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

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<ul><li><p>Martnez del Ro, C. (2008) Metabolic</p><p>theory or metabolic models? Trends in</p><p>Ecology and Evolution, 23, 256260.McInerny, G.J. &amp; Etienne, R.S. (2012a)</p><p>Ditch the niche is the niche a usefulconcept in ecology or species distribu-</p><p>tion modelling? Journal of Biogeography,</p><p>39, 20962102.McInerny, G.J. &amp; Etienne, R.S. (2012b) Stitch</p><p>the niche a practical philosophy andvisual schematic for the niche concept.</p><p>Journal of Biogeography, 39, 21032111.McInerny, G.J. &amp; Etienne, R.S. (2012c)</p><p>Pitch the niche taking responsibilityfor the concepts we use in ecology and</p><p>species distribution modelling. Journal of</p><p>Biogeography, 39, 21122118.Peterson, A.T. (2006) Uses and require-</p><p>ments of ecological niche models and</p><p>related distributional models. Biodiversity</p><p>Informatics, 3, 5972.Peterson, A.T., Soberon, J., Pearson, R.G.,</p><p>Anderson, R., Martnez-Meyer, E.,</p><p>Nakamura, M. &amp; Araujo, M.B. (2011)</p><p>Ecological niches and geographic distributions.</p><p>Princeton University Press, Princeton, NJ.</p><p>Pulliam, R. (2000) On the relationship</p><p>between niche and distribution. Ecology</p><p>Letters, 3, 349361.Saupe, E.E., Barve, V., Myers, C.E.,</p><p>Soberon, J., Barve, N., Hensz, C.M., Peter-</p><p>son, A.T., Owens, H.L. &amp; Lira-Noriega, A.</p><p>(2012) Variation in niche and distribu-</p><p>tion model performance: the need for a</p><p>priori assessment of key causal factors.</p><p>Ecological Modelling, 237238, 1122.Schurr, F.M., Pagel, J., Cabral, J.S., Groeneveld,</p><p>J., Bykova, O., OHara, R.B., Hartig, F.,</p><p>Kissling, W.D., Linder, H.P., Midgley, G.F.,</p><p>Schroder, B., Singer, A. &amp; Zimmermann, N.E.</p><p>(2012) How to understand species niches</p><p>and range dynamics: a demographic</p><p>research agenda for biogeography. Journal</p><p>of Biogeography, 39, 21462162.Soberon, J. (2007) Grinnellian and Elto-</p><p>nian niches and geographic distributions</p><p>of species. Ecology Letters, 10, 11151123.Soberon, J. (2010) Niche and area of dis-</p><p>tribution modeling: a population ecol-</p><p>ogy perspective. Ecography, 33, 159167.Wisz, M.S., Pottier, J., Kissling, W.D. et al.</p><p>(2013) The role of biotic interactions in</p><p>shaping distributions and realised assem-</p><p>blages of species: implications for species</p><p>distribution modelling. Biological Reviews,</p><p>88, 1530.</p><p>Editor: Steven Higgins</p><p>doi:10.1111/jbi.12258</p><p>The need for richness-independent measures ofturnover when delineatingbiogeographical regions</p><p>ABSTRACT</p><p>Delineating biogeographical regions is one</p><p>of the primary steps when analysing bio-</p><p>geographical patterns. In their proposed</p><p>quantitative framework, Kreft &amp; Jetz (2010,</p><p>Journal of Biogeography, 37, 20292053)recommended the use of the bsim index todelineate biogeographical regions because</p><p>this turnover measure is weakly affected by</p><p>differences in species richness between</p><p>localities. A recent study by Carvalho et al.</p><p>(2012, Global Ecology and Biogeography, 21,</p><p>760771) critiziced the use of bsim in eco-logical and biogeographical studies, and</p><p>proposed the b-3 index. Here we used sim-ple numerical examples and an empirical</p><p>case study (European freshwater fishes) to</p><p>highlight potential pitfalls associated with</p><p>the use of b-3 for bioregionalization. Weshow that b-3 is not a richness-independentmeasure of species turnover. We also show</p><p>that this index violates the complementar-</p><p>ity property, namely that localities without</p><p>species in common have the largest dissim-</p><p>ilarity, which is an essential prerequisite for</p><p>beta diversity studies.</p><p>Keywords bsim index, b-3 index, betadiversity, bioregionalization, clustering,</p><p>compositional dissimilarity, freshwater</p><p>fishes, species richness, species turnover.