Putting Beta-Diversity on the Map:
Broad-Scale Congruence and Coincidence
in the Extremes
Meghan W. McKnight1*, Peter S. White2, Robert I. McDonald3, John F. Lamoreux4,5, Wes Sechrest6,
Robert S. Ridgely7, Simon N. Stuart4
1 Curriculum in Ecology, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America, 2 Department of Biology, University of North Carolina
at Chapel Hill, Chapel Hill, North Carolina, United States of America, 3 Graduate School of Design, Harvard University, Cambridge, Massachusetts, United States of America,
4 IUCN/SSC–CI/CABS Biodiversity Assessment Unit, Conservation International, Arlington, Virginia, United States of America, 5 Department of Wildlife and Fisheries Sciences,
Texas A&M University, College Station, Texas, United States of America, 6 Department of Environmental Sciences, University of Virginia, Charlottesville, Virginia, United States
of America, 7 World Land Trust–US, Deerfield, New Hampshire, United States of America
Beta-diversity, the change in species composition between places, is a critical but poorly understood component of
biological diversity. Patterns of beta-diversity provide information central to many ecological and evolutionary
questions, as well as to conservation planning. Yet beta-diversity is rarely studied across large extents, and the degree
of similarity of patterns among taxa at such scales remains untested. To our knowledge, this is the first broad-scale
analysis of cross-taxon congruence in beta-diversity, and introduces a new method to map beta-diversity continuously
across regions. Congruence between amphibian, bird, and mammal beta-diversity in the Western Hemisphere varies
with both geographic location and spatial extent. We demonstrate that areas of high beta-diversity for the three taxa
largely coincide, but areas of low beta-diversity exhibit little overlap. These findings suggest that similar processes
lead to high levels of differentiation in amphibian, bird, and mammal assemblages, while the ecological and
biogeographic factors influencing homogeneity in vertebrate assemblages vary. Knowledge of beta-diversity
congruence can help formulate hypotheses about the mechanisms governing regional diversity patterns and should
inform conservation, especially as threat from global climate change increases.
PLoS Biol 5(10): e272. doi:10.1371/journal.pbio.0050272
Beta-diversity, the change in species composition between
places, represents the differentiation component of diversity,
as opposed to the inventory component, which describes the
species composition of a single place [1–3]. Although beta-
diversity was originally defined as the differentiation of
communities along environmental gradients , the concept
applies more widely to the phenomenon of species composi-
tional change at any scale, regardless of mechanism [2–7].
Beta-diversity sensu lato is determined through a complex
array of processes relating to the interaction of species traits
(e.g., vagility and niche width) and characteristics of the
physical landscape (e.g., environmental dissimilarity, topo-
graphic complexity, and isolation) over time [3,8–11]. Geo-
graphic variation in beta-diversity, from gradual changes to
abrupt transitions, reflects past and present differences in
environment, ecological interactions, and biogeographic
history, including barriers to dispersal [4,7,9–15].
As beta-diversity quantifies the change, or turnover, in
species across space, it is central to a wide array of ecological
and evolutionary topics, such as the scaling of diversity [16–
19], the delineation of biotic regions or biotic transitions
[20,21], and the mechanisms through which regional biotas are
formed [15,20–22]. Beta-diversity also provides information
critical to conservation planning, which strives to represent all
biodiversity within practical constraints such as area and cost
[11,14,16,23,24]. While the total number of species, endemic
species, or threatened species often contributes to the relative
importance of an area [25–29], it is the rate of species turnover
between sites that dictates the optimal spatial arrangement of
conservation areas [10,11,16]. Although the principles behind
most approaches to systematic planning, such as complemen-
tarity, are driven by patterns of beta-diversity [23,30], few
methods make explicit use of turnover measures [6,31].
Directly incorporating beta-diversity patterns into priority
setting, however, benefits conservation efforts. For example,
modeling compositional dissimilarity to develop surrogates
for data-poor regions can improve biodiversity representa-
tion [6,30,32]. Moreover, including turnover estimates in area
selection algorithms captures variation inspecies assemblages,
which helps to preserve ecological and evolutionary processes
as well as underlying environmental heterogeneity necessary
for long-term persistence [28,31].
Despite the importance of beta-diversity, relatively little is
known about diversity’s ‘‘other component,’’ particularly at
Academic Editor: Georgina M. Mace, Imperial College London, United Kingdom
Received May 15, 2006; Accepted August 17, 2007; Published October 9, 2007
Copyright: ? 2007 McKnight et al. This is an open-access article distributed under
the terms of the Creative Commons Attribution License, which permits unrestricted
use, distribution, and reproduction in any medium, provided the original author
and source are credited.
