Mart�ınez del R�ıo, C. (2008) Metabolic
theory or metabolic models? Trends in
Ecology and Evolution, 23, 256–260.McInerny, G.J. & Etienne, R.S. (2012a)
Ditch the niche – is the niche a useful
concept in ecology or species distribu-
tion modelling? Journal of Biogeography,
39, 2096–2102.McInerny, G.J. & Etienne, R.S. (2012b) Stitch
the niche – a practical philosophy and
visual schematic for the niche concept.
Journal of Biogeography, 39, 2103–2111.McInerny, G.J. & Etienne, R.S. (2012c)
Pitch the niche – taking responsibility
for the concepts we use in ecology and
species distribution modelling. Journal of
Biogeography, 39, 2112–2118.Peterson, A.T. (2006) Uses and require-
ments of ecological niche models and
related distributional models. Biodiversity
Informatics, 3, 59–72.Peterson, A.T., Sober�on, J., Pearson, R.G.,
Anderson, R., Mart�ınez-Meyer, E.,
Nakamura, M. & Ara�ujo, M.B. (2011)
Ecological niches and geographic distributions.
Princeton University Press, Princeton, NJ.
Pulliam, R. (2000) On the relationship
between niche and distribution. Ecology
Letters, 3, 349–361.Saupe, E.E., Barve, V., Myers, C.E.,
Sober�on, J., Barve, N., Hensz, C.M., Peter-
son, A.T., Owens, H.L. & Lira-Noriega, A.
(2012) Variation in niche and distribu-
tion model performance: the need for a
priori assessment of key causal factors.
Ecological Modelling, 237–238, 11–22.Schurr, F.M., Pagel, J., Cabral, J.S., Groeneveld,
J., Bykova, O., O’Hara, R.B., Hartig, F.,
Kissling, W.D., Linder, H.P., Midgley, G.F.,
Schr€oder, B., Singer, A. & Zimmermann, N.E.
(2012) How to understand species’ niches
and range dynamics: a demographic
research agenda for biogeography. Journal
of Biogeography, 39, 2146–2162.Sober�on, J. (2007) Grinnellian and Elto-
nian niches and geographic distributions
of species. Ecology Letters, 10, 1115–1123.Sober�on, J. (2010) Niche and area of dis-
tribution modeling: a population ecol-
ogy perspective. Ecography, 33, 159–167.Wisz, M.S., Pottier, J., Kissling, W.D. et al.
(2013) The role of biotic interactions in
shaping distributions and realised assem-
blages of species: implications for species
distribution modelling. Biological Reviews,
88, 15–30.
Editor: Steven Higgins
doi:10.1111/jbi.12258
The need for richness-independent measures ofturnover when delineatingbiogeographical regions
ABSTRACT
Delineating biogeographical regions is one
of the primary steps when analysing bio-
geographical patterns. In their proposed
quantitative framework, Kreft & Jetz (2010,
Journal of Biogeography, 37, 2029–2053)recommended the use of the bsim index to
delineate biogeographical regions because
this turnover measure is weakly affected by
differences in species richness between
localities. A recent study by Carvalho et al.
(2012, Global Ecology and Biogeography, 21,
760–771) critiziced the use of bsim in eco-
logical and biogeographical studies, and
proposed the b-3 index. Here we used sim-
ple numerical examples and an empirical
case study (European freshwater fishes) to
highlight potential pitfalls associated with
the use of b-3 for bioregionalization. We
show that b-3 is not a richness-independent
measure of species turnover. We also show
that this index violates the ‘complementar-
ity’ property, namely that localities without
species in common have the largest dissim-
ilarity, which is an essential prerequisite for
beta diversity studies.
Keywords bsim index, b-3 index, beta
diversity, bioregionalization, clustering,
compositional dissimilarity, freshwater
fishes, species richness, species turnover.
The delineation of biogeographical regions
(or bioregionalization) consists of group-
ing localities according to their composi-
tional dissimilarity, and hence in
distinguishing among regional faunas and
floras with distinct biogeographical histo-
ries (Kreft & Jetz, 2010). Delineating bio-
geographical regions provides important
information for conservation planning and
presents an opportunity to explore the rel-
ative roles of ecological, evolutionary and
historical factors in shaping regional pools
of species over large spatial scales (Ladle &
Whittaker, 2011). Recently, Kreft & Jetz
(2010) proposed a quantitative framework
to delineate biogeographical regions, based
on clustering and ordination techniques.
