TY - JOUR
AU - Real,, Raimundo
AB - Abstract This study uses the amphibian species of the Mediterranean basin to develop a consistent procedure based on fuzzy sets with which biogeographic regions and biotic transition zones can be objectively detected and reliably mapped. Biogeographical regionalizations are abstractions of the geographical organization of life on Earth that provide frameworks for cataloguing species and ecosystems, for answering basic questions in biogeography, evolutionary biology, and systematics, and for assessing priorities for conservation. On the other hand, limits between regions may form sharply defined boundaries along some parts of their borders, whereas elsewhere they may consist of broad transition zones. The fuzzy set approach provides a heuristic way to analyse the complexity of the biota within an area; significantly different regions are detected whose mutual limits are sometimes fuzzy, sometimes clearly crisp. Most of the regionalizations described in the literature for the Mediterranean biogeographical area present a certain degree of convergence when they are compared within the context of fuzzy interpretation, as many of the differences found between regionalizations are located in transition zones, according to our case study. Compared with other classification procedures based on fuzzy sets, the novelty of our method is that both fuzzy logic and statistics are used together in a synergy in order to avoid arbitrary decisions in the definition of biogeographic regions and transition zones. Biodiversity, biological geography, biogeographical regionalization, species composition, fuzzy boundaries, fuzzy sets, amphibians, Mediterranean basin Following the scheme of Wallace (1876), Udvardy (1975) described biogeography as proceeding along 2 main lines: 1) “geographical biology,” which studies the space-related properties of species and focuses on distribution regularities (as chorotypes or biotic elements: Baroni-Urbani et al. 1978; Birks 1987; Hausdorf 2002; Olivero et al. 2011) and 2) “biological geography,” which attempts to divide the Earth's surface into geographic units based on similarities in the occurrence of species and ecosystems. A system of these geographic units is a “biogeographical regionalization,” an abstraction of the geographical organization of life on Earth in response to past and current physical and biological forces (Kreft and Jetz 2010). Both chorotypes and biotic regions (BRs) are a result of the assemblage of species distributions. However, these 2 types of spatial patterns concentrate on different features of biogeography: chorotypes analyse distributions, that is a property of species (geographical biology)—chorotypes are complex aggregations of species distributions that may respond to environmental and historical attractors (Olivero et al. 2011)— whereas regions arise from the analysis of species composition, that is a property of land (biological geography). The species composition of an area may be shaped by the regional overlap of several chorotypes (see Myklestad and Birks 1993), but composition can reasonably be seen as a biogeographical characteristic with properties beyond the simple sum of its parts because it is interwoven with finer levels of integration of biodiversity, as is the case of ecological communities. The former worldwide biogeographical regionalizations date from the 19th century (see Sclater 1858; Wallace 1876; Engler 1879, 1882; and subsequent updates in Good 1947; Holdridge 1947; Dasmann 1973, 1974; Udvardy 1975; Smith 1983; Cox 2001; Olson et al. 2001; Morrone 2002). Regionalizations provide frameworks for cataloguing species and ecosystems; for analyzing basic questions in historical and ecological biogeography, evolutionary biology, and systematics; and for assessing priorities for conservation (Dasmann 1973; Margules 1986; Carey et al. 1995; Morrone 2009). Environmental and historical characterizations of biotic regionalizations have been used as ways to test and propose hypotheses about ecological factors conditioning species composition (e.g., Olivero et al. 1998; Báez et al. 2004; Escalante et al. 2007; Moya et al. 2012), and about historical events that could underlie the current organization of the biota (e.g., Carmona et al. 2000; Báez et al. 2004; Escalante et al. 2004; Morrone 2009). In conservation policy, classifying geographical areas into regions with different species composition is necessary to define contexts for representativeness, that is, to ensure that the whole range of biotic variation—all areas with characteristic combinations of species—is represented in the selection of natural reserves (Austin and Margules 1986; Margules 1986; Carey et al. 1995; Mackey 2008; Patten and Smith-Patten 2008; Escalante 2009). Land classifications also provide consistent units for environmental management, where common patterns and principles can be established to perform a comprehensive organization of natural resources (Bunce et al. 1996; Wright et al. 