Abbreviations: ess, estimated sample size
* To whom correspondence should be addressed. E-mail: meghan.mcknight@
PLoS Biology | www.plosbiology.orgOctober 2007 | Volume 5 | Issue 10 | e2722424
P PL Lo oS S BIOLOGY
broad scales. This is largely because measures of beta-diversity
require knowledge of species identities rather than just
species counts. Recent advances in species distributional data
have made beta-diversity analyses possible at large extents
[17,20,21], but these studies have been limited to single taxa.
Cross-taxon congruence in beta-diversity has been tested only
at small scales, with varying methods and results [14,22,32,33],
in contrast to the wide range of scales at which concordance in
both species richness and endemism has been studied [34–38].
Here, we present what is to our knowledge the first analysis of
beta-diversity congruence across large spatial scales, based on
distributional data for three groups of terrestrial vertebrates
in the continental Western Hemisphere.
Beta-diversity of amphibians (n¼2,174) , breeding birds
(n¼3,882) , and mammals (n¼1,611)  was estimated as
a function of the distance decay of similarity—the decrease in
compositional similarity with increasing geographic distance
between sites [4,7,10,14]. We modeled distance decay from
each 100 km 3 100 km grid cell, and used these models to
calculate our measure of beta-diversity, bsim-d: the estimated
proportional turnover in species composition at a distance of
100 km (see Materials and Methods). This individual-cell-
based technique accounts for the considerable geographic
variation in the rate at which similarity decays, and can be
used to produce a continuous layer of compositional change
similar to past grid-based neighborhood analyses of broad-
scale beta-diversity (e.g., [18,20,21]). Considering comparisons
over a range of distances reduces possible bias in similarity
levels that could arise from the differences in centroid to
centroid distance and in shared perimeter length that occur
between orthogonal and diagonal neighbors of a rectangular
grid. The smoothing that results from the distance decay
regressions also limits the influence of artifacts due to small-
scale errors in range map boundary placement.
Our approach to quantifying the distance decay relation-
ship makes several improvements to methods used in
previous studies [4,7,10,14]. For instance, we modeled
distance decay using logistic regression, which has advantages
over linear or log-linear ordinary least-square regressions
[4,7,14], particularly for proportional data . Furthermore,
following Lennon et al. , we measured similarity with a
metric shown to be independent of differences in species
richness between grid cells in order to isolate change due to
species replacement  (see Materials and Methods).
We tested congruence in bsim-dfor the three taxa using two
different approaches. With the first, we measured congruence
in overall bsim-dpatterns and examined whether congruence
levels were consistent across multiple spatial extents and
among different geographic locations. In the second ap-
proach, we quantified spatial overlap in the extremes of bsim-d.
We report that the strength of congruence depends on the
location and extent at which it is measured, and that overlap
in high bsim-dis much greater than in low bsim-d. Furthermore,
the pairs of taxa varied substantially in level of congruence
and degree of overlap.
Amphibian, bird, and mammal bsim-dmapped at this scale
(Figure 1) provide a striking contrast to well-known patterns
of broad-scale species richness for these vertebrate groups.
Whereas high richness is generally concentrated in the tropics
and decreases towards both poles , bsim-dof all levels is
found across a wide range of latitudes. High bsim-dstretches
along the mountainous Pacific edge of the continents, while
low bsim-d is found within more environmentally uniform
portions of northern South America and boreal North
America. Accordingly, bsim-dhas a positive relationship with
both elevation and number of biome boundaries (bsim-dand
elevation: Spearman rank q ¼ 0.219–0.427, p , 0.05 for
amphibian bsim-d, p , 0.001 for other taxa; bsim-dand biome
edge: q¼0.295–0.320, p , 0.001 for all; Table S1; see Materials
and Methods). Although the variables show considerable
spread (Figure S1), high bsim-dgrid cells of all three groups
occur at significantly higher elevations and on a greater
number of biome edges than expected by chance alone, while
low bsim-dgrid cells have significantly lower elevations and
fewer biome edges than expected by chance (Table S2; 10,000
random sets, p , 0.05 for elevation in amphibian low bsim-d
grid cells, p , 0.001 for all others; see Materials and Methods).
The weaker significance for elevation in amphibian low bsim-d
grid cells is likely due to the wood frog (Rana sylvatica) being
the only amphibian species to occur throughout much of the
boreal region, including high-altitude areas such as the Alaska
panhandle . This amphibian homogeneity differs greatly
from the high bsim-dof birds at northern latitudes, which
captures the presence of a strong Holarctic element in the
avifauna along the arctic coast . Such differences in bsim-d
reveal the individual biogeographic histories of the taxa and
may arise from variation in dispersal ability, particularly in
relation to historical factors such as glaciation and faunal
interchange [45,47]. For instance, the elevated mammal bsim-d
in South America’s southern cone reflects a transition in the
region’s diverse mammal lineages, notably the radiation of
narrowly ranging hystricognath rodents , while the high
amphibian bsim-d of the southern Appalachian Mountains
results from the diversification of salamanders within this
area’s stable, moist environments .