Specifically, they pointed out that measures
of species turnover (or species replace-
ment) that are weakly influenced by
species richness differences are more infor-
mative for the purpose of bioregionaliza-
tion than classical metrics, such as the
Jaccard and Sørensen dissimilarity indices.
Kreft & Jetz (2010) therefore recom-
mended the use of the bsim index, which is
known to be weakly affected by differences
in species richness (see Koleff et al., 2003;
Baselga, 2010; Mouillot et al., 2013). For
instance, Mouillot et al. (2013) showed
that the bsim index minimized the poten-
tial confounding effect of the relative mag-
nitude of sampling areas when delineating
biogeographical regions, as a sampling
design that comprises wide variation in
sampling area can itself induce large differ-
ences in species richness. The bsim is for-
mulated as follows:
bsim ¼ minðb; cÞaþminðb; cÞ (1)
where a is the number of species com-
mon to both sites, b is the number of
species that occur in the first site but
not in the second, and c is the number
of species that occur in the second site
but not in the first. The bsim index var-
ies between 0 (low dissimilarity, identi-
cal or nested taxa lists) and 1 (high
dissimilarity, no shared taxa).
The bsim index has recently been criti-
cized by Carvalho et al. (2012), who argued
that it overestimates species replacement
because it measures replacement relative to
the species-poorer site and not as a propor-
tion of all species. Therefore, Carvalho
et al. (2012) recommended the use of the
b-3 index, which was initially proposed by
Cardoso et al. (2009):
b-3 ¼ 2� minðb; cÞaþ bþ c
(2)
According to Cardoso et al. (2009), the
b-3 index, which varies between 0 (identi-
cal taxa lists) and 1 (no shared taxa), is
insensitive to differences in species richness
between localities. Similarly to bsim, b-3 is
also equal to 0 when the two compared
assemblages are nested (e.g. a = 10, b = 0
and c = 5).
In response to Carvalho et al. (2012),
Baselga (2012) argued that the b-3 index
underestimates species replacement
because it accounts for the total number of
species in the denominator and not for the
total number of species that would poten-
tially be replaced. Baselga (2012) therefore
proposed a modified version of the b-3,namely the bjtu index, which is formulated
as follows:
bjtu ¼ 2minðb; cÞaþ 2minðb; cÞ (3)
Journal of Biogeographyª 2013 John Wiley & Sons Ltd
417
Correspondence
The bjtu index measures the proportion
of species that would be replaced between
assemblages if both had the same number
of species and, hence, accounts for species
replacement without the influence of dif-
ferences in richness. The bjtu varies
between 0 (low dissimilarity, identical or
nested taxa lists) and 1 (high dissimilarity,
no shared taxa). Baselga (2012) showed
that the closely related bjtu and bsim pro-
vided roughly similar results.
Here we used simple numerical exam-
ples and an empirical case study (Euro-
pean freshwater fish fauna; Leprieur et al.,
2009) to provide a clear understanding of
the potential pitfalls associated with the
use of the b-3 index in the context of
bioregionalization.
Let us consider nine localities (A to I)
and the comparisons between the locality
A and the localities B to I (see Table 1).
The number of species unique to A was
kept constant (b = 10) while the number
of species unique to the other localities (c)
increased from 10 to 40. In the first four
comparisons, the number of shared species
(a) was equal to 10 while no species were
shared among localities for the last four
comparisons. First, comparisons between A
and B, C, D, E revealed that the b-3 index
decreased from 0.66 to 0.33 with increas-
ing differences in species richness, while
the number of shared species (a) was con-
stant across comparisons (Table 1). By
contrast, the bsim and bjtu indices showed
constant pairwise dissimilarity values along
this richness gradient (bsim = 0.5 and
bjtu = 0.66). Second, comparisons between
A and F, G, H, I showed that the b-3 indexdecreased from 1 (maximum value) to
0.40 with increasing differences in species
richness, while no species were shared
between the compared localities (Table 1).
Again by contrast, the bsim and bjtu indices
showed constant and maximal pairwise
dissimilarity values even though no species
were shared between localities (bsim = 1
and bjtu = 1), and this was the case what-
ever their differences in species richness.
The fact that b-3 decreased with increas-
ing differences in species richness, even
when no species were shared, may clearly
be misleading in the context of bioregio-
nalization. For instance, the b-3 indicated
that A had as much dissimilarity in species
composition with I as with D (b-3 = 0.4,
see Table 1). This means that I and D were
equally likely to be grouped with A within
a hierarchical clustering procedure. Yet, no
species were shared between A and I while
10 species were shared between A and D.