1998; Vargas et al. 2006). Limits between regions may form sharply defined boundaries along some parts of their borders, whereas elsewhere they may consist of broad transition zones or gradients (Williams 1996). Drude (1890), a pioneer in biogeographical regionalization, noted that demarcating absolute lines between regions was often impossible and, in the absence of clear net limits, he opted for drawing undulating lines. Transition zones are usually described as complex and varied areas where different fauna and flora overlap (Halffter 1976), and that may be represented by strong gradients in species richness, high spatial species turnover, or a combination of both (Ruggiero and Ezcurra 2003). Even though species turnover or replacement does not necessarily imply interaction between individual organisms or historical relationships (Williams et al. 1999), transition zones are often considered evolutionarily active zones where several speciation events have taken place in the past (Escalante et al. 2004; Morrone 2004), and where population dynamics could be potentially influenced by biological interactions (Ruggiero and Ezcurra 2003). Gradual species replacement might reflect a response of the biota to prior ecological changes and to current environmental gradients sometimes combined with physiographic barriers (Peters 1955; Ruggiero and Ezcurra 2003; Morrone 2004). Exploring zones of biotic transition is thus essential for the study of the processes that influence the distribution of the biota (Ruggiero and Ezcurra 2003; Escalante et al. 2004); it has even been suggested that the global conservation strategy should take transition zones into account to maximize the probability of a viable response of species to changing climatic conditions (Smith et al. 2001). There are several methods to detect, locate, and quantify the magnitudes of transitional areas (relevant reviews include Williams et al. 1999 and Ruggiero and Ezcurra 2003): visual analysis of gradients in species richness (Rabinovich and Rapoport 1975) and in the density of species range limits (McAllister et al. 1986); analysis of the β-diversity along transects across biogeographic boundaries (e.g., Whittaker 1960; Harrison et al. 1992); mapping environmental resistance and anisotropy (Rapoport 1975; Ruggiero and Ezcurra 2003); the measurement of rates of change in species presences between adjacent grid cells (“Wombling”: Womble 1951; Fortin 1994); mapping species turnover (Williams 1996); detecting conflicts between general area cladograms (Marshall and Liebherr 2000; Morrone 2004); the location of “nodes”—geobiotic convergences—between generalized tracks in panbiogeography (Croizat 1958, 1964; Escalante et al. 2004; Morrone 2004); ordination, by which locations are arranged throughout theoretical or environmental gradients (e.g., Jonsgard and Birks 1993; Myklestad and Birks 1993); and fuzzy logic, which allows representing biogeographic boundaries as gradient zones rather than lines (Leung 1987; Jacquez et al. 2000). Despite the complexity of the available techniques, some parts of the boundaries described in the literature are arbitrary constructs (Williams 1996) as biogeographical regionalizations are still presented as sets of regions perfectly delimited by lines (e.g., see Heikinheimo et al. 2007; Reyjol et al. 2007; Kreft and Jetz 2010; Romo and García-Barros 2010; Rueda et al. 2010). When transition zones are drawn, they either lack an objective method to define the limits between biogeographic regions (e.g., Procheş 2006) or define biogeographic regions and transition zones as results of independent analyses whose results are expected to fit geographically in each other (e.g., Williams 1996). Conceptualizing biogeographic regions as fuzzy sets enables the formal representation of imprecision in regional limits (Gale 1976). A fuzzy set is a class of objects which is characterized by a membership function that assigns to each object a real number in the interval [0, 1] (Zadeh 1965); thus, fuzzy membership values indicate that each class exists for each object to some degree (Brown 1998). According to Leung (1987), a region is generally a fuzzy concept and a boundary is generally a fuzzy line whose extent can be exactly demarcated. From this perspective, each location would have a certain degree of membership in every biogeographic region that can be mathematically defined as a function of its biotic composition, and each biogeographic boundary could be fuzzily formulated as a transition zone for which it is operationally possible to determine more than a single region in which it is a member (Leung 1987). Imprecise biogeographic boundaries are highly fuzzy, whereas boundaries become crisp lines if imprecision is eliminated (Leung 1987; Jacquez et al. 2000); that is, crisp boundaries are a special case of fuzzy boundaries in which fuzziness is extremely low. Fuzzy sets have been used in the biotic and ecological classification of areas for the analysis of forest types (e.g., Olano