</p><p>The delineation of biogeographical regions</p><p>(or bioregionalization) consists of group-</p><p>ing localities according to their composi-</p><p>tional dissimilarity, and hence in</p><p>distinguishing among regional faunas and</p><p>floras with distinct biogeographical histo-</p><p>ries (Kreft &amp; Jetz, 2010). Delineating bio-</p><p>geographical regions provides important</p><p>information for conservation planning and</p><p>presents an opportunity to explore the rel-</p><p>ative roles of ecological, evolutionary and</p><p>historical factors in shaping regional pools</p><p>of species over large spatial scales (Ladle &amp;</p><p>Whittaker, 2011). Recently, Kreft &amp; Jetz</p><p>(2010) proposed a quantitative framework</p><p>to delineate biogeographical regions, based</p><p>on clustering and ordination techniques.</p><p>Specifically, they pointed out that measures</p><p>of species turnover (or species replace-</p><p>ment) that are weakly influenced by</p><p>species richness differences are more infor-</p><p>mative for the purpose of bioregionaliza-</p><p>tion than classical metrics, such as the</p><p>Jaccard and Srensen dissimilarity indices.</p><p>Kreft &amp; Jetz (2010) therefore recom-</p><p>mended the use of the bsim index, which isknown to be weakly affected by differences</p><p>in species richness (see Koleff et al., 2003;</p><p>Baselga, 2010; Mouillot et al., 2013). For</p><p>instance, Mouillot et al. (2013) showed</p><p>that the bsim index minimized the poten-tial confounding effect of the relative mag-</p><p>nitude of sampling areas when delineating</p><p>biogeographical regions, as a sampling</p><p>design that comprises wide variation in</p><p>sampling area can itself induce large differ-</p><p>ences in species richness. The bsim is for-mulated as follows:</p><p>bsim minb; c</p><p>aminb; c (1)</p><p>where a is the number of species com-</p><p>mon to both sites, b is the number of</p><p>species that occur in the first site but</p><p>not in the second, and c is the number</p><p>of species that occur in the second site</p><p>but not in the first. The bsim index var-ies between 0 (low dissimilarity, identi-</p><p>cal or nested taxa lists) and 1 (high</p><p>dissimilarity, no shared taxa).</p><p>The bsim index has recently been criti-cized by Carvalho et al. (2012), who argued</p><p>that it overestimates species replacement</p><p>because it measures replacement relative to</p><p>the species-poorer site and not as a propor-</p><p>tion of all species. Therefore, Carvalho</p><p>et al. (2012) recommended the use of the</p><p>b-3 index, which was initially proposed byCardoso et al. (2009):</p><p>b-3 2minb; ca b c (2)</p><p>According to Cardoso et al. (2009), the</p><p>b-3 index, which varies between 0 (identi-cal taxa lists) and 1 (no shared taxa), is</p><p>insensitive to differences in species richness</p><p>between localities. Similarly to bsim, b-3 isalso equal to 0 when the two compared</p><p>assemblages are nested (e.g. a = 10, b = 0and c = 5).</p><p>In response to Carvalho et al. (2012),</p><p>Baselga (2012) argued that the b-3 indexunderestimates species replacement</p><p>because it accounts for the total number of</p><p>species in the denominator and not for the</p><p>total number of species that would poten-</p><p>tially be replaced. Baselga (2012) therefore</p><p>proposed a modified version of the b-3,namely the bjtu index, which is formulatedas follows:</p><p>bjtu 2minb; c</p><p>a 2minb; c (3)</p><p>Journal of Biogeography 2013 John Wiley &amp; Sons Ltd</p><p>417</p><p>Correspondence</p></li><li><p>The bjtu index measures the proportionof species that would be replaced between</p><p>assemblages if both had the same number</p><p>of species and, hence, accounts for species</p><p>replacement without the influence of dif-</p><p>ferences in richness. The bjtu variesbetween 0 (low dissimilarity, identical or</p><p>nested taxa lists) and 1 (high dissimilarity,</p><p>no shared taxa). Baselga (2012) showed</p><p>that the closely related bjtu and bsim pro-vided roughly similar results.