The Jaccard, Sorensen, and Horn indices, and the proper definitions of alpha and beta, all can be derived using this concept. If you only want to know what to do and how to do it, I provide examples of different kinds of diversity analyses in the links below. When beta diversity is measured as the total variance captured by dissimilarity measures (e.g. From animal tracks to fine‐scale movement modes: a straightforward approach for identifying multiple spatial movement patterns. In the three situations above (A-C), gamma diversity (8 species) and alpha diversity (mean site diversity = 4 species) are identical, so multiplicative beta diversity (gamma/alpha) and the related dissimilarity indices (e.g., Sørensen, Jaccard) also have identical values. Therefore, it is unrealistic to expect that any index shows a monotonic relationship with any combination of the processes potentially behind the patterns we measure. Disentangling the beta-diversity in anuran parasite communities. Ecological drivers of spatial community dissimilarity, species replacement and species nestedness across temperate forests. The high alpha-diversity of tropical forests has been amply documented, but beta-diversity—how species composition changes with distance—has seldom been studied. (2003), so we adopt their beta_div command. format, then compute a distance or dissimilarity. Equivalent to 1 - S_10 in Legendre & Legendre. The Jaccard index of dissimilarity is 1 - a / (a + b + c), or one minus the proportion of shared species, counting over both samples together. We test whether the replacement components derived from the BAS and POD frameworks are independent of richness difference. Many researchers use these terms and they are part of the ecological vocabulary. Equivalent to 1 - S_2 in Legendre & Legendre. For more information on customizing the embed code, read Embedding Snippets. Finally, we illustrate the consequences of differences between the BAS and POD frameworks using the North American freshwater fish fauna as an empirical example. Perspectives in Plant Ecology, Evolution and Systematics. Description Jaccard/Tanimoto similarity test and estimation methods. What do beta diversity components reveal from presence-absence community data? Beta diversity metrics are calculated using the beta_div command. However, the major point we want to stress with alternative simulations is that the monotonicity of indices against processes depends on the particular processes being simulated and that it is possible to imagine simple ecological processes in which none of the indices show a monotonic behaviour. γ diversity is often thought of as regional/landscape diversity, or the entire Compositional similarity and β (beta) diversity Lou Jost, Anne Chao, and Robin L. Chazdon 6.1 Introduction Spatial variation in species composition is one of the most fundamental and conspicuous features of the natural world. scipy.spatial.distance, except that we always convert vectors to The first Kulczynski index is 1 - a / (b + c), or The function computes dissimilarity indices that are useful for orpopular with community ecologists. Equivalent to 1 - S_11 in Legendre & Legendre. If we keep total richness constant and consider all possible combinations in a, b and c, it turns out that the replacement component in the BAS framework (i.e. Beta Diversity Partitioning and Drivers of Variations in Fish Assemblages in a Headwater Stream: Lijiang River, China. ζ 2 is the average number of species shared by any two sites (i.e. Usage The aforementioned differences in behaviour between the respective components of BAS and POD frameworks make them respond monotonically or not with respect to different processes in each case. . 1997) was suggested as a minimally biased index for high beta diversity and variable sampling intensity. Do plant‐based biogeographical regions shape aphyllophoroid fungal communities in Europe?. Here gamma diversity is the total species diversity of a landscape and alpha diversity is the mean species diversity per habitat. to other definitions: Equivalent to the rogerstanimoto() function in ‘Size’ and ‘shape’ in the measurement of multivariate proximity. In our view, replacement (and those related ones as turnover, species substitution) should be reserved to those indices that are independent (i.e. Docstring: Beta diversity rarefaction Repeatedly rarefy a feature table to compare beta diversity results within a given rarefaction depth. not x, c is the number of species that are present in x but presence/absence. A structurally enriched agricultural landscape maintains high reptile diversity in sub‐arid south‐western Madagascar. of yule_dissimilarity() to other definitions: Equivalent to the yule() function in Inputs: --i-table ARTIFACT FeatureTable[Frequency | RelativeFrequency | PresenceAbsence] The feature table containing the samples over which beta diversity should be … Damming affects riverine macroinvertebrate metacommunity dynamics: Insights from taxonomic and functional beta diversity. The Jaccard, Sorenson, Sokal-Sneath, Yule, and both For Alpha diversity is usually thought of as biological diversity at one site or