et al. 1998; Brown 1998), phytosociological associations (e.g., Biondi et al. 2004; Bastin et al. 2007; De Cáceres et al. 2009), faunistic areas (e.g., Tepavčevic and Vujić 1996; Eyre et al. 2003; Marchini and Marchini 2006; Lanz et al. 2008; Sylaios et al. 2010), and remote sensing imagery applied to the study of landscapes (e.g., Townsend and Walsh 2001; Arnot et al. 2004; Rocchini and Ricotta 2007; Amici et al. 2010; Rocchini 2010). However, except for rare exceptions such as Brown (1998), fuzzy logic has rarely been used for the representation of biotic transition zones in the context of biogeography. Instead, it has been used to assign localities to predetermined classes by applying linguistic rules (e.g., Marchini and Marchini 2006; Rocchini and Ricotta 2007), to evaluate a previous classification (Townsend and Walsh 2001), or to define the classes themselves (Eyre et al. 2003; Arnot et al. 2004). Boundaries have been fuzzily mapped, however, in studies on soil science (Lee and Lee 2006) and climatology (Leung 1987). Our objective is to develop a consistent procedure based on fuzzy sets with which both biogeographic regions and biotic transition zones can be objectively detected and reliably mapped. Our approach is framed within hierarchical cluster analysis that applies McCoy et al.'s (1986) approach to the detection of biogeographic boundaries and regions. The methodological basis of this method was introduced in Real et al. (1992a), described in detail by Olivero et al. (1998), and has been used to define zoogeographic and phytogeographic regionalizations (Real et al. 1992b; Olivero et al. 1998; Carmona et al. 2000; Márquez et al. 2001; Vargas et al. 2003; Báez et al. 2004). This approach belongs to the same family as the method described in Olivero et al. (2011) for the analysis of fuzzy chorotypes. Our method is introduced using a case study based on the amphibian species of the Mediterranean biogeographical area. Materials and Methods Species and Study Area We analysed the distributions of 112 amphibian species occurring in the Mediterranean basin. Objective regionalizations are particularly interesting when the territory analysed is itself a natural biogeographic unit (Romo and García-Barros 2010), as is the case of the Mediterranean basin, a hotspot of species diversity for many taxonomic groups (Blondel and Aronson 1995) that is considered to be a “subregion” by Wallace (1876) and Smith (1983), a “floristic province” by Good (1947), a “biogeographic province” by Udvardy (1975), a “region” by Cox (2001), a “biome” by Olson et al. (2001), and a “biogeographical area” by Blondel et al. (2010). We based our system of operational geographic units (OGUs) on river basins of the Mediterranean basin, by merging the Level 6 subdivisions of the HYDRO1k data set (courtesy of the U.S. Geological Survey, http://www.usgs.gov) for Europe and Africa, thus obtaining 488 units (Fig. 1). River basins have been considered suitable OGUs in several biogeographical studies on species that use freshwater ecosystems (e.g., Sepkoski and Rex 1974; Doadrio 1988; Matthews and Robinson 1988; Real et al. 1993; Olivero et al. 1998; Carmona et al. 2000) because they are natural domains that represent a level of ecosystem integration (Austin and Margules 1986). All river and endorheic basins within the 4 Mediterranean peninsulas (Iberian, Italian, Balkan, and Anatolian, including their isthmuses), northern Africa, and the Mediterranean terrains of Near East were considered. Islands close to the mainland were merged to their nearest continental OGU, and the rest were either grouped in archipelagos, considered as separate OGUs, or subdivided. Figure 1. Open in new tabDownload slide Study area. The 488 watershed subdivisions and archipelagos used as operational biogeographic units are delimited with black lines, and rivers courses are drawn in grey. Figure 1. Open in new tabDownload slide Study area. The 488 watershed subdivisions and archipelagos used as operational biogeographic units are delimited with black lines, and rivers courses are drawn in grey. Maps of the extent of occurrence for each amphibian species known to inhabit the study area were downloaded as polygon shapefiles from IUCN et al. (2010). Extent-of-occurrence range maps typically provide a reasonable balance between accuracy and detail with OGU sizes around 1○ or 2○ (Hurlbert and Jetz 2007), which is approximately the size of most of the OGUs used. We only considered extant ranges, either native or reintroduced. The IUCN et al. (2010) maps were slightly modified: the Portuguese occurrences of Pelodytes punctatus were ascribed to Pelodytes ibericus following Sánchez-Herráiz et al. (2000), and populations of Hyla meridionalis in France, Italy, and north-eastern Spain, currently thought to be the result of a modern introduction (Recuero et al. 2007), were deleted. The species × OGUs matrix is available as supplementary material at http://datadryad.org, doi:10.5061/dryad.1cq8n52h. Fuzzy Regions and Transition