiple meanings of β
diversity: a roadmap for the practicing ecologist. Ecology
Letters, 14, 19–28.
Arita, H.T. & Rodríguez, P. (2004) Local-regional relationships
and the geographical distribution of species. Global Ecology
and Biogeography, 13, 15–21.
Buckley, L.B. & Jetz, W. (2008) Linking global turnover
of species and environments. Proceedings of the National
Academy of Sciences USA, 105, 17836–17841.
Chase, J.M. (2010) Stochastic community assembly causes
higher biodiversity in more productive environments. Science,
328, 1388–1391.
Chase, J.M. & Knight, T.M. (2013) Scale-dependent effect sizes
of ecological drivers on biodiversity: why standardised sampling is not enough. Ecology Letters, 16, 17–26.
Cheng, J.J., Mi, X.C., Nadrowski, K., Ren, H.B., Zhang, J.L. & Ma,
K.P. (2012) Separating the effect of mechanisms shaping
species-abundance distributions at multiple scales in a subtropical forest. Oikos, 121, 236–244.
Condit, R., Ashton, P.S., Baker, P., Bunyavejchewin, S.,
Gunatilleke, S., Gunatilleke, N., Hubbell, S.P., Foster, R.B.,
Itoh, A., LaFrankie, J.V., Lee, H.S., Losos, E., Manokaran, N.,
Sukumar, R. & Yamakura, T. (2000) Spatial patterns in
the distribution of tropical tree species. Science, 288, 1414–
1418.
Condit, R., Pitman, N., Leigh, E.G., Chave, J., Terborgh, J.,
Foster, R.B., Núnez, P., Aguilar, S., Valencia, R., Villa, G.,
Muller-Landau, H.C., Losos, E. & Hubbell, S.P. (2002) Betadiversity in tropical forest trees. Science, 295, 666–669.
Crawley, M.J. & Harral, J.E. (2001) Scale dependence in plant
biodiversity. Science, 291, 864–868.
Crist, T.O., Veech, J.A., Gering, J.C. & Summerville, K.S. (2003)
Partitioning species diversity across landscapes and regions: a
hierarchical analysis of α, β, and γ diversity. The American
Naturalist, 162, 734–743.
De Cáceres, M., Legendre, P., Valencia, R. et al. (2012) The variation of tree beta diversity across a global network of forest
plots. Global Ecology and Biogeography, 21, 1191–1202.
Fang, J., Shen, Z., Tang, Z., Wang, X., Wang, Z., Feng, J., Liu, Y.,
Qiao, X., Wu, X. & Zheng, C. (2012) Forest community
survey and the structural characteristics of forests in China.
Ecography, 35, 1059–1071.
Gaston, K.J. (2000) Global patterns in biodiversity. Nature, 405,
220–227.
Gaston, K.J. & He, F. (2011) Species occurrence and occupancy.
Biological diversity: frontiers in measurement and assessment
(ed. by A.E. Magurran and B.J. McGill), pp. 141–151. Oxford
University Press, Oxford.
Harte, J., Zillio, T., Conlisk, E. & Smith, A.B. (2008) Maximum
entropy and the state-variable approach to macroecology.
Ecology, 89, 2700–2711.
Global Ecology and Biogeography, 24, 1170–1180, © 2015 John Wiley & Sons Ltd
Latitudinal gradients of β-diversity
Harte, J., Smith, A.B. & Storch, D. (2009) Biodiversity scales
from plots to biomes with a universal species-area curve.
Ecology Letters, 12, 789–797.
Hawkins, B.A., Field, R., Cornell, H.V., Currie, D.J., Guégan, J.-F.,
Kaufman, D.M., Kerr, J.T., Mittelbach, G.G., Oberdorff, T.,
O’Brien, E.M., Porter, E.E. & Turner, J.R.G. (2003) Energy,
water, and broad-scale geographic patterns of species richness. Ecology, 84, 3105–3117.
He, F. & Gaston, K.J. (2000) Estimating species abundance from
occurrence. The American Naturalist, 156, 553–559.
He, F. & Gaston, K.J. (2003) Occupancy, spatial variance, and the
abundance of species. The American Naturalist, 162, 366–375.
He, F. & Legendre, P. (2002) Species diversity patterns derived
from species-area models. Ecology, 83, 1185–1198.
He, F., Gaston, K.J. & Wu, J. (2002) On species occupancyabundance models. Ecoscience, 9, 119–126.
Hubbell, S.P. (2001) The unified neutral theory of biodiversity and
biogeography. Princeton University Press, Princeton, NJ.
Hui, C., McGeoch, M.A. & Warren, M. (2006) A spatially explicit
approach to estimating species occupancy and spatial correlation. Journal of Animal Ecology, 75, 140–147.
Johnson, D.J., Beaulieu, W.T., Bever, J.D. & Clay, K. (2012)
Conspecific negative density dependence and forest diversity.
Science, 336, 904–907.
Karlson, R.H., Connolly, S.R. & Hughes, T.P. (2011) Spatial variance in abundance and occupancy of corals across broad geographic scales. Ecology, 92, 1282–1291.
Kraft, N.J.B., Comita, L.S., Chase, J.M., Sanders, N.J., Swenson,
N.G., Crist, T.O., Stegen, J.C., Vellend, M., Boyle, B., Anderson,
M.J., Cornell, H.V., Davies, K.F., Freestone, A.L., Inouye, B.D.,
Harrison, S.P. & Myers, J.A. (2011) Disentangling the drivers
of beta diversity along latitudinal and elevational gradients.