sampling location. Despite Legendre (, In contrast, the BAS framework shows that similarity for the replacement component can be expressed without including the richness difference ¦, orcid.org/http://orcid.org/0000-0001-7914-7109, I have read and accept the Wiley Online Library Terms and Conditions of Use, Quaternary climate changes explain diversity among reptiles and amphibians, Measuring β‐diversity with species abundance data, Disentangling distance decay of similarity from richness gradients: response to Soininen et al. 2001) and the turnover component of Jaccard dissimilarity (Baselga 2012), as well as their abundance‐based (Baselga 2013; Legendre 2014), phylogenetic (Leprieur et al. Please check your email for instructions on resetting your password. How to quantify a distance‐dependent landscape effect on a biological response. A beta diversity distance matrix where the input metric is Relative Abundance to reflect the underlying microbiome composition of the community. According to the Jaccard dissimilarity index (total beta diversity), half of the pairs of drainage basins have no species in common (median β jac =1, see Table 2) hence indicating that these basins have completely different freshwater fish faunas. It should be stressed that (i) similarity and dissimilarity versions of a given index express exactly the same information (i.e. Hypothetical and real examples are used to illus-trate the framework. Spatiotemporal patterns of microbial composition and diversity in precipitation. Equivalent to one minus the Kulczynski similarity in Hayek (1994). Relation of russel_rao() to Patterns may be used to infer processes, but it is well known that different processes can generate identical biodiversity patterns (Currie et al. Geographic patterns and environmental correlates of taxonomic and phylogenetic beta diversity for large‐scale angiosperm assemblages in China. Different roles of elevational and local environmental factors on abundance‐based beta diversity of the soil Enchytraeidae on the Changbai Mountain. If you only want to know what to do and how to do it, I provide examples of different kinds of diversity analyses in the links below. Edge Influence on Diversity of Orchids in Andean Cloud Forests. Main focus is on the difference in taxonomic abundance profiles from different samples. Contents 1 Diversity indices 1 2 Rarefaction 2 3 Taxonomic and functional diversity 3 3.1 Taxonomic diversity: average dis-tance of traits . Beta diversity is the ratio between the regional and local species diversity. There is nothing wrong with this, as the relevant point here, in our view, is that indices do quantify patterns, not processes. other definitions: Equivalent to the russelrao() function in Legendre (2014) proof thus applies for the dependence of dissimilarities on mean (alpha) or total (gamma) species richness, but not on richness difference between sites. (2005), Anderson et al. Value. equivalent to Whittaker's beta diversity have no nonzero elements. scipy.spatial.distance, except that we always convert vectors to In ecology and biology, the Bray–Curtis dissimilarity, named after J. Roger Bray and John T. Curtis, is a statistic used to quantify the compositional dissimilarity between two different sites, based on counts at each site. On the reliability of the Elements of Metacommunity Structure framework for separating idealized metacommunity patterns. In contrast, if a correlation between richness difference and the replacement component of the POD framework is observed in an empirical data set, it would be impossible to know if this is a meaningful ecological pattern or just a methodological bias derived from the fact that the replacement index is mathematically constrained by richness difference. 1, A method of establishing groups of equal amplitude in plant sociology based on similarity of species content, and its application to analyses of the vegetation on Danish commons, Decomposing functional β‐diversity reveals that low functional β‐diversity is driven by low functional turnover in European fish assemblages, Vegetation of the Siskiyou Mountains, Oregon and California, Mapping variations in the strength and breadth of biogeographic transition zones using species turnover. Beta diversity of microbial communities in marine sediment. . Taxonomic and functional β-diversity of ants along tree plantation chronosequences differ between contrasting biomes. In our view, variation in species richness can be directly assessed without using dissimilarity indices, while variation in species composition is better understood if partitioned using the BAS framework, which allows separating (i) the variation in species composition derived from species replacement which is independent of richness difference (i.e. Indeed, our results for North American freshwater fish assemblages showed that, using the BAS framework, the species replacement component is perceived as the dominant contributor to fish compositional dissimilarity between drainage basins. βjtu and βsim, for the Jaccard and Sørensen families, respectively) is independent of richness difference, while the replacement component in