Zones Our methodology for the objective identification of initially crisp biogeographic regions and boundaries is explained in detail in the Appendix. Once boundaries have been detected and regions have been delimited, fuzzy logic is used to analyse and represent both biogeographic entities in fuzzy terms, so that crisp limits between regions can be treated as fuzzier or less fuzzy transition zones. Crisply delimited regions serve, nonetheless, as the seed of fuzzy regions, that is, as objective references for the construction of the characteristic functions that mathematically define membership, which is the most challenging aspect of describing fuzzy regions (Jacquez et al. 2000). In the following procedure, the parameters described for the study of fuzzy chorotypes in Olivero et al. (2011) are adapted to regionalization. The analysis is based on the identification between the degree of similarity and the degree of membership (Salski 2007). Thus, the degree of membership of every OGU in a BR was calculated as the average of the similarities (Sij) between a certain OGUi and all n OGUs initially assigned to the crisp region: Some useful fuzzy parameters proposed by Zadeh (1965), Dubois and Prade (1980), Kosko (1986), and Kuncheva (2001) were computed to describe the fuzzy nature of every region: where N is the total number of OGUs into which the study area has been subdivided, fuzzy cardinality measures the relative importance of a fuzzy region—which depends on how many OGUs have a high degree of membership in it—and both relative cardinality and height provide a context to evaluate the membership of any particular OGU in a region. The degrees of membership in the union and in the intersection between 2 BRs 1 and 2 are Union and intersection were used to calculate the fuzzy similarity—or overlap (O)—between 2 regions, the fuzzy inclusion (I) of one region (BR2) in another (BR1), and a region's fuzzy entropy (E): where BR′ is the fuzzy complement of region BR, the membership function for it being: μBR′(OGUi)=1−μBR(OGUi). The fuzzy entropy of a region is a measure of its degree of fuzziness (Kosko 1986). A region's fuzzy cardinality: ⁠. A region's relative cardinality: Card(BR) A region's height: H(BR)=max[μBR(OGUi)], ∀OGUi, Finally, we used the concept “fuzzy difference” for the fuzzy representation of BRs and boundaries. Let A and B be 2 fuzzy sets and x be any element belonging to them, then: which can also be expressed as A−B=A∩B′ (where B′ is the fuzzy complement of set B; see Alsina and Trillas 2008). This is the “traditional” definition of difference between fuzzy sets (see Tolias et al. 2001), and its formulation can be easily applied to biogeographical regionalization as regions should combine maximum internal similarities with maximum differences compared with other regions (Kreft and Jetz 2010). Our aim was to represent a fuzzy BR by mapping each OGU's degree of membership in the fuzzy difference between the region (BR) and the rest of the study area (RSA): On the other hand, the “symmetric” difference (see Szmidt and Kacprzyk 2000; Kuncheva 2001; Alsina and Trillas 2005) was used to create fuzzy biotic boundaries: The degree of membership in the symmetric difference between 2 neighbouring regions (BR1 and BR2) is defined as follows: which measures the degree to which a certain OGUi is a member in both regions but not in their intersection. We propose the fuzzy complement of BR1ΔBR2 as a way to measure of an OGU's degree of membership in a biotic boundary, that is, the OGU's degree of membership in a biogeographic transition zone: Mapping all transition zones together in a single representation of the study area required representing the fuzzy union of all the fuzzy boundaries detected, which was performed separately for weak and strong boundaries. Biotic Characterization of Regions BRs were characterized using 2 different methods. First, we defined each species' membership in every region by computing the similarity between species distributions (1 = presence; 0 = absence) and BRs (1 = crisp membership in a region; 0 = crisp lack of membership in a region), for which Jaccard's (1901) index was used. In a second approach, we searched for the fuzzy chorotypes of amphibians in the Mediterranean area using the method described in Olivero et al. (2011). Myklestad and Birks (1993) represented the relationships between floristic regions and chorotypes using a two-way table. Similarly, we used Pearson's coefficient to measure the correlation between the membership of each OGU in every region, but not in the rest of the study area (i.e., μBR–RSA(OGUi)), and each chorotype's fuzzy species richness (FSRch) in every OGU (see Olivero et al. 2011): which is calculated for every OGU. In this formula, μch(di) is the degree of membership of the i-species distribution (di) in chorotype ch (see Olivero et al. 2011), and pi is either equal to 1 if di includes that OGU or it is equal to 0 if the reported distribution di does not include that OGU. Ordination We