Congruence in Overall bsim-dPatterns
Pair-wise correlations of amphibian, bird, and mammal
bsim-d across the Western Hemisphere were positive and
significant (q ¼ 0.340–0.553, p , 0.001 for all; see Materials
and Methods) (Table 1; Figure 2). When measured at the
extent of a single biogeographic realm, however, we found
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Broad-Scale Beta-Diversity Congruence
Beta-diversity—how species composition varies from place to
place—is a fundamental attribute of biodiversity. However, despite
its recognized importance, beta-diversity is rarely studied across
large spatial scales. Here we use a new method to compare
amphibian, bird, and mammal beta-diversity across large regions
within the Western Hemisphere. We show that although the areas of
low beta-diversity are different for the three groups, areas of high
beta-diversity largely coincide. Moreover, we find that the degree to
which the groups exhibit similar patterns of beta-diversity depends
on the geographic location and extent at which it is measured. Beta-
diversity is high where species are most susceptible to climate
change, such as in areas with complex topography or high
environmental variation. Identifying where areas of high beta-
diversity coincide for different species groups is essential to the
design of effective protected area networks.
that pair-wise congruence was greater within the Neotropics
(q ¼ 0.636–0.695, p , 0.001 for all) than at the hemisphere
extent, but was comparatively weak within the Nearctic
(amphibians and mammals: q ¼ 0.390, p , 0.05; birds and
mammals: q ¼ 0.405, p , 0.001) or even lacking (amphibians
and birds: q ¼ 0.032, not significant) (Table 1; Figure 2). The
disparity in congruence strength between the realms indi-
cates that congruence measured across large regions can hide
incongruities that manifest at reduced spatial extents [35,36].
To examine congruence at even smaller extents, we used a
moving-window algorithm that calculated the correlation in
bsim-dbetween each pair of taxa within a 350-km radius of
each grid cell (see Materials and Methods). Composite maps
of the resulting correlation coefficients for the pairs revealed
considerable geographic variation in congruence (Figure 3).
Although the majority of correlations were strongly positive,
others were weak or strongly negative. The latter were most
apparent in the Nearctic realm for correlations with
amphibians. Understanding the dependence of diversity
relationships on observational scale is of pressing concern
for ecology, biogeography, and conservation planning
[10,18,23,36]. Our analyses demonstrate that both the geo-
graphic location and the spatial extent of analysis affect the
level of congruence observed in bsim-d, and emphasize the
need for tests across multiple scales and regions in order to
make objective comparisons among ecological studies.
Spatial Overlap in High and Low bsim-d
Correlations across all grid cells do not necessarily indicate
the level of cross-taxon spatial coincidence in areas of highest
or lowest bsim-d—a more useful measure for conservation
planning and biogeographic delineation [34,35,49]. Congru-
ence in the extremes of diversity is frequently measured as
Table 1. Correlations in Beta-Diversity (bsim-d) within the Western Hemisphere, Nearctic Realm, and Neotropical Realm
ExtentAmphibians and Birds Amphibians and MammalsBirds and Mammals
Spearman rank correlation coefficients (q), number of grid cells (n), and corrected sample size (ess) for each pair-wise comparison are shown.
*, p , 0.05; **, p , 0.001.
Figure 1. Beta-Diversity of Amphibians, Birds, and Mammals Mapped Continuously across the Continental Western Hemisphere
Beta-diversity (bsim-d) values for each taxon are divided into 20 quantiles, represented by warm (higher bsim-d) to cool (lower bsim-d) colors. The scale
accompanying the color ramp for each taxon shows minimum, first quartile, median, third quartile, and maximum values of bsim-d. Gray grid cells do not
contain amphibian species. (A) Amphibians. (B) Birds. (C) Mammals.
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Broad-Scale Beta-Diversity Congruence
the degree of overlap in matching percentage sets of two
groups [34,50]. We evaluated high and low bsim-dcongruence
for the pairs of taxa and between all three groups as the
proportion of maximum possible overlap  in matching
percentage sets of the highest 2.5% and lowest 2.5% of each
taxon’s bsim-dgrid cells (see Materials and Methods).
