The need for richness-independent measures of turnover when delineating biogeographical regions

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    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, 20292053)recommended the use of the bsim index todelineate 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,

    760771) 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. Weshow that b-3 is not a richness-independentmeasure 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, betadiversity, 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 Srensen dissimilarity indices.

    Kreft & Jetz (2010) therefore recom-

    mended the use of the bsim index, which isknown 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 minb; c

    aminb; c (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 byCardoso et al. (2009):

    b-3 2minb; ca b 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 isalso equal to 0 when the two compared

    assemblages are nested (e.g. a = 10, b = 0and c = 5).

    In response to Carvalho et al. (2012),

    Baselga (2012) argued that the b-3 indexunderestimates 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 formulatedas follows:

    bjtu 2minb; c

    a 2minb; c (3)

    Journal of Biogeography 2013 John Wiley & Sons Ltd

    417

    Correspondence

  • The bjtu index measures the proportionof 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 variesbetween 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 ofbioregionalization.

    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 numberof 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 indexdecreased 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 showedconstant pairwise dissimilarity values along

    this richness gradient (bsim = 0.5 andbjtu = 0.66). Second, comparisons betweenA 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 = 1and 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 indicatedthat 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 Caceres, 2013). As indi-

    cated by Legendre & De Caceres (2013),

    compositional dissimilarity indices that

    violate the complementarity property are

    not suitable for beta diversity studies. This

    simple numerical example emphasizes that

    the b3 index does not respect the com-plementarity property. In contrast to what

    Cardoso et al. (2009) stated, the b-3 indexis not always maximal (i.e. equal to 1)

    when the two communities being com-

    pared share no species (a = 0, see Table 1and comparison AI for example). Indeed,an additional condition for the b-3 to beequal to one (maximum) is that the num-

    ber of species unique to each community

    must be equal (b = c, see Table 1 andcomparison AF). All evidence indicatesthat 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 andb-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; Merigot 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), Wards

    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-

    leyGardnerSutcliffe (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 riverbasin (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 Iberianriver 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 dissimilarityvalues 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

    AB 10 10 10 0.50 0.66 0.66 0AC 10 10 20 0.50 0.66 0.50 10

    AD 10 10 30 0.50 0.66 0.40 20AE 10 10 40 0.50 0.66 0.33 30

    AF 10 0 10 1 1 1 0AG 10 0 20 1 1 0.66 10

    AH 10 0 30 1 1 0.50 20AI 10 0 40 1 1 0.40 30

    Correspondence

    Journal of Biogeography 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 thebsim index indicated a high level of speciesturnover (bsim = 0.83). This result basedon b-3 could clearly lead to misleadinginterpretations 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 ofthe 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 and0.021 for bsim and bjtu, respectively,P > 0.05). Because the above results maybe 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 differencesin species richness between grid cells (Man-

    tel test: rM = 0.55, P < 0.001). By con-trast, both bsim and bjtu were weaklyassociated with differences in species

    richness (Mantel test: rM = 0.163 and0.157 for bsim and bjtu, respectively,P < 0.001). These results using empiricalcase studies are not fundamentally surpris-

    ing (see the numerical examples in

    Table 1) as the denominator of b-3 reflectsspecies 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 inspecies 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 levelof 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 Caceres, 2013). Based on

    these results, the b-3 index should not beused to delineate biogeographical regions.

    By contrast, we recommend the use of

    the bsim and bjtu indices because they havedesirable properties for bioregionalization

    Figure 1 Clustering of European river basins according to native freshwater fishcompositional dissimilarity. The hierarchical cluster analysis was performed according theUPGMA linkage method and two dissimilarity indices: (a) bsim and (b) b-3. The numberscorrespond to the optimal groups of river basins according to the KelleyGardnerSutcliffe (KGS) penalty function (see main text for more details).

    Correspondence

    Journal of Biogeography 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* ANDAnthi Oikonomou2

    1Laboratoire Ecologie des Systemes Marins

    Cotiers UMR 5119, Universite Montpellier 2,

    cc 093, Place Eugene 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: fabien.leprieur@univ-montp2.fr

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    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 andb-3 indices.

    Editor: Richard Ladle

    doi: 10.1111/jbi.12266

    Correspondence

    Journal of Biogeography 2013 John Wiley & Sons Ltd

    420

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