compared the results of our classification with those obtained with a biotic ordination of OGUs along axes of gradual change, for which a detrended correspondence analysis (DCA; Hill and Gauch 1980) was performed using the amphibian species compositional data. Results Seven strong biotic boundaries were identified for amphibians in the Mediterranean area, and 7 clusters of the dendrogram fulfilled the conditions to be considered strong BRs (Figs. 2 and 3a and Table 1). These have been named according to their geographic position in the Mediterranean context: 1) Iberian (including the French river basins), 2) Italian–Balkan, 3) Eastern (including Asia Minor, Near East, and most of the Aegean islands), 4) Nilotic, 5) North African, 6) Western Islands (i.e., Balearic Islands, Corsica, and Sardinia), and 7) Sicilian (including Malta, Pantelleria, and Lampedusa). The OGUs' membership in each of these regions but not in the rest of the study area is mapped in Figure 4. An eighth cluster, including Crete, Rhodes, and some small islands, was delimited by a strong boundary but did not fulfil the conditions to be described as a strong BR itself and thus was numbered 0; 3 out of the 6 amphibian species in this cluster, Pseudepidalea viridis, Pelophylax bedriagae, and Hyla arborea, are widespread throughout one or more BRs, and 3 other species, Lyciasalamandra helverseni, Pelophylax cerigensis, and Pelophylax cretensis, are endemics whose distributions do not overlap. Figure 2. Open in new tabDownload slide Classification tree of the operational biogeographic units in Figure 1, based on the similarity of their amphibian fauna (Baroni-Urbani and Buser's (1976) index). S and W show, respectively, the position of strong and weak boundaries, and arrows point to nodes constituting BRs. Broken lines on the left represent gradualness in the biotic overlap between regions and areas that are not regions themselves (numbered 0). Numbers in each node of the tree indicate how many of the 112 species considered occur on both sides of the boundary (centre) and on just one side of the boundary (top and bottom). Figure 2. Open in new tabDownload slide Classification tree of the operational biogeographic units in Figure 1, based on the similarity of their amphibian fauna (Baroni-Urbani and Buser's (1976) index). S and W show, respectively, the position of strong and weak boundaries, and arrows point to nodes constituting BRs. Broken lines on the left represent gradualness in the biotic overlap between regions and areas that are not regions themselves (numbered 0). Numbers in each node of the tree indicate how many of the 112 species considered occur on both sides of the boundary (centre) and on just one side of the boundary (top and bottom). Figure 3. Open in new tabDownload slide BRs and boundaries for amphibians in the Mediterranean area. a) Crisp representation of boundaries; broken lines represent gradualness in the biotic overlap between regions and areas that are not regions themselves (numbered 0). b) Fuzzy membership of OGUs in transition zones around strong biotic boundaries, based on fuzzy symmetric differences between neighbouring strong regions; arrows point to bordering regions with which there is a fuzzy transition zone. c) Fuzzy membership of OGUs in transition zones around weak biotic boundaries; transition zones are contextualized within each strong BR. Note that, with visualization purposes, scale bars in (b) and (c) are different. Figure 3. Open in new tabDownload slide BRs and boundaries for amphibians in the Mediterranean area. a) Crisp representation of boundaries; broken lines represent gradualness in the biotic overlap between regions and areas that are not regions themselves (numbered 0). b) Fuzzy membership of OGUs in transition zones around strong biotic boundaries, based on fuzzy symmetric differences between neighbouring strong regions; arrows point to bordering regions with which there is a fuzzy transition zone. c) Fuzzy membership of OGUs in transition zones around weak biotic boundaries; transition zones are contextualized within each strong BR. Note that, with visualization purposes, scale bars in (b) and (c) are different. Figure 4. Open in new tabDownload slide Fuzzy mapping of strong BRs. Membership in a region is represented as the fuzzy “traditional” difference between this region and the rest of the study area. Figure 4. Open in new tabDownload slide Fuzzy mapping of strong BRs. Membership in a region is represented as the fuzzy “traditional” difference between this region and the rest of the study area. Table 1. Significant boundaries between river-basin clusters of the dendrogram shown in Figure 2 (clusters A and B are upper and lower in the fork, respectively) Cluster A . Cluster B . DW . G(W) . IHA . G(IHA) . IHB . G(IHB) . DS . G(S) . 