Spatial coincidence in high bsim-d was greatest between
amphibians and birds (51.6%). These taxa showed lower, but
similar levels of overlap in high bsim-dwith mammals (21.5%
and 29.2%, respectively), and coincidence between all three
groups was minimal (15.1%). Grid cells with overlapping high
bsim-dprimarily occurred in the northern and southern Andes
(Figure 4), consistent with the former as a center of endemism
for all three taxa and with the extreme climatic gradient
within the latter [44,45]. A substantial proportion of grid cells
were found only in the high bsim-dpercentage sets of one
taxon. For example, 41.9% of amphibian high bsim-dgrid cells
were unique, as were 35.4% of bird high bsim-dgrid cells and
64.6% of mammal high bsim-dgrid cells. The distribution of
these grid cells reflects the specific biogeographies of each
taxon. Whereas unique grid cells were predominantly located
in the northern Andes for birds and in the Central American
highlands for amphibians, unique mammal grid cells were
largely outside the tropics (Figure 4).
There was comparatively little spatial coincidence in the
lowest 2.5% of bsim-d. Low bsim-d of birds and mammals
showed the most overlap, at only 11.5%. Coincidence was
negligible for the other two pairs of taxa (amphibians and
mammals, 5.4%; amphibians and birds, 2.2%), and there was
no overlap among all three groups. Accordingly, the majority
of grid cells in the low bsim-dpercentage sets were restricted
to one taxon (83.3%–92.5%). These grid cells were located
mainly in the boreal and arctic regions of the Nearctic realm
for amphibians and mammals, respectively (Figure 4). Con-
versely, most unique bird grid cells occurred in the Neo-
tropics within several biomes, including a substantial number
in the Amazon Basin (Figure 4).
The degree of overlap in matching percentage sets,
however, does not provide a complete picture of spatial
coincidence in the extremes of bsim-d. In fact, the majority of
highest bsim-dgrid cells for all three taxa actually had relatively
high levels of bsim-dfor the other groups (Figure 5), indicating
that areas of high beta-diversity largely coincide. On average,
more than two-thirds of grid cells in the highest 2.5% of one
taxon’s bsim-dgrid cells were also in the highest 10% of bsim-d
for the other taxa (70.0% 6 8.7%, range ¼ 61.5%–81.7%).
This was not true for low bsim-d. Low bsim-dgrid cell sets
exhibited greater variation in bsim-dvalues for the other taxa
than did the high bsim-dsets. Moreover, less than one-quarter
of the lowest 2.5% of one taxon’s bsim-dgrid cells were in the
lowest 10% of bsim-d for the other taxa (21.9% 6 14.6%,
range ¼ 2.9%–40.6%)—further evidence that areas of low
bsim-dare spatially distinct (Figure 5).
Figure 2. Cross-Taxon Relationships in Beta-Diversity of Amphibians, Birds, and Mammals
and the Neotropical realm (NT, bottom row). The axes for each plot are scaled according to the maximum bsim-dvalue of the two taxa within the extent
specified. Note that maximum values are much greater for amphibians than for either birds or mammals and that all three taxa reach higher rates of
assemblage change in the Neotropics than in the Nearctic. (A) Amphibians and birds. (B) Amphibians and mammals. (C) Birds and mammals.
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Broad-Scale Beta-Diversity Congruence
Congruence in beta-diversity of three groups of terrestrial
extent of analysis, reflecting taxonomic and regional variation
mental factors [4,7,10,14,15]. Our results show that although
correlations in amphibian, bird, and mammal bsim-dmeasured
at small extents vary in strength throughout the Western
Hemisphere, congruence is generally stronger within the
Neotropical realm than within the Nearctic. This difference
may be part of a broader asymmetry in biodiversity patterns
between the Northern Hemisphere and the Southern Hemi-
sphere [51,52]. The weak pair-wise correlations within the
Nearctic realm,as wellas theminimal overlapin bothhigh and
in the Neotropics is indicative of common patterns of
speciation and extinction histories. This is particularly appa-
rent within the Neotropical mountains, where the substantial
overlap in high bsim-damong the three groups underscores the
importance of this region in generating diversity. Variation in
bsim-d congruence also has implications for conservation,
because the efficacy of conservation surrogates and efforts to
model overall biodiversity distribution depend on taxa having
concordant patterns of compositional change . Our results
largely support these approaches, but it is important to
levels among biogeographic realms.
Regions of rapid species turnover require increased
attention to the placement and size of conservation areas in
order to protect biodiversity. Spatial coincidence in areas of
high bsim-dis therefore encouraging, as successful conserva-
tion strategies in these places may be resource intensive.