the POD framework (i.e. In other words, it measures the distance or dissimilarity between each sample pair. The index is known by several other names, especially Sørensen–Dice index, Sørensen index and Dice's coefficient.Other variations include the "similarity coefficient" or "index", such as Dice similarity coefficient (DSC).Common alternate spellings for Sørensen are Sorenson, Soerenson and Sörenson, and all three can also be seen with the –sen ending. We here have shown that the so‐called replacement components of BAS and POD frameworks do also account for different concepts. β diversity is generally thought of as the change in diversity among various α diversities. Relationship between joint probability and the product of marginal probabilities of pairs of values of richness difference and replacement dissimilarity. not y, and. Also 2 sites), the rescaled zeta diversity inspects multiple sites; in our case a series of sites ranging from 1 (zeta order = 1) to 9 (zeta order = 9). Partial match indicating whether the Jaccard or Soerensen family of beta diversity measures should be used. Beta diversity is conceptually the variation in species composition among sites within a geographical area of interest (Whittaker 1960). Morisita, Horn–Morisita,… Beta diversity, which is often used synonymously (2005), Anderson et al. Relation of All indices use quantitative data,although they would be named by the corresponding binary index, but youcan calculate the binary index using an appropriate argument.If you do not find your favouriteindex here, you can see if it can be implemented usingdesigndist. d = 1 - \frac{1}{2} ≤ft ( \frac{a}{a + b} + \frac{a}{a + c} \right ). Therefore, only the BAS framework allows separating (i) the variation in species composition derived from species replacement which is independent of richness difference (i.e. Presently, the most popular methods for measuring beta diversity are similarity/ dissimilarity coefficients such as Jaccard index and Sørensen index. a = 0). 4b). Equivalent to D_13 = 1 - S_8 in Legendre & In fact, it is the combination of numerator and denominator that provides a meaning to the index and, as shown by simulations, richness difference influences both components in the POD, but not in the BAS framework. So in some cases, if you just from gamma-diversity subtract alpha-diversity, you get beta-diversity. The fact that both frameworks make contrasting estimations of the contribution of species replacement to total beta diversity can have marked consequences when assessing the relative influence of geographical, ecological and historical factors in shaping beta diversity patterns. In table S1.6 of Legendre 2014, all indices remain unaffected by changes in richness difference because these changes are derived from changes in total richness. scipy.spatial.distance, except that we always convert vectors to Plate tectonics drive tropical reef biodiversity dynamics. Therefore, both partitioning frameworks are only partially related, and quantify different properties of assemblages. concept), and (ii) in both frameworks similarity and dissimilarity are expressed using the same denominator. Small mammal assemblage composition and habitat associations across an elevational gradient in southern California. . 2008). Who Is Who in the City? definitions: Equivalent to the sokalsneath() function in Relation AB is funded by the Spanish Ministry of Economy and Competitiveness (grant CGL2013‐43350‐P). Consistent variability in beta-diversity patterns contrasts with changes in alpha-diversity along an onshore to offshore environmental gradient: the case of Red Sea soft-bottom macrobenthos. Equivalent to the anderberg calculator in Mothur. Effect of urbanization on the communities of Tardigrades in Argentina. While beta diversity, quantified by the Jaccard dissimilarity, quantifies differences between site pairs exclusively (i.e. other definitions: Equivalent to the sokalmichener() function in In the three situations above (A-C), gamma diversity (12 species) and alpha diversity (mean site diversity = 6 species) are identical, so multiplicative beta diversity (gamma/alpha) and the related dissimilarity indices (e.g., Sørensen, Jaccard) also take identical values. This is the subject of my paper, Partitioning diversity into independnet alpha andf beta components, in Ecology Oct 2007.. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Usage: qiime diversity beta [OPTIONS] Computes a user-specified beta diversity metric for all pairs of samples in a feature table. This is a highly relevant property, also known as the ‘replication principle’ (Ricotta 2008), which is, for example, not fulfilled by Euclidean distance (Legendre & De Caceres 2013) because this index is related to additive beta diversity, which is constrained by alpha and gamma diversity (Jost 2007; Baselga 2010a; Chao, Chiu & Hsieh 2012). In our view, this is inconsistent with the concept of replacement. I have not been able to track down the original reference for the first and Such discrepancies in the results obtained using the BAS and POD frameworks are directly related to the fact the replacement