1+2+3+0+4+5 6+7 0.01 1782.3** −0.31 1780.7** 0.33 105.9** 0.38 2674.8** 1+2+3+0 4+5 0.40 27 025.9** 0.09 21 619.0** 0.70 24 244.1** 0.59 36 330.7** 1+2+3 0. Cretan 0.46 345.7** 0.03 345.7** 0.89 1.2 ns 0.44 405.0** 6. Western Islands 7. Sicilian 0.74 39.9** 0.74 27.1** 0.74 19.0** 0.24 12.3** 4. Nilotic 5. North African 0.52 4130.5** 0.49 285.4** 0.54 4102.4** 0.06 2503.4** 1+2 3. Eastern 0.55 19 660.1** 0.33 12 213.4** 0.77 18 586.1** 0.32 9168.9** 1. Iberian 2. Italian–Balkan 0.75 14 843.9** 0.76 13 186.4** 0.74 5572.5** 0.24 5820.2** 1. Iberian BR 1.1+1.2 1.0+1.3 0.06 430.1** 0.06 280.2** 0.07 267.7** -0.93 — 1.1 1.2 0.03 137.5** 0.03 129.4** 0.03 16.3** -0.97 0.1 ns 1.0 1.3 0.01 11.1** 0.01 0.5 ns 0.01 10.2** −0.99 — 2. Italian–Balkan BR 2.0+2.1 2.2 0.10 298.0** 0.10 173.3** 0.10 188.1** −0.90 — 2.0 2.1 0.01 7.8** 0.01 1.6 ns 0.01 5.7* −0.99 — 3. Eastern BR 3.1+3.2+3.0 3.3+3.4 0.13 1184.1** 0.14 1103.4** 0.13 274.7** −0.83 70.7** 3.1+3.2 3.0 0.02 8.5** 0.02 8.5** 0.02 1.8 ns −0.98 — 3.3 3.4 0.04 32.8** 0.03 27.4** 0.04 8.2** −0.96 — 3.1 3.2 0.02 73.2** 0.02 67.4** 0.02 9.8** −0.98 4.0* 4. Nilotic BR 4.0 4.1 0.27 19.1** 0.27 — 0.27 19.1** −0.43 14.1** 5. North African BR 5.1 5.2 0.01 36.9** 0.01 24.4** 0.01 15.7** −1.00 — Cluster A . Cluster B . DW . G(W) . IHA . G(IHA) . IHB . G(IHB) . DS . G(S) . 1+2+3+0+4+5 6+7 0.01 1782.3** −0.31 1780.7** 0.33 105.9** 0.38 2674.8** 1+2+3+0 4+5 0.40 27 025.9** 0.09 21 619.0** 0.70 24 244.1** 0.59 36 330.7** 1+2+3 0. Cretan 0.46 345.7** 0.03 345.7** 0.89 1.2 ns 0.44 405.0** 6. Western Islands 7. Sicilian 0.74 39.9** 0.74 27.1** 0.74 19.0** 0.24 12.3** 4. Nilotic 5. North African 0.52 4130.5** 0.49 285.4** 0.54 4102.4** 0.06 2503.4** 1+2 3. Eastern 0.55 19 660.1** 0.33 12 213.4** 0.77 18 586.1** 0.32 9168.9** 1. Iberian 2. Italian–Balkan 0.75 14 843.9** 0.76 13 186.4** 0.74 5572.5** 0.24 5820.2** 1. Iberian BR 1.1+1.2 1.0+1.3 0.06 430.1** 0.06 280.2** 0.07 267.7** -0.93 — 1.1 1.2 0.03 137.5** 0.03 129.4** 0.03 16.3** -0.97 0.1 ns 1.0 1.3 0.01 11.1** 0.01 0.5 ns 0.01 10.2** −0.99 — 2. Italian–Balkan BR 2.0+2.1 2.2 0.10 298.0** 0.10 173.3** 0.10 188.1** −0.90 — 2.0 2.1 0.01 7.8** 0.01 1.6 ns 0.01 5.7* −0.99 — 3. Eastern BR 3.1+3.2+3.0 3.3+3.4 0.13 1184.1** 0.14 1103.4** 0.13 274.7** −0.83 70.7** 3.1+3.2 3.0 0.02 8.5** 0.02 8.5** 0.02 1.8 ns −0.98 — 3.3 3.4 0.04 32.8** 0.03 27.4** 0.04 8.2** −0.96 — 3.1 3.2 0.02 73.2** 0.02 67.4** 0.02 9.8** −0.98 4.0* 4. Nilotic BR 4.0 4.1 0.27 19.1** 0.27 — 0.27 19.1** −0.43 14.1** 5. North African BR 5.1 5.2 0.01 36.9** 0.01 24.4** 0.01 15.7** −1.00 — Notes: DW>0 and significant G(W) indicate a weak boundary between the clusters; DS>0 and significant G(S) indicate a strong boundary; IH>0 and significant G(IH) indicate that clusters delimited by boundaries can be considered BRs. Statistical significance associated with the G-tests (degrees of freedom = 1): ns = P≥ 0.05; *P<0.05; **P<0.005;—, either significant dissimilarities to calculate G(S) are nonexistent, or the cluster is constituted by only one river basin (and so similarity values to calculate G(IH) are nonexistent). BRs are named as in Figure 2. Open in new tab Table 1. Significant boundaries between river-basin clusters of the dendrogram shown in Figure 2 (clusters A and B are upper and lower in the fork, respectively) Cluster A . Cluster B . DW . G(W) . IHA . G(IHA) . IHB . G(IHB) . DS . G(S) . 1+2+3+0+4+5 6+7 0.01 1782.3** −0.31 1780.7** 0.33 105.9** 0.38 2674.8** 1+2+3+0 4+5 0.40 27 025.9** 0.09 21 619.0** 0.70 24 244.1** 0.59 36 330.7** 1+2+3 0. Cretan 0.46 345.7** 0.03 345.7** 0.89 1.2 ns 0.44 405.0** 6. Western Islands 7. Sicilian 0.74 39.9** 0.74 27.1** 0.74 19.0** 0.24 12.3** 4. Nilotic 5. North African 0.52 4130.5** 0.49 285.4** 0.54 4102.4** 0.06 2503.4** 1+2 3. Eastern 0.55 19 660.1** 0.33 12 213.4** 0.77 18 586.1** 0.32 9168.9** 1. Iberian 2. Italian–Balkan 0.75 14 843.9** 0.76 13 186.4** 0.74 5572.5** 0.24 5820.2** 1. Iberian BR 1.1+1.2 1.0+1.3 0.06 430.1** 0.06 280.2** 0.07 267.7** -0.93 — 1.1 1.2 0.03 137.5** 0.03 129.4** 0.03 16.3** -0.97 0.1 ns 1.0 1.3 0.01 11.1** 0.01 0.5 ns 0.01 10.2** −0.99 — 2. Italian–Balkan BR 2.0+2.1 2.2 0.10 298.0** 0.10 173.3** 0.10 188.1** −0.90 — 2.0 2.1 0.01 7.8** 0.01 1.6 ns 0.01 5.7* −0.99 — 3. Eastern BR 3.1+3.2+3.0 3.3+3.4 0.13 1184.1** 0.14 1103.4** 0.13 274.7** −0.83 70.7** 3.1+3.2 3.0 0.02 8.5** 0.02 8.5** 0.02 1.8 ns −0.98 — 3.3 3.4 0.04 32.8** 0.03 27.4** 0.04 8.2** −0.96 — 3.1 3.2 0.02 73.2** 0.02 67.4** 0.02 9.8** −0.98 4.0* 4. Nilotic BR 4.0 4.1 0.27 19.1** 0.27 — 0.27 19.1** −0.43 14.1** 5. North African BR 5.1 5.2 0.01 36.9** 0.01 24.4** 0.01 15.7** −1.00 — Cluster A . Cluster B . DW . G(W) . IHA . G(IHA) . IHB . G(IHB) . DS . G(S) . 