Conservation planning, of course, must occur across hier-
archical scales in order to ensure adequate representation
[23,28]. Broad-scale analyses of bsim-dhighlight regions where
protected areas should be closely spaced to effectively
conserve biodiversity; however, the optimal configuration
for conservation networks will depend on finer-scale beta-
diversity patterns . Mapping broad-scale bsim-dcan also
identify areas where species face increasing threat to
persistence. For example, because bsim-dis high where species’
ranges are particularly susceptible to climatic variability, such
as at steep environmental gradients and centers of endemism
[54–56], or at biome transitions where range shifts are most
noticeable [54,55], we suggest that areas of high bsim-dare
likely to be especially vulnerable to climate change.
The unique biogeography of the Western Hemisphere—the
great variation in the effects of Pleistocene glaciation, the
complex of mountain chains along much of the western coast,
and the relative isolation of the continents—has played a
major role in shaping the distribution and evolution of
biodiversity. More work is needed to determine if our findings
will extend to other parts of the world with different geologic
and environmental histories. Furthermore, the relative con-
tribution of historical factors and current ecological inter-
in beta-diversity across taxa is an important area of inquiry.
Our results describe patterns of species turnover at a
100 km 3 100 km resolution. As comprehensive finer-
resolution data become available, further analyses will
confirm whether the levels of beta-diversity and congruence
we found are consistent with those measured at smaller grain
sizes. Future research is also needed to ascertain the degree to
which our results can be generalized to other taxa, especially
Figure 3. Geographic Variation in Beta-Diversity Congruence of
Amphibians, Birds, and Mammals at Small Spatial Extents
The color of each grid cell indicates the strength of beta-diversity (bsim-d)
congruence calculated within a 350-km-radius window around that grid
cell. Orange shades represent strong (darkest) to weak (lightest) negative
correlations. Purple shades show strong (darkest) to weak (lightest)
positive correlations. Dark gray indicates very weak correlations of either
sign, or no correlation. Light gray grid cells do not contain amphibian
species. Shown to the right of each map are frequency distributions of
correlation coefficients for windows located within the entire Western
Hemisphere (WH), the Nearctic realm (NA), and the Neotropical realm
(NT), which are consistent with the overall level of congruence measured
at these extents. The black line marks the boundary between the
two realms. (A) Amphibians and birds. (B) Amphibians and mammals.
(C) Birds and mammals.
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Broad-Scale Beta-Diversity Congruence
more distantly related groups or those that show large
variation in dispersal ability. For instance, taxa with poor
dispersal and low rates of gene flow are apt to exhibit higher
beta-diversity than those groups that have high dispersal and
high rates of gene flow. However, we believe that some of our
findings, such as the strong relationship between topography
and beta-diversity congruence, will prove true for most taxa.
Materials and Methods
Data. Analyses were based on range data for extant species of
in the Western Hemisphere [39–41]. The range maps used for this study
were obtained as digital vector files (ArcView format) from the Web sites
indicated by [39–41], where one can also find information on updates,
detailed descriptions of the production process, and complete lists of
sources. Note that these datasets are periodically updated, and the
files used for these analyses may differ from the most recent versions
available from [39–41]. We confined our analyses to terrestrial
breeding birds, and we provide a map of bird bsim-dbased on both
breeding and non-breeding ranges of all terrestrial birds (n ¼ 3,890)
for comparison. bsim-dfor all birds (Figure S2) was highly correlated
with bsim-dfor breeding birds (Figure 1) (q ¼ 0.954, estimated sample
size [ess] ¼ 249.12, p , 0.001). The number of species in these
vertebrate groups is not static, as new species, especially of
amphibians, continue to be discovered . However, the areas from
which species are most often described tend to be the same and will
likely accentuate the patterns we present . In relation to this
point, systematic bias in the data may result from differences in
sampling efforts, as the distributions of certain groups (e.g., birds) or
geographic areas (e.g., temperate regions) for which sampling efforts
have been intense will be more reliable than those that are
undersampled (e.g., amphibians or tropical regions). As a precaution
against such bias, we excluded from the analyses the 630 amphibian
Figure 5. Levels of Beta-Diversity for Vertebrate Taxa within Areas of High and Low Beta-Diversity of Amphibians, Birds, and Mammals
Percentage sets of the highest (A) and lowest (B) 2.5% of beta-diversity (bsim-d) grid cells for one taxon (x-axis) contain a range of bsim-dlevels for the
other taxa (y-axis), as shown by the box plots (white lines within boxes indicate the median; top and bottom box edges indicate first and third quartiles;
black lines indicate minimum and maximum percentage rank of bsim-d). The red dashed line indicates the highest or lowest 10% of bsim-d.