</p><p>Here we used simple numerical exam-</p><p>ples and an empirical case study (Euro-</p><p>pean freshwater fish fauna; Leprieur et al.,</p><p>2009) to provide a clear understanding of</p><p>the potential pitfalls associated with the</p><p>use of the b-3 index in the context ofbioregionalization.</p><p>Let us consider nine localities (A to I)</p><p>and the comparisons between the locality</p><p>A and the localities B to I (see Table 1).</p><p>The number of species unique to A was</p><p>kept constant (b = 10) while the numberof species unique to the other localities (c)</p><p>increased from 10 to 40. In the first four</p><p>comparisons, the number of shared species</p><p>(a) was equal to 10 while no species were</p><p>shared among localities for the last four</p><p>comparisons. First, comparisons between A</p><p>and B, C, D, E revealed that the b-3 indexdecreased from 0.66 to 0.33 with increas-</p><p>ing differences in species richness, while</p><p>the number of shared species (a) was con-</p><p>stant across comparisons (Table 1). By</p><p>contrast, the bsim and bjtu indices showedconstant pairwise dissimilarity values along</p><p>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</p><p>0.40 with increasing differences in species</p><p>richness, while no species were shared</p><p>between the compared localities (Table 1).</p><p>Again by contrast, the bsim and bjtu indices</p><p>showed constant and maximal pairwise</p><p>dissimilarity values even though no species</p><p>were shared between localities (bsim = 1and bjtu = 1), and this was the case what-ever their differences in species richness.</p><p>The fact that b-3 decreased with increas-ing differences in species richness, even</p><p>when no species were shared, may clearly</p><p>be misleading in the context of bioregio-</p><p>nalization. For instance, the b-3 indicatedthat A had as much dissimilarity in species</p><p>composition with I as with D (b-3 = 0.4,see Table 1). This means that I and D were</p><p>equally likely to be grouped with A within</p><p>a hierarchical clustering procedure. Yet, no</p><p>species were shared between A and I while</p><p>10 species were shared between A and D.</p><p>A required property of a compositional</p><p>dissimilarity index, namely the comple-</p><p>mentarity property, is that localities with-</p><p>out species in common have the largest</p><p>dissimilarity (e.g. Clarke et al., 2006;</p><p>Legendre &amp; De Caceres, 2013). As indi-</p><p>cated by Legendre &amp; De Caceres (2013),</p><p>compositional dissimilarity indices that</p><p>violate the complementarity property are</p><p>not suitable for beta diversity studies. This</p><p>simple numerical example emphasizes that</p><p>the b3 index does not respect the com-plementarity property. In contrast to what</p><p>Cardoso et al. (2009) stated, the b-3 indexis not always maximal (i.e. equal to 1)</p><p>when the two communities being com-</p><p>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-</p><p>ber of species unique to each community</p><p>must be equal (b = c, see Table 1 andcomparison AF). All evidence indicatesthat the natural world is characterized by</p><p>multi-scale gradients of species richness</p><p>(Field et al., 2009) and so this above con-</p><p>dition is almost never fulfilled.</p><p>Using the occurrences of 136 native</p><p>freshwater fish species in 26 major Euro-</p><p>pean river basins (see Leprieur et al.,</p><p>2009; and see Appendix S1a in Supporting</p><p>Information), we compared the results of</p><p>clustering obtained using the bsim, bjtu andb-3 indices. For each compositional dis-similarity matrix, we applied a hierarchical</p><p>clustering analysis (HCA) to produce a</p><p>dendrogram representing the relative dis-</p><p>tance between river basins based on the</p><p>composition of their fish fauna. To do</p><p>so, we used the unweighted pair-group</p><p>method using arithmetic averages (UP-</p><p>GMA) linkage method as recommended</p><p>by Kreft &amp; Jetz (2010). Based on a</p><p>recently proposed goodness-of-fit measure</p><p>(the 2-norm; Merigot et al., 2010), preli-</p><p>minary analyses confirmed that UPGMA</p><p>provided a more faithful representation of</p><p>the initial dissimilarity matrix than other</p><p>linkage methods [unweighted pair-group</p><p>method using centroids (UPGMC),</p><p>weighted pair-group method using arith-</p><p>metic averages (WPGMA), Wards</p><p>method, single linkage, complete linkage].