1+2+3+0+4+5 6+7 0.01 1782.3** −0.31 1780.7** 0.33 105.9** 0.38 2674.8** 1+2+3+0 4+5 0.40 27 025.9** 0.09 21 619.0** 0.70 24 244.1** 0.59 36 330.7** 1+2+3 0. Cretan 0.46 345.7** 0.03 345.7** 0.89 1.2 ns 0.44 405.0** 6. Western Islands 7. Sicilian 0.74 39.9** 0.74 27.1** 0.74 19.0** 0.24 12.3** 4. Nilotic 5. North African 0.52 4130.5** 0.49 285.4** 0.54 4102.4** 0.06 2503.4** 1+2 3. Eastern 0.55 19 660.1** 0.33 12 213.4** 0.77 18 586.1** 0.32 9168.9** 1. Iberian 2. Italian–Balkan 0.75 14 843.9** 0.76 13 186.4** 0.74 5572.5** 0.24 5820.2** 1. Iberian BR 1.1+1.2 1.0+1.3 0.06 430.1** 0.06 280.2** 0.07 267.7** -0.93 — 1.1 1.2 0.03 137.5** 0.03 129.4** 0.03 16.3** -0.97 0.1 ns 1.0 1.3 0.01 11.1** 0.01 0.5 ns 0.01 10.2** −0.99 — 2. Italian–Balkan BR 2.0+2.1 2.2 0.10 298.0** 0.10 173.3** 0.10 188.1** −0.90 — 2.0 2.1 0.01 7.8** 0.01 1.6 ns 0.01 5.7* −0.99 — 3. Eastern BR 3.1+3.2+3.0 3.3+3.4 0.13 1184.1** 0.14 1103.4** 0.13 274.7** −0.83 70.7** 3.1+3.2 3.0 0.02 8.5** 0.02 8.5** 0.02 1.8 ns −0.98 — 3.3 3.4 0.04 32.8** 0.03 27.4** 0.04 8.2** −0.96 — 3.1 3.2 0.02 73.2** 0.02 67.4** 0.02 9.8** −0.98 4.0* 4. Nilotic BR 4.0 4.1 0.27 19.1** 0.27 — 0.27 19.1** −0.43 14.1** 5. North African BR 5.1 5.2 0.01 36.9** 0.01 24.4** 0.01 15.7** −1.00 — Notes: DW>0 and significant G(W) indicate a weak boundary between the clusters; DS>0 and significant G(S) indicate a strong boundary; IH>0 and significant G(IH) indicate that clusters delimited by boundaries can be considered BRs. Statistical significance associated with the G-tests (degrees of freedom = 1): ns = P≥ 0.05; *P<0.05; **P<0.005;—, either significant dissimilarities to calculate G(S) are nonexistent, or the cluster is constituted by only one river basin (and so similarity values to calculate G(IH) are nonexistent). BRs are named as in Figure 2. Open in new tab The Iberian, Italian–Balkan, Eastern, and North African regions were subdivided by weak boundaries into some weak BRs (Figs. 2 and 3a and Table 1). They have been named by adding a second number following that of the corresponding strong region. For example, the Eastern strong region, numbered above as 3, was subdivided into the weak BRs 3.1, 3.2, 3.3, and 3.4. Again, clusters that were delimited by weak boundaries but did not fulfil the conditions to be described as BRs themselves were numbered 0 (e.g., 3.0). Values for the parameters describing BRs as fuzzy sets and quantifying their fuzzy relationships are listed in Table 2. Figure 3b,c maps strong and weak biotic boundaries as fuzzy transition zones. Each species' membership in every BR is shown in Figure 5. Figure 5. Open in new tabDownload slide Classification tree of amphibian distributions in the Mediterranean area according to the Baroni-Urbani and Buser (1976) similarity index. The degree to which each species is a member of each chorotype (C1–C16) and of each gradual distribution pattern (C1′−C13′) is shown on a grey scale. The fuzzy overlap between species distributions and BRs is also represented. *indicates strong BRs in which every species occurs; endemic species in the regions indicated are written in bold; and species also occurring outside the study area are written in brackets. Figure 5. Open in new tabDownload slide Classification tree of amphibian distributions in the Mediterranean area according to the Baroni-Urbani and Buser (1976) similarity index. The degree to which each species is a member of each chorotype (C1–C16) and of each gradual distribution pattern (C1′−C13′) is shown on a grey scale. The fuzzy overlap between species distributions and BRs is also represented. *indicates strong BRs in which every species occurs; endemic species in the regions indicated are written in bold; and species also occurring outside the study area are written in brackets. Table 2. Parameters to quantify the fuzzy relationships between neighbouring BRs: the cardinalities of the degree of inclusion of each BR in the others, and their fuzzy overlap; parameters that describe BRs as fuzzy sets: cardinality, relative cardinality, height, and entropy BRs . . Fuzzy inclusion . F. overlap . Fuzzy parameters for BR1 . BR1 . BR2 . BR1 into BR2 . BR2into BR1 . BR1 and BR2 . Cardinality . R. card. . Height . Entropy . 1. Iberian 2. Ital.–Balk. 0.78 0.83 0.67 201.4 0.42 0.81 0.38 1. Iberian 5. N-African 0.32 0.42 0.07 1. Iberian 6. W-Islands 0.07 0.73 0.22 2. Ital.–Balk. 3. Eastern 0.77 0.73 0.60 190.9 0.40 0.81 0.40 2. Ital.–Balk. 6. W-Islands 0.09 0.81 0.09 2. Ital.–Balk. 7. Sicilian 0.53 0.78 0.46 2. Ital.–Balk. 0. Cretan 0.35 0.84 0.33 3. Eastern 4. Nilotic 0.21 0.54 0.18 201.3 0.42 0.82 0.37 3. Eastern 0. Cretan 0.39 0.98 0.39 4. Nilotic 5. N-African 0.81 0.42 0.38 77.3 0.16 0.91 0.15 5. N-African 6. W-Islands 0.04 0.26 0.03 150.9 0.32 0.88 0.19 5. N-African 7. Sicilian 0.58 0.67 0.45 6. W-Islands 7. Sicilian 0.83 0.13 0.13 20.4 0.04 0.87 0.04 7. Sicilian 129.9 0.27 0.84 0.33 0. Cretan 80.3 0.17 0.85 0.19\down 1. Iberian BR 1.1 1.2 0.87 0.93 0.82 207.1 0.43 0.89 0.37 1.1 1.0 0.91 0.95 0.87 1.2 1.3 0.93 0.92 0.86 194.2 0.41 0.93 0.35 1.0 1.3 0.92 0.92 0.85 197.9 0.41 0.96 0.35 1.3 197.5 0.41 0.93 0.37 2. Italian–Balkan BR 2.0 2.1 0.91 0.97 0.88 178.7 0.37 0.95 0.37 2.0 2.2 0.95 0.80 0.77 2.1 166.2 0.35 0.91 0.37 2.2 213.0 0.44 0.93 0.39 3. Eastern BR 3.0 216.2 0.45 0.90 0.46 3.1 3.0 0.88 0.90 0.80 222.4 0.46 0.93 0.38 3.1 3.2 0.92 0.92 0.85 3.2 3.0 0.89 0.92 0.82 223.0 0.47 0.93 0.43 3.1 3.3 0.67 0.91 0.63 3.2 3.3 0.69 0.94 0.66 3.3 3.4 0.64 0.71 0.50 163.8 0.34 0.90 0.27 3.4 147.6 0.31 0.93 0.26 \down 4. Nilotic BR 4 4.1 0.13 0.96 0.13 10.9 0.02 1.00 0.01 4.1 81.0 0.17 0.91 0.16 5. North African BR 5.1 5.2 0.73 0.86 0.47 185.1 0.39 0.91 0.32 5.2 108.0 0.23 0.97 0.05 BRs . . Fuzzy inclusion . F. overlap . Fuzzy parameters for BR1 . BR1 . BR2 . BR1 into BR2 . BR2into BR1 . BR1 and BR2 . Cardinality . R. card. . Height . Entropy . 