Figure 4. Geographic Distribution of Amphibian, Bird, and Mammal High and Low Beta-Diversity Overlap
Spatial overlap in beta-diversity (bsim-d) for percentage sets of each taxon’s lowest (left) and highest (right) 2.5% of bsim-dgrid cells is shown. Primary
colors indicate grid cells unique to one taxon (yellow, amphibians; blue, birds; red, mammals), secondary colors indicate overlap between two groups,
and white indicates overlap of all three groups. The height of the grid cells reflects the number of overlapping groups. Note the greater degree of
spatial coincidence in high bsim-dthan in low bsim-d.
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Broad-Scale Beta-Diversity Congruence
species with an IUCN Red List category of ‘‘data deficient’’ (http://
www.redlist.org/) because of the unreliability of their range maps. The
exclusion of these species did not substantially affect our results
(correlation between amphibian bsim-dusing all mapped species and
amphibian bsim-d excluding ‘‘data deficient’’ species; q ¼ 0.993,
ess ¼ 158.6, p , 0.001).
equal-area grid cells, roughly equivalent to 18 3 18 at the equator
(Behrmann projection, WGS84 datum); a species was considered
present if any portion of its range (exclusive of polygons coded as
area of the grid cell. However, the range maps used approximate the
the mapped range [59,60]. Such biases are inherent in range data
compiled across large regions, and remind us that while the patterns
a replacement for finer-scale distributional information.
Grid cells on the perimeter of the continents vary considerably in
the amount of land they contain, particularly those along the narrow
Isthmus of Panama. To avoid potential effects of species–area
relationships or errors from range map boundary placement, only
grid cells containing ?40% of continental land were included in the
analyses (grid cells: n ¼ 3,693 for amphibians; n ¼ 3,821 for birds and
mammals). Estimates of bsim-dusing this cutoff were not appreciably
different from those based on a more conservative cutoff of 75% land
area, but allowed for the inclusion of additional species. Grid cells
were classified as either Nearctic (n¼1,744 for amphibians; n¼1,862
for birds and mammals), Neotropical (n ¼ 1,878, amphibians; n ¼
1,888, birds and mammals), or transitional between the two biogeo-
graphic realms (n ¼ 71 for all taxa) . Transitional grid cells were
not included in analyses at the realm extent.
Analyses. We used a moving-window algorithm to model the
distance decay of similarity from each individual grid cell, and used
the resulting regression parameters to calculate a value of beta-
diversity, bsim-d, as the estimated proportional turnover from that
grid cell at a distance of 100 km. Considering comparisons between
grid cells over a range of distances helps alleviate concerns typical of
gridded nearest-neighbor analyses of large-scale species distributions.
For example, artifacts may arise from the small-scale errors that can
occur in range boundary placement when converting polygon maps
into gridded data, as well as from the discrepancy in centroid to
centroid distance and shared perimeter length between orthogonal
and diagonal neighbors in a rectangular grid.
Similarity (S) between two grid cells was calculated as the
complement of bsim, a dissimilarity metric that isolates change due
to species replacement from differences in species richness:
a þ minðb;cÞ;
where a is the number of species shared, b is the number of species
found only in the second grid cell, and c is the number of species
found only in the first grid cell, making min(b, c) the number of
unshared species in the more depauperate grid cell [18,43].
Therefore, as the complement of bsim(i.e., 1 ? bsim),
S ¼ 1 ? bsim¼
a þ minðb;cÞ;
or the proportion of species in the more depauperate grid cell that
also occur in the other grid cell.
Note that S/1?S is a transformation of the ratio of shared species
to unshared species in the more depauperate grid cell, or a/min(b, c).
This enables us to model distance decay using a logistic regression
functional form defined such that
where d is the centroid to centroid distance, and I and r are fitted
intercept and slope coefficients. This functional form has an
advantage over linear and log-linear forms, in that S^is bound between
zero and one, as is appropriate for a similarity index. The observed
data are counts, and we use a binomial error distribution for our
regression. This has several advantages over linear and log-linear
regressions with a normal error distribution, resulting in a better
empirical fit than other techniques . First, the special cases where
estimation process, as these are valid possibilities under the binomial
distribution. Second, the binomial error distribution accounts for the
greater variance in a/min(b, c) (and hence S) at low species numbers.
¼ I þ r3ln d ð Þ;
The distance decay regression at each window was built using
between-grid-cell comparisons of the focal grid cell and all grid cells
within a ?500-km centroid to centroid radius. Thus, unlike most
published distance decay regressions, which compute a rate of change
based on comparisons between all samples within a region, our
regressions are based on comparisons only with the focal grid cell and
therefore reflect the change from a particular point (i.e., grid cell).
The arbitrary distance of 500 km was chosen after experimenting
with several other maximum distances (350, 1,000, 1,500, 2,000, and
3,000 km) because it provided a sufficient total number of between-
grid comparisons (i.e., sample size), spread over a range of distances,
to ensure a robust distance decay relationship, but did not result in
an over-smoothed beta-diversity surface, as occurred with greater
maximum distances (as judged by visual comparisons of the maps). By
transforming the above defined regression equation as
1 ? S^d ¼
it is possible to use any set of distance decay regression coefficients
(I and r) to predict the proportional dissimilarity at any distance (d).