A required property of a compositional
dissimilarity index, namely the ‘comple-
mentarity’ property, is that localities with-
out species in common have the largest
dissimilarity (e.g. Clarke et al., 2006;
Legendre & De C�aceres, 2013). As indi-
cated by Legendre & De C�aceres (2013),
compositional dissimilarity indices that
violate the ‘complementarity’ property are
not suitable for beta diversity studies. This
simple numerical example emphasizes that
the b�3 index does not respect the ‘com-
plementarity’ property. In contrast to what
Cardoso et al. (2009) stated, the b-3 index
is not always maximal (i.e. equal to 1)
when the two communities being com-
pared share no species (a = 0, see Table 1
and comparison A–I for example). Indeed,
an additional condition for the b-3 to be
equal to one (maximum) is that the num-
ber of species unique to each community
must be equal (b = c, see Table 1 and
comparison A–F). All evidence indicates
that the natural world is characterized by
multi-scale gradients of species richness
(Field et al., 2009) and so this above con-
dition is almost never fulfilled.
Using the occurrences of 136 native
freshwater fish species in 26 major Euro-
pean river basins (see Leprieur et al.,
2009; and see Appendix S1a in Supporting
Information), we compared the results of
clustering obtained using the bsim, bjtu and
b-3 indices. For each compositional dis-
similarity matrix, we applied a hierarchical
clustering analysis (HCA) to produce a
dendrogram representing the relative dis-
tance between river basins based on the
composition of their fish fauna. To do
so, we used the unweighted pair-group
method using arithmetic averages (UP-
GMA) linkage method as recommended
by Kreft & Jetz (2010). Based on a
recently proposed goodness-of-fit measure
(the 2-norm; M�erigot et al., 2010), preli-
minary analyses confirmed that UPGMA
provided a more faithful representation of
the initial dissimilarity matrix than other
linkage methods [unweighted pair-group
method using centroids (UPGMC),
weighted pair-group method using arith-
metic averages (WPGMA), Ward’s
method, single linkage, complete linkage].
Note here that the dendrogram based on
bjtu is not shown because the bsim and bjtuindices provided similar results. Following
Kelley et al. (1996), we then used a Kel-
ley–Gardner–Sutcliffe (KGS) penalty func-
tion to determine the optimal number of
groups of river basins. Last, we performed
a Mantel test (999 permutations) to assess
the linear relationship between the compo-
sitional dissimilarity matrices based on
bsim, bjtu and b-3 and the absolute differ-
ences in species richness between river
basins.
The dendrogram based on bsim (Fig. 1a,
Appendix S1b) showed a clear grouping of
the four major river basins of the Iberian
Peninsula (Ebro, Douro, Tagus and Gua-
dalquivir), hence indicating that the Ibe-
rian Peninsula has a unique freshwater
fish fauna (Fig. 1a, Appendix S1b). Sup-
porting this result, we found that the aver-
age level of species turnover between the 4
Iberian river basins and the 22 other
European river basins was very high (aver-
age bsim = 0.814). Similarly, the Po river
basin (Italian Peninsula) displayed a dis-
tinct freshwater fish fauna according to
the dendrogram based on bsim (Fig. 1a,
Appendix S1b). In contrast, according to
the dendrogram based on b-3, the Iberian
river basins were not grouped together,
with the exception of the Douro and Ta-
gus river basins (Fig. 1b, Appendix S1c).
For instance, the Ebro river basin was
found to be as dissimilar in species com-
Table 1 Numerical examples based on artificial data showing compositional dissimilarity
values between the locality A and the localities B to I according to the bsim, bjtu and b-3indices (see equations 1, 2 and 3 in the text). a: number of shared species between the
two localities compared; b and c: number of species unique to the two localitiescompared. Delta SR: absolute difference in species richness between localities.