</p><p>Note here that the dendrogram based on</p><p>bjtu is not shown because the bsim and bjtuindices provided similar results. Following</p><p>Kelley et al. (1996), we then used a Kel-</p><p>leyGardnerSutcliffe (KGS) penalty func-tion to determine the optimal number of</p><p>groups of river basins. Last, we performed</p><p>a Mantel test (999 permutations) to assess</p><p>the linear relationship between the compo-</p><p>sitional dissimilarity matrices based on</p><p>bsim, bjtu and b-3 and the absolute differ-ences in species richness between river</p><p>basins.</p><p>The dendrogram based on bsim (Fig. 1a,Appendix S1b) showed a clear grouping of</p><p>the four major river basins of the Iberian</p><p>Peninsula (Ebro, Douro, Tagus and Gua-</p><p>dalquivir), hence indicating that the Ibe-</p><p>rian Peninsula has a unique freshwater</p><p>fish fauna (Fig. 1a, Appendix S1b). Sup-</p><p>porting this result, we found that the aver-</p><p>age level of species turnover between the 4</p><p>Iberian river basins and the 22 other</p><p>European river basins was very high (aver-</p><p>age bsim = 0.814). Similarly, the Po riverbasin (Italian Peninsula) displayed a dis-</p><p>tinct freshwater fish fauna according to</p><p>the dendrogram based on bsim (Fig. 1a,Appendix S1b). In contrast, according to</p><p>the dendrogram based on b-3, the Iberianriver basins were not grouped together,</p><p>with the exception of the Douro and Ta-</p><p>gus river basins (Fig. 1b, Appendix S1c).</p><p>For instance, the Ebro river basin was</p><p>found to be as dissimilar in species com-</p><p>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</p><p>two localities compared; b and c: number of species unique to the two localitiescompared. Delta SR: absolute difference in species richness between localities.</p><p>b a c bsim bjtu b-3 Delta SR</p><p>AB 10 10 10 0.50 0.66 0.66 0AC 10 10 20 0.50 0.66 0.50 10</p><p>AD 10 10 30 0.50 0.66 0.40 20AE 10 10 40 0.50 0.66 0.33 30</p><p>AF 10 0 10 1 1 1 0AG 10 0 20 1 1 0.66 10</p><p>AH 10 0 30 1 1 0.50 20AI 10 0 40 1 1 0.40 30</p><p>Correspondence</p><p>Journal of Biogeography 2013 John Wiley &amp; Sons Ltd</p><p>418</p></li><li><p>position with the Tagus and Douro river</p><p>basins as it was with the western and cen-</p><p>tral European basins (e.g. Danube, see</p><p>Fig. 1b). The Guadalquivir and Po basins</p><p>were grouped together when they are geo-</p><p>graphically distant and separated by two</p><p>major geographical barriers, the Pyrennees</p><p>and the Alps (Fig. S1c). Indeed, the b-3index indicated that the Guadalquivir and</p><p>Po river basins displayed a medium level</p><p>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-</p><p>nalization as the Guadalquivir and Po</p><p>river basins only share 2 species and the</p><p>number of species unique to each basin is</p><p>10 and 26, respectively.</p><p>Unlike the results based on bsim, thosebased on b-3 are not consistent with previ-ous studies showing that the Iberian and</p><p>Italian peninsulas displayed distinct fresh-</p><p>water fish faunas and a high level of ende-</p><p>mism (e.g. Griffiths, 2006; Leprieur et al.,</p><p>2009). In Europe, spatial discontinuity in</p><p>fish faunal composition is mainly related</p><p>to the Pyrenees and Alps, which prevented</p><p>exchanges of freshwater fish between the</p><p>Iberian and Italian peninsulas, and the rest</p><p>of Europe, respectively, in response to past</p><p>climatic fluctuations (Griffiths, 2006).</p><p>Despite these dicrepancies, both the bsimand b-3 indices showed the grouping ofthe river basins of continental Europe (i.e.</p><p>the group 3, see Fig. 1 and Appendix S1).</p><p>This result is related to the fact that both</p><p>the bsim and b-3 indices indicate a low level</p><p>of species turnover when t...</p></li></ul>

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