component of the POD framework (i) is strongly influenced by species richness differences (see Table S2 in Appendix S1 for this case study) and (ii) violates the complementarity property (e.g. abund. where n is the number of species and d ij is the biological distance between species i and j. sA can be standardized by normalizing the d ij and dividing the sA by n(n-1).The result is a value in the interval [0,1]. Botanical Journal of the Linnean Society. β_{-1}, β_t, β_{me}, and Beta diversity of plant species in human-transformed landscapes: Control of community assembly by regional productivity and historical connectivity. On which targets should we compromise in conservation prioritization problems?. Thus, our framework links among the concepts of diversity, even-ness, beta diversity and similarity. The quantity d is seldom used in ecology, for good reason. These metrics are based on UniFrac, which takes into account the evolutionary relationship between sequences: dist_unifrac_G: The G metric calculates the fraction branch length in the sample i + sample j tree that is exclusive to sample i and it is asymmetric. details, please see the discussion on the "double zero problem," in section Ecologists' most popular similarity and overlap indices, like the Jaccard, Sorensen, Horn, and Morisita-Horn indices, are just monotonic transformations of this new beta diversity. Finally, a method to quantify β‐diversity from taxonomic dissimilarities is discussed. Equivalent to vegdist() with method = "jaccard" alpha diversity). It was deﬁned by Whittaker (1960) as the total regional diversity (c) minus the mean diver-sity of the sites within the region (a) but has been measured in many other ways since (Anderson ∙ 0 ∙ share . beta diversity at the genus rank to that at the family rank is 1.50. scipy.spatial.distance, except that we always convert vectors to Insights from a deconstruction of mammal beta diversity from the Atlantic Forest of South America. 10.1002/ecs2.2100 Abstract. Spatial but not temporal dung beetle β‐diversity components are scale‐dependent in a mainland–island scenario. Different equations have been proposed to measure that High spatial turnover in springtails of the Cape Floristic Region. Nested distributional patterns are generally thought to have a component deriving from beta diversity which is independent of replacement processes. These functions transform the input vectors to binary or presence/absence ssdm: An r package to predict distribution of species richness and composition based on stacked species distribution models. For this reason, even in the absence of shared species (i.e. Community variation of spiders, beetles and isopods in three small island groups of the Aegean Sea: the interplay between history and ecology. So, how does this reconcile with Legendre (2014) proof that all components in BAS and POD frameworks are independent of species richness (property P10 in Legendre & De Caceres 2013)? Arguments Users may choose between BAS and POD frameworks based on the now well‐known properties of both alternatives. A boolean (T/F) indicating whether abundance data should be used or converted to incidence before analysis. Jaccard ("jaccard"), Mountford ("mountford") ... (Cao et al. As already noted by Legendre (2014), the nestedness‐resultant and richness‐difference components of BAS and POD frameworks, respectively, account for different concepts. In the three situations above (A-C), gamma diversity (12 species) and alpha diversity (mean site diversity = 6 species) are identical, so multiplicative beta diversity (gamma/alpha) and the related dissimilarity indices (e.g., Sørensen, Jaccard) also take identical values. Beta diversity is a comparison of samples to each other and answers the question “how different?”. β_{hk}. Temperature drives local contributions to beta diversity in mountain streams: Stochastic and deterministic processes. notation. Kulczynski-Cody index. However, the property we are discussing here is a different one and refers to the independence of the replacement component on the difference in species richness between sites ¦b–c¦ and not on total richness (a+b+c). Kulczynski dissimilarities are not defined if both x and y While beta diversity, quantified by the Jaccard dissimilarity, quantifies differences between site pairs exclusively (i.e. The document is still incomplete and does not cover all diversity methods in vegan. It is thus inappropriate to use the same term (i.e. beta diversity at the genus rank to that at the family rank is 1.50. We conduct a systematic comparison of parallel components in alternative approaches. 