b a c bsim bjtu b-3 Delta SR
A–B 10 10 10 0.50 0.66 0.66 0
A–C 10 10 20 0.50 0.66 0.50 10
A–D 10 10 30 0.50 0.66 0.40 20
A–E 10 10 40 0.50 0.66 0.33 30
A–F 10 0 10 1 1 1 0
A–G 10 0 20 1 1 0.66 10
A–H 10 0 30 1 1 0.50 20
A–I 10 0 40 1 1 0.40 30
Correspondence
Journal of Biogeographyª 2013 John Wiley & Sons Ltd
418
position with the Tagus and Douro river
basins as it was with the western and cen-
tral European basins (e.g. Danube, see
Fig. 1b). The Guadalquivir and Po basins
were grouped together when they are geo-
graphically distant and separated by two
major geographical barriers, the Pyrennees
and the Alps (Fig. S1c). Indeed, the b-3index indicated that the Guadalquivir and
Po river basins displayed a medium level
of species turnover (b-3 = 0.52), while the
bsim index indicated a high level of species
turnover (bsim = 0.83). This result based
on b-3 could clearly lead to misleading
interpretations in the context of bioregio-
nalization as the Guadalquivir and Po
river basins only share 2 species and the
number of species unique to each basin is
10 and 26, respectively.
Unlike the results based on bsim, thosebased on b-3 are not consistent with previ-
ous studies showing that the Iberian and
Italian peninsulas displayed distinct fresh-
water fish faunas and a high level of ende-
mism (e.g. Griffiths, 2006; Leprieur et al.,
2009). In Europe, spatial discontinuity in
fish faunal composition is mainly related
to the Pyrenees and Alps, which prevented
exchanges of freshwater fish between the
Iberian and Italian peninsulas, and the rest
of Europe, respectively, in response to past
climatic fluctuations (Griffiths, 2006).
Despite these dicrepancies, both the bsimand b-3 indices showed the grouping of
the river basins of continental Europe (i.e.
the group 3, see Fig. 1 and Appendix S1).
This result is related to the fact that both
the bsim and b-3 indices indicate a low level
of species turnover when the degree of
nestedness is high (Baselga, 2010; Carvalho
et al., 2012), which is the case for the river
basins of continental Europe (see Leprieur
et al., 2009, for more details).
The Mantel test showed a significant
negative correlation between b-3 and differ-
ences in species richness between river
basins (rM = �0.4314, P < 0.001), indicat-
ing that species turnover between river
basins decreases with increasing difference
in their species richness. By contrast, nei-
ther bsim nor bjtu was associated with dif-
ferences in species richness between river
basins (Mantel test: rM = �0.05 and
�0.021 for bsim and bjtu, respectively,
P > 0.05). Because the above results may
be related to a small sample size (n = 26),
we also assessed the relationship between
bsim, bjtu, b-3 and species richness differ-
ences using the data provided by Heikinhe-
imo et al. (2007) on the distribution of
European land mammals (124 species in
2183 grid cells). We found a strong nega-
tive correlation between b-3 and differences
in species richness between grid cells (Man-
tel test: rM = �0.55, P < 0.001). By con-
trast, both bsim and bjtu were weakly
associated with differences in species
richness (Mantel test: rM = �0.163 and
�0.157 for bsim and bjtu, respectively,
P < 0.001). These results using empirical
case studies are not fundamentally surpris-
ing (see the numerical examples in
Table 1) as the denominator of b-3 reflects
species richness differences between locali-
ties (i.e. accounts for both b and c, see
equation 2). While Cardoso et al. (2009)
and Carvalho et al. (2012) claimed that the
b-3 index is insensitive to differences in
species richness between localities, the cur-
rent analyses show that this is not the case.
Overall, both the numerical example
and the case study emphasize that the
b-3 index tends to underestimate the level
of spatial species turnover by accounting
for species richness differences in the
denominator (see also Baselga, 2012),
which can lead to spurious associations
between localities based on their species
composition (e.g. the Guadalquivir and
Po river basins). Furthermore, this index
violates the ‘complementarity’ property,
which is a prerequisite when analysing
patterns and processes of beta diversity
(Legendre & De C�aceres, 2013). Based on
these results, the b-3 index should not be
used to delineate biogeographical regions.
By contrast, we recommend the use of
the bsim and bjtu indices because they have
desirable properties for bioregionalization
Figure 1 Clustering of European river basins according to native freshwater fish
compositional dissimilarity. The hierarchical cluster analysis was performed according theUPGMA linkage method and two dissimilarity indices: (a) bsim and (b) b-3. The numbers
correspond to the optimal groups of river basins according to the Kelley–Gardner–Sutcliffe (KGS) penalty function (see main text for more details).
Correspondence
Journal of Biogeographyª 2013 John Wiley & Sons Ltd
419
studies. These indices are indeed weakly
sensitive to species richness differences
and they also respect the ‘complementar-
ity’ property.