Thus, we used the coefficients from the distance decay regression for
each grid cell to estimate our measure of beta-diversity, bsim-d, as
(1 ? S^d) for d ¼ 100 km, or the estimated proportional turnover in
composition from that grid cell at a distance of 100 km.
The predicted degree of dissimilarity at a given distance, bsim-d,
differs from the average observed dissimilarity (bsim) at the same
distancebecauseit accounts for the rate at which dissimilarity changes
with increasing distance (i.e., the effect of extent). At the same time,
bsim-ddiffers from the rate of distance decay in the following ways.
(i) Estimates of bsim-d depend on both the intercept and slope
parameters of the distance decay relationship. The former, as initial
similarity level, reflects dissimilarity at near distances and the latter, as
the rate of distance decay, captures dependency of dissimilarity on
extent [62,63]. (ii) bsim-dis the estimated dissimilarity at a specified
would result in different values, reflecting the effect of spatial extent
on compositional change. Turnover at this distance, which is the
minimum distance between adjacent grid cells, is more intuitive than
that between distant grid cells for discussion and graphical repre-
sentation of beta-diversity as a continuous surface, and makes it easier
to compare our results to other broad-scale diversity analyses.
Although the number of grid cells included in a regression model
decreased with increased proximity to the coast (including major
interior water bodies), graphical examination of scatter plots and the
resulting maps showed that coastal effects were negligible for
amphibians and mammals and varied geographically for birds. The
elevated bird bsim-don some coastal sections likely has a biological
rather than methodological basis . It is important to remember
that bsim-dquantifies change in species composition between 100 km
3 100 km grid cells, and therefore does not reflect the level of
heterogeneity within a grid cell. Furthermore, bsim-dis a measure of
proportional species turnover and does not represent the absolute
number of species gained or lost between grid cells. Lastly, while the
smooth surface that results from modeling the effect of distance on
similarity reduces the effect of potential errors in gridded large-scale
range data, extremely abrupt transitions may be attenuated. How-
ever, the major patterns found for bsim-dwere also apparent in maps
of average nearest-neighbor beta-diversity (the average dissimilarity
[bsim] of a focal grid cell and its orthogonal and diagonal neighbors)
(Figure S3). Further, a comparison of Table 1 with pair-wise
correlations of average bsim(Table S3) shows that the congruence
levels we report are not artifacts of the smoothing process.
We tested whether grid cells containing high bsim-dor those with
low bsim-d differed significantly in elevation or were found on a
greater number of biome edges than could be expected by chance
. To do this, we selected sets of grid cells containing the highest
2.5% and the lowest 2.5% of bsim-dvalues for each taxon (2.5% ¼ 93
grid cells for amphibians, 96 grid cells for birds and mammals), and
calculated the mean elevation and mean number of biome edges for
each set. We then compared these values to distributions of values for
the mean elevation and mean number of biome edges, respectively,
calculated for 10,000 sets of randomly selected grid cells (grid cells per
random set: n¼93 for amphibians; n¼96 for birds and mammals). For
each comparison, we computed a one-tailed p-value by counting the
number of values in the random distribution greater than or equal to
the value of a high bsim-dset—or less than or equal to the value of a
low bsim-dset. Elevation was measured as the mean elevation within a
grid cell from a digital elevation model of approximately 1 km31 km
resolution (the Global 30 Arc Second Elevation Data Set, http://www1.
PLoS Biology | www.plosbiology.orgOctober 2007 | Volume 5 | Issue 10 | e2722430
Broad-Scale Beta-Diversity Congruence
van Rensburg et al. , we considered a grid cell to be on a biome
edge if a biome (as delineated by Olson et al. ) covering ?5% of
that grid cell also covered ,5% of any of the neighboring grid cells.
The number of biome edges was then calculated as the number of
biomes in that grid cell meeting this definition.
To evaluate the overall relationships between bsim-dand elevation
andbetweenbsim-dand number ofbiomeboundaries withina gridcell,
we calculated the correlation between bsim-dfor the three taxa and
each environmental variable. Correlations were calculated with
Spearman rank correlation coefficients to accommodate the non-
normal distributions of bsim-d. Standard significance tests are not
appropriate for autocorrelated data because the assumption of
independence is violated; therefore, we tested for significance using
a method developed by Clifford et al.  that corrects the sample size
of two variables based on the level of the spatial dependency in and
between them . We calculated the ess for each pair of variables
degrees of freedom to test the significance of each correlation.