Science, 333, 1755–1758.
Krebs, C.J. (1999) Ecological methodology, 2nd edn. Addison
Wesley Educational Publishers, Menlo Park.
Kůrka, P., Šizling, A.L. & Rosindell, J. (2010) Analytical evidence
for scale-invariance in the shape of species abundance distributions. Mathematical Biosciences, 223, 151–159.
Legendre, P., Mi, X., Ren, H., Ma, K., Yu, M., Sun, I.-F. & He, F.
(2009) Partitioning beta diversity in a subtropical broadleaved forest of China. Ecology, 90, 663–674.
Locey, K.J. & White, E.P. (2013) How species richness and total
abundance constrain the distribution of abundance. Ecology
Letters, 16, 1177–1185.
Loreau, M. (2000) Are communities saturated? On the relationship between α, β and γ diversity. Ecology Letters, 3, 73–76.
McGill, B.J., Etienne, R.S., Gray, J.S., Alonso, D., Anderson, M.J.,
Benecha, H.K., Dornelas, M., Enquist, B.J., Green, J.L., He, F.,
Hurlbert, A.H., Magurran, A.E., Marquet, P.A., Maurer, B.A.,
Ostling, A., Soykan, C.U., Ugland, K.I. & White, E.P. (2007)
Species abundance distributions: moving beyond single
prediction theories to integration within an ecological framework. Ecology Letters, 10, 995–1015.
McGlinn, D.J., Xiao, X. & White, E.P. (2013) An empirical evaluation of four variants of a universal species-area relationship.
PeerJ, 1, e212.
Mittelbach, G.G., Schemske, D.W., Cornell, H.V. et al.
(2007) Evolution and the latitudinal diversity gradient:
speciation, extinction and biogeography. Ecology Letters, 10,
315–331.
Mori, A.S., Shiono, T., Koide, D., Kitagawa, R., Ota, A.T. &
Mizumachi, E. (2013) Community assembly processes shape
an altitudinal gradient of forest biodiversity. Global Ecology
and Biogeography, 22, 878–888.
Morlon, H., Chuyong, G., Condit, R., Hubbell, S., Kenfack, D.,
Thomas, D., Valencia, R. & Green, J.L. (2008) A general framework for the distance–decay of similarity in ecological communities. Ecology Letters, 11, 904–917.
Myers, J.A., Chase, J.M., Jiménez, I., Jørgensen, P.M.,
Araujo-Murakami, A., Paniagua-Zambrana, N. & Seidel, R.
(2013) Beta-diversity in temperate and tropical forests reflects
dissimilar mechanisms of community assembly. Ecology
Letters, 16, 151–157.
Okuda, T., Noda, T., Yamamoto, T., Hori, M. & Nakaoka, M.
(2009) Latitudinal gradients in species richness in assemblages of sessile animals in rocky intertidal zone: mechanisms
determining scale-dependent variability. Journal of Animal
Ecology, 78, 328–337.
Phillips, O. & Miller, J.S. (2002) Global patterns of plant diversity:
Alwyn H. Gentry’s forest transect data set. Missouri Botanical
Press, St Louis, MO.
Qian, H. & Ricklefs, R.E. (2007) A latitudinal gradient in largescale beta diversity for vascular plants in North America.
Ecology Letters, 10, 737–744.
Qian, H., Chen, S., Mao, L. & Ouyang, Z. (2013) Drivers
of β-diversity along latitudinal gradients revisited. Global
Ecology and Biogeography, 22, 659–670.
Qiao, X., Tang, Z., Wang, S., Liu, Y. & Fang, J. (2012) Effects of
community structure on the species-area relationship in
China’s forests. Ecography, 35, 1117–1123.
Rosenzweig, M.L. (1995) Species diversity in space and time.
Cambridge University Press, London.
Šizling, A.L., Storch, D., Šizlingová, E., Reif, J. & Gaston, K.J.
(2009) Species abundance distribution results from a spatial
analogy of central limit theorem. Proceedings of the National
Academy of Sciences USA, 106, 6691–6695.
Šizling, A.L., Kunin, W.E., Šizlingová, E., Reif, J. & Storch, D.
(2011) Between geometry and biology: the problem of universality of the species-area relationship. The American Naturalist, 178, 602–611.
Stegen, J.C., Freestone, A.L., Crist, T.O., Anderson, M.J., Chase,
J.M., Comita, L.S., Cornell, H.V., Davies, K.F., Harrison, S.P.,
Hurlbert, A.H., Inouye, B.D., Kraft, N.J.B., Myers, J.A.,
Sanders, N.J., Swenson, N.G. & Vellend, M. (2013) Stochastic
and deterministic drivers of spatial and temporal turnover in
breeding bird communities. Global Ecology and Biogeography,
22, 202–212.
Tang, Z., Fang, J., Chi, X., Feng, J., Liu, Y., Shen, Z., Wang, X.,
Wang, Z., Wu, X., Zheng, C. & Gasten, K.J. (2012) Patterns
of plant beta-diversity along elevational and latitudinal
gradients in mountain forests of China. Ecography, 35, 1083–
1091.
Global Ecology and Biogeography, 24, 1170–1180, © 2015 John Wiley & Sons Ltd
1179
W. Xu et al.
Tjørve, E., Kunin, W.E., Polce, C. & Tjørve, K.M.C. (2008)
Species-area relationship: separating the effects of species
abundance and spatial distribution. Journal of Ecology, 96,
1141–1151.
White, E.P., Thibault, K.M. & Xiao, X. (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