Fabien Leprieur 1* AND
Anthi Oikonomou2
1Laboratoire Ecologie des Syst�emes Marins
Cotiers UMR 5119, Universit�e Montpellier 2,
cc 093, Place Eug�ene Bataillon, Montpellier
Cedex 5, 34095, France, 2Department of
Biological Applications and Technology,
Laboratory of Zoology, University of
Ioannina, University Campus of Ioannina,
Ioannina, 45110, Greece,
*E-mail: [email protected]
REFERENCES
Baselga, A. (2010) Partitioning the turn-
over and nestedness components of beta
diversity. Global Ecology and Biogeogra-
phy, 19, 134–143.Baselga, A. (2012) The relationship between
species replacement, dissimilarity derived
from nestedness, and nestedness. Global
Ecology and Biogeography, 21, 1223–1232.Cardoso, P., Borges, P.A.V. & Veech, J.A.
(2009) Testing the performance of beta
diversity measures based on incidence
data: the robustness to undersampling.
Diversity and Distributions, 15, 1081–1090.Carvalho, J.C., Cardoso, P. & Gomes, P.
(2012) Determining the relative roles of
species turnover and species richness dif-
ferences in generating beta-diversity pat-
terns. Global Ecology and Biogeography,
21, 760–771.
Clarke, K.R., Somerfield, P.J. & Chap-
man, M.G. (2006) On resemblance
measures for ecological studies, includ-
ing taxonomic dissimilarities and a
zero-adjusted Bray–Curtis measure for
denuded assemblages. Journal of Experi-
mental Marine Biology and Ecology,
330, 55–80.Field, R., Hawkins, B.A., Cornell, H.V., Currie,
D.J., Diniz-Filho, J.A.F., Gu�egan, J.-F.,
Kaufman, D.M., Kerr, J.T., Mittelbach,
G.G., Oberdorff, T., O’Brien, E.M. & Turner,
J.R.G. (2009) Spatial species-richness
gradients across scales: a meta-analysis.
Journal of Biogeography, 36, 132–147.Griffiths, D. (2006) Pattern and process in
the ecological biogeography of European
freshwater fishes. Journal of Animal Ecol-
ogy, 75, 734–751.Heikinheimo, H., Fortelius, M., Eronen, J.
& Mannila, H. (2007) Biogeography of
European land mammals shows environ-
mentally distinct and spatially coherent
clusters. Journal of Biogeography, 34,
1053–1064.Kelley, L.A., Gardner, S.P. & Sutcliffe, M.J.
(1996) An automated approach for clus-
tering an ensemble of NMR-derived pro-
tein structures into conformationally
related subfamilies. Protein Engineering,
9, 1063–1065.Koleff, P., Gaston, K.J. & Lennon, J.J.
(2003) Measuring beta diversity for pres-
ence–absence data. Journal of Animal
Ecology, 72, 367–382.Kreft, H. & Jetz, W. (2010) A framework
for delineating biogeographical regions
based on species distributions. Journal of
Biogeography, 37, 2029–2053.
Ladle, R.J. & Whittaker, R.J. (2011) Con-
servation biogeography. Wiley-Blackwell,
Oxford.
Legendre, P. & De C�aceres, M. (2013)
Beta diversity as the variance of com-
munity data: dissimilarity coefficients
and partitioning. Ecology Letters, 16,
951–963.Leprieur, F., Olden, J.D., Lek, S. & Brosse, S.
(2009) Contrasting patterns and mecha-
nisms of spatial turnover for native and
exotic freshwater fishes in Europe. Journal
of Biogeography, 36, 1899–1912.M�erigot, B., Durbec, J.P. & Gaertner, J.C.
(2010) On goodness-of-fit measure for
dendrogram-based analyses. Ecology, 91,
1850–1859.Mouillot, D., De Bortoli, J., Leprieur, F.,
Parravicini, V., Kulbicky, M. & Bell-
wood, D.R. (2013) The challenge of
delineating biogeographical regions:
nestedness matters for Indo-Pacific coral
reef fishes. Journal of Biogeography, 40,
2228–2237.
SUPPORTING INFORMATION
Additional Supporting Information may be
found in the online version of this article:
Appendix S1 Maps showing the 26 major
European river basins examined in this
study and the results of the hierarchical
clustering analyses based on the bsim and
b-3 indices.
Editor: Richard Ladle
doi: 10.1111/jbi.12266
Correspondence
Journal of Biogeographyª 2013 John Wiley & Sons Ltd
420
Recommended