Pair-wise congruence at the hemisphere and biogeographic realm
examine congruence at extents smaller than a biogeographic realm,
we calculated the correlation in bsim-dvalues within a ?350-km-radius
window (centroid to centroid distance) around each grid cell. We used
this window size because it provided a better representation of the
geographic variation in bsim-dat small extents than the other window
sizes we experimented with (radii of 150, 250, and 450 km). The same
overall pattern was also apparent using larger windows but became
increasingly muted as the extent widened. Moreover, larger windows
had a greater discrepancy in the number of grid cells occurring within
considerably decreased the number of grid cells across which
affected by either of these issues, and differences that did exist in the
number of grid cells within coastal and interior windows did not
appear to influence the geographical variation in congruence.
Spatial overlap between matching percentage sets of the highest
2.5% and lowest 2.5% of bsim-dgrid cells for each pair of taxa and for
all three groups was calculated as the maximum overlap possible :
Nc/Nt, where Ncis the number of grid cells common to the sets and Nt
is the total number of grid cells in the smallest set (amphibians have
slightly fewer grid cells than birds or mammals).
Figure S1. Scatter Plots Showing Relationships between Beta-
Diversity and Two Environmental Variables (Elevation and Number
of Biome Edges within Grid Cells)
For each panel, untransformed (left plots) and transformed (right
plots) values of bsim-d(y-axis) against either grid cell elevation (x-axis,
upper plots) or number of biome edges within grid cell (x-axis, lower
plots). In each plot, the red dots represent the highest 2.5% of bsim-d
grid cells, and the purple dots show the lowest 2.5% of bsim-dgrid
cells. (A) Amphibians. (B) Birds. (C) Mammals.
Found at doi:10.1371/journal.pbio.0050272.sg001 (472 KB PDF).
Figure S2. Bird Beta-Diversity Based on Both Breeding and Non-
Beta-diversity (bsim-d) values are divided into 20 quantiles, repre-
sented by warm (higher bsim-d) to cool (lower bsim-d) colors. The scale
accompanying the color ramp shows minimum, first quartile, median,
third quartile, and maximum values of bsim-d.
Found at doi:10.1371/journal.pbio.0050272.sg002 (210 KB PDF).
Figure S3. Average Nearest-Neighbor Beta-Diversity of Amphibians,
Birds, and Mammals Mapped Continuously across the Continental
Average nearest-neighbor beta-diversity (bsim) values are divided into
20 quantiles, represented by warm (higher bsim) to cool (lower bsim)
colors. The scale accompanying the color ramp shows minimum, first
quartile, median, third quartile, and maximum values of bsim. Gray
grid cells do not contain amphibian species. (A) Amphibians.
(B) Birds. (C) Mammals.
Found at doi:10.1371/journal.pbio.0050272.sg003 (503 KB PDF).
Table S1. Correlations between Beta-Diversity (bsim-d) and Two
Environmental Variables (Elevation and Number of Biome Edges of
Found at doi:10.1371/journal.pbio.0050272.st001 (81 KB PDF).
Table S2. Mean Elevation and Mean Number of Biome Edges for Sets
of the Highest 2.5% and Lowest 2.5% of Beta-Diversity Grid Cells
Found at doi:10.1371/journal.pbio.0050272.st002 (56 KB PDF).
Table S3. Correlations in Average Nearest-Neighbor Beta-Diversity
(bsim) within the Western Hemisphere, Nearctic Realm, and
Found at doi:10.1371/journal.pbio.0050272.st003 (81 KB PDF).
We thank Thomas Brooks, Jack Lennon, David Orme, Jake Overton,
John Terborgh, Dean Urban, and an anonymous reviewer for
comments on the manuscript; John Bruno, Kevin Gaston, Aaron
Moody, and Robert Peet for collaboration and discussion; and
Gerardo Ceballos, Bruce Patterson, Marcelo Tognelli, James Zook,
The Nature Conservancy, Conservation International, World Wildlife
Fund, and Environment Canada–WILDSPACE for contributions to
the compilation of bird and mammal range maps. Amphibian data
were developed as part of the Global Amphibian Assessment and were
provided by IUCN, Conservation International, and NatureServe.
Author contributions. MWM and PSW conceived and designed the
study. RIM contributed new analytical tools. MWM, RIM, and JFL
analyzed the data. WS, RSR, and SNS were responsible for the
collection, organization, and verification of the species range maps.
MWM, PSW, and JFL wrote the paper, with extensive input from RIM,
WS, RSR, and SNS.
Funding. MWM thanks the US National Science Foundation
Graduate Research Fellowship Program for financial support.
Competing interests. The authors have declared that no competing
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