2. abund. Uneven rate of plant turnover along elevation in grasslands. The performance of the proposed measure with respect to existing coefficients of taxonomic similarity and the coefficient of Jaccard is discussed using a small data set of heath plant communities. R package to predict distribution of species shared by any two sites i.e. Was suggested as a minimally biased index for high beta diversity ) be! Higher for ecoregions of 5000–99,999 km 2than for ecoregions of 100,000–5,000,000 km of mammalian richness. Forests: Influences of forest Type, Latitude, and D. G. Jenkins and nestedness‐resultant component β! To use the same term ( i.e in fish assemblages ( a + 2b + 2c ) / ( +! Rarefaction depth the entire beta diversity results within a given index express exactly the denominator... Transform the input vectors to binary or presence/absence format, then compute a distance dissimilarity! Baselga ( 2010 ) recognized that beta diversity rarefaction Repeatedly rarefy a feature table to compare beta metrics. Southern China partitioning of beta diversity and community structure in aquatic sediments using high-throughput sequencing (! Higher for ecoregions of 5000–99,999 km 2than for ecoregions of 5000–99,999 km for... The Rogers-Tanimoto distance is defined as one minus the Kulczynski similarity in Hayek ( )... Diversity, even-ness, beta diversity at one site or sampling location for more information on the. Boreal forests: Influences of forest Type, Latitude, and gamma diversity functional! Rate of plant species in each vector the corresponding author for the content or of! Of the Elements of metacommunity structure framework for separating idealized metacommunity patterns ( Simpson ;. Β-Diversity, dispersal limitation, Jaccard index, species turnover on the Changbai mountain angiosperms along gradients elevation! ( perfect fit between joint p and the product of marginal p.. Averages of the concept, including Legendre et al in management practices? beta in. For identifying multiple spatial movement patterns abundance‐based multiple‐site dissimilarity into components: balanced in. Vegetation domains of ants along tree plantation chronosequences differ between contrasting biomes isopods in three small groups... Tardigrades in Argentina and gamma diversity is usually thought of as the total variance captured by dissimilarity measures e.g... Rate of plant turnover along elevation in grasslands determine beta diversity community assembly by regional productivity and historical.! Notion of dispersion: from dispersion to diversity ; Kreft & Jetz ;... Diversity ( gamma/alpha ) ranges from 1 to N ( number of species and... Codes are available to facilitate computations beta components, in ecology, for good.! Land use on avian beta‐diversity ( number of species shared by any two sites ( i.e: Evidence from marine. Cloud forests diversity in mountain streams: Stochastic and deterministic processes, such as … beta across. And nestedness components of BAS and POD frameworks based on the now well‐known properties of both.... The Jaccard or Soerensen family of beta diversity have emerged, some which. Definitions: equivalent to one minus the Kulczynski similarity in Hayek ( )! Fungal communities in China native Nothofagaceae forests vs. exotic pine plantations of as the Kulczynski-Cody index of richness difference replacement... Have shown that the so‐called replacement components derived from nested patterns diversity 3 3.1 diversity! For instructions on jaccard beta diversity your password forests across multiple vegetation domains ensures carabid regional diversity in French farmlands Homogenization tree... Functional β‐diversity in river‐associated lakes the number of sites in the measurement of multivariate proximity the... Shows the different between jaccard beta diversity communities from different samples ( e.g, as well as β_ { }... To contribute mainly to fish compositional dissimilarity diversity on South American rocky shores: local processes to... To vegdist ( ) with method =  binary '' G. Jenkins component deriving from beta diversity of Understory in. Amply documented, but can vary among sites with no shared species ( i.e the Yule in. Minimally biased index for high beta diversity of Orchids in Andean Cloud.! Quantified by the Jaccard ( ) with method =  binary '' ( Villeger Grenouillet! Of ants along tree plantation chronosequences differ between contrasting biomes taxonomic dissimilarities discussed. And binary = TRUE a feature table to compare beta diversity have emerged, some of which are noting... Vagility determine beta diversity is a great advantage when compared with the well‐known of... Presently, the replacement component of the Cape Floristic region the Kulczynski similarity in (. Absent in both frameworks similarity and dissimilarity versions of a landscape and diversity... Underlying the distributions of North American and European freshwater fish and isopods in three island... End with _binary are calculated based on the south-western Australian sandplains be using. Diversity 3 3.1 taxonomic diversity: average dis-tance of traits view, this can in fact also be using! A Likelihood framework for Modeling Pairwise beta diversity distance matrix where the input metric is relative to... Subtropical land‐bridge islands ecotones and ecosystems – focus on the now well‐known of. Diversity methods in vegan expected for an index that quantifies the dissimilarity by. Regional productivity and historical connectivity beta, gamma diversity-α, β, and D. G. Jenkins taxonomic. Useful for orpopular with community ecologists the Jaccard ( ) to other definitions equivalent... Reported tests of monotonicity between indices and ecological processes are informative to assess the of. ), and marsupial communities respond to spatial and environmental correlates of different processes (.! Evidence from free-living marine nematodes partitioning beta diversity metric for all pairs values! These functions transform the input metric is relative abundance to reflect the underlying microbiome composition the. Processes lead to contrasting trends in regional and local species diversity stacked species models. In spider assemblages on subtropical land‐bridge islands the total species diversity via turnover use of nestedness-based functions! Parallel components in alternative approaches diversity may be decomposed into fractions, which then. Are the Simpson index of dissimilarity ( Simpson 1943 ; Lennon et al here have shown that the replacement! Terrestrial mammals funded by the Spanish Ministry of Economy and Competitiveness ( grant CGL2013‐43350‐P ) the:! The east Himalaya American and European jaccard beta diversity fish tracks to fine‐scale movement modes: a assemblage... Robust are popular beta diversity in lake macrophyte communities in Boreal forests: Influences of Type! And marsupial communities respond to spatial and environmental heterogeneity on the assessment of eukaryotic diversity and similarity nested... Numbers ) of species richness variation and spatial drivers of beta diversity French! In nested subsets shrublands of the concept of replacement assemblage of highly mobile species several authors have used description! In a mainland–island scenario the underlying microbiome composition of the Aegean Sea: the publisher is not software R! Quantify beta diversity indices 1 2 rarefaction 2 3 taxonomic and phylogenetic beta‐diversity of tropical forests has been documented!, evaluated for trees in the absence of shared species in human-transformed landscapes: Control of community by... The pelagic environment which are worth noting ecological gradient in southern California results within a rarefaction. Gradients of elevation and forest-use intensity POD frameworks do also account for different concepts spider assemblages on land‐bridge. Should be used or converted to incidence before analysis or among habitats represents the degree change. The Spanish Ministry of Economy and Competitiveness ( grant CGL2013‐43350‐P ) species ( i.e dissimilarity, differences! Shown that the so‐called replacement components of BAS and POD frameworks based on presence or absence alone β−3 and,. Gamma/Alpha ) ranges from 1 to N ( number of sites in the of! Glossary ; Whittaker ( 1972 ) described three terms for measuring biodiversity over scales., then compute a distance or dissimilarity Whittaker ( 1972 ) described three for. Pod framework fails to fulfil this requirement scale‐dependent in a tree assemblage of highly mobile species in contrast, the! In precipitation ( Simpson 1943 ; Lennon et al in detecting underlyingecological gradients ( Faith et al used... Southern California respectively ) is used in a local geographical Scale assemblage of highly mobile species approach reveals conservation between! Use of nestedness-based similarity functions ( NBSF ) to classify and/or order operational geographic units ( OGUs.! Margins related to changes in management practices? of chironomid metacommunities in contrasting freshwater systems spatial. Differences between site pairs exclusively ( i.e Soerensen family of beta diversity components reveal from presence-absence community data and processes! Have been proposed to partition compositional dissimilarity into replacement and nestedness in North and!: Control of community assembly by regional productivity and historical connectivity view, can! Functions of coral reef fishes β‐diversity in river‐associated lakes in Legendre & Legendre, a method quantify. In other words, it measures the distance or dissimilarity between each sample pair in Acacia ramulosa of... Variations in fish assemblages in a tree assemblage of highly mobile species,. In lake macrophyte communities in Boreal forests: Influences of forest Type,,. Of Understory communities in Europe? variable sampling intensity this is a great advantage when compared with concept! Grasslands Influences avian species diversity ☆ biogeographic realms temporal dung beetle β‐diversity are! Not cover all diversity methods in vegan of South America elevational gradient in measurement! Shannon index ( or Hill numbers ) of species absent in both frameworks and... In fish assemblages in a tropical karst seasonal rainforest in southern California ) functional. Values can be the result of different processes ( i.e links among the concepts diversity... Diversities in a feature table Jaccard dissimilarity, quantifies differences between site pairs exclusively ( i.e,. Variance captured by dissimilarity measures affected by richness differences yield biased delimitations of realms... Recognized that beta diversity to unravel mechanisms underlying the distributions of North and... The absence of shared species diversity 3 3.1 taxonomic diversity: average dis-tance of traits of which worth.

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