1. Iberian 2. Ital.–Balk. 0.78 0.83 0.67 201.4 0.42 0.81 0.38 1. Iberian 5. N-African 0.32 0.42 0.07 1. Iberian 6. W-Islands 0.07 0.73 0.22 2. Ital.–Balk. 3. Eastern 0.77 0.73 0.60 190.9 0.40 0.81 0.40 2. Ital.–Balk. 6. W-Islands 0.09 0.81 0.09 2. Ital.–Balk. 7. Sicilian 0.53 0.78 0.46 2. Ital.–Balk. 0. Cretan 0.35 0.84 0.33 3. Eastern 4. Nilotic 0.21 0.54 0.18 201.3 0.42 0.82 0.37 3. Eastern 0. Cretan 0.39 0.98 0.39 4. Nilotic 5. N-African 0.81 0.42 0.38 77.3 0.16 0.91 0.15 5. N-African 6. W-Islands 0.04 0.26 0.03 150.9 0.32 0.88 0.19 5. N-African 7. Sicilian 0.58 0.67 0.45 6. W-Islands 7. Sicilian 0.83 0.13 0.13 20.4 0.04 0.87 0.04 7. Sicilian 129.9 0.27 0.84 0.33 0. Cretan 80.3 0.17 0.85 0.19\down 1. Iberian BR 1.1 1.2 0.87 0.93 0.82 207.1 0.43 0.89 0.37 1.1 1.0 0.91 0.95 0.87 1.2 1.3 0.93 0.92 0.86 194.2 0.41 0.93 0.35 1.0 1.3 0.92 0.92 0.85 197.9 0.41 0.96 0.35 1.3 197.5 0.41 0.93 0.37 2. Italian–Balkan BR 2.0 2.1 0.91 0.97 0.88 178.7 0.37 0.95 0.37 2.0 2.2 0.95 0.80 0.77 2.1 166.2 0.35 0.91 0.37 2.2 213.0 0.44 0.93 0.39 3. Eastern BR 3.0 216.2 0.45 0.90 0.46 3.1 3.0 0.88 0.90 0.80 222.4 0.46 0.93 0.38 3.1 3.2 0.92 0.92 0.85 3.2 3.0 0.89 0.92 0.82 223.0 0.47 0.93 0.43 3.1 3.3 0.67 0.91 0.63 3.2 3.3 0.69 0.94 0.66 3.3 3.4 0.64 0.71 0.50 163.8 0.34 0.90 0.27 3.4 147.6 0.31 0.93 0.26 \down 4. Nilotic BR 4 4.1 0.13 0.96 0.13 10.9 0.02 1.00 0.01 4.1 81.0 0.17 0.91 0.16 5. North African BR 5.1 5.2 0.73 0.86 0.47 185.1 0.39 0.91 0.32 5.2 108.0 0.23 0.97 0.05 Note: BRs are named as in Figure 2. Open in new tab Table 2. Parameters to quantify the fuzzy relationships between neighbouring BRs: the cardinalities of the degree of inclusion of each BR in the others, and their fuzzy overlap; parameters that describe BRs as fuzzy sets: cardinality, relative cardinality, height, and entropy BRs . . Fuzzy inclusion . F. overlap . Fuzzy parameters for BR1 . BR1 . BR2 . BR1 into BR2 . BR2into BR1 . BR1 and BR2 . Cardinality . R. card. . Height . Entropy . 1. Iberian 2. Ital.–Balk. 0.78 0.83 0.67 201.4 0.42 0.81 0.38 1. Iberian 5. N-African 0.32 0.42 0.07 1. Iberian 6. W-Islands 0.07 0.73 0.22 2. Ital.–Balk. 3. Eastern 0.77 0.73 0.60 190.9 0.40 0.81 0.40 2. Ital.–Balk. 6. W-Islands 0.09 0.81 0.09 2. Ital.–Balk. 7. Sicilian 0.53 0.78 0.46 2. Ital.–Balk. 0. Cretan 0.35 0.84 0.33 3. Eastern 4. Nilotic 0.21 0.54 0.18 201.3 0.42 0.82 0.37 3. Eastern 0. Cretan 0.39 0.98 0.39 4. Nilotic 5. N-African 0.81 0.42 0.38 77.3 0.16 0.91 0.15 5. N-African 6. W-Islands 0.04 0.26 0.03 150.9 0.32 0.88 0.19 5. N-African 7. Sicilian 0.58 0.67 0.45 6. W-Islands 7. Sicilian 0.83 0.13 0.13 20.4 0.04 0.87 0.04 7. Sicilian 129.9 0.27 0.84 0.33 0. Cretan 80.3 0.17 0.85 0.19\down 1. Iberian BR 1.1 1.2 0.87 0.93 0.82 207.1 0.43 0.89 0.37 1.1 1.0 0.91 0.95 0.87 1.2 1.3 0.93 0.92 0.86 194.2 0.41 0.93 0.35 1.0 1.3 0.92 0.92 0.85 197.9 0.41 0.96 0.35 1.3 197.5 0.41 0.93 0.37 2. Italian–Balkan BR 2.0 2.1 0.91 0.97 0.88 178.7 0.37 0.95 0.37 2.0 2.2 0.95 0.80 0.77 2.1 166.2 0.35 0.91 0.37 2.2 213.0 0.44 0.93 0.39 3. Eastern BR 3.0 216.2 0.45 0.90 0.46 3.1 3.0 0.88 0.90 0.80 222.4 0.46 0.93 0.38 3.1 3.2 0.92 0.92 0.85 3.2 3.0 0.89 0.92 0.82 223.0 0.47 0.93 0.43 3.1 3.3 0.67 0.91 0.63 3.2 3.3 0.69 0.94 0.66 3.3 3.4 0.64 0.71 0.50 163.8 0.34 0.90 0.27 3.4 147.6 0.31 0.93 0.26 \down 4. Nilotic BR 4 4.1 0.13 0.96 0.13 10.9 0.02 1.00 0.01 4.1 81.0 0.17 0.91 0.16 5. North African BR 5.1 5.2 0.73 0.86 0.47 185.1 0.39 0.91 0.32 5.2 108.0 0.23 0.97 0.05 BRs . . Fuzzy inclusion . F. overlap . Fuzzy parameters for BR1 . BR1 . BR2 . BR1 into BR2 . BR2into BR1 . BR1 and BR2 . Cardinality . R. card. . Height . Entropy . 1. Iberian 2. Ital.–Balk. 0.78 0.83 0.67 201.4 0.42 0.81 0.38 1. Iberian 5. N-African 0.32 0.42 0.07 1. Iberian 6. W-Islands 0.07 0.73 0.22 2. Ital.–Balk. 3. Eastern 0.77 0.73 0.60 190.9 0.40 0.81 0.40 2. Ital.–Balk. 6. W-Islands 0.09 0.81 0.09 2. Ital.–Balk. 7. Sicilian 0.53 0.78 0.46 2. Ital.–Balk. 0. Cretan 0.35 0.84 0.33 3. Eastern 4. Nilotic 0.21 0.54 0.18 201.3 0.42 0.82 0.37 3. Eastern 0. Cretan 0.39 0.98 0.39 4. Nilotic 5. N-African 0.81 0.42 0.38 77.3 0.16 0.91 0.15 5. N-African 6. W-Islands 0.04 0.26 0.03 150.9 0.32 0.88 0.19 5. N-African 7. Sicilian 0.58 0.67 0.45 6. W-Islands 7. Sicilian 0.83 0.13 0.13 20.4 0.04 0.87 0.04 7. Sicilian 129.9 0.27 0.84 0.33 0. Cretan 80.3 0.17 0.85 0.19\down 1. Iberian BR 1.1 1.2 0.87 0.93 0.82 207.1 0.43 0.89 0.37 1.1 1.0 0.91 0.95 0.87 1.2 1.3 0.93 0.92 0.86 194.2 0.41 0.93 0.35 1.0 1.3 0.92 0.92 0.85 197.9 0.41 0.96 0.35 1.3 197.5 0.41 0.93 0.37 2. Italian–Balkan BR 2.0 2.1 0.91 0.97 0.88 178.7 0.37 0.95 0.37 2.0 2.2 0.95 0.80 0.77 2.1 166.2 0.35 0.91 0.37 2.2 213.0 0.44 0.93 0.39 3. Eastern BR 3.0 216.2 0.45 0.90 0.46 3.1 3.0 0.88 0.90 0.80 222.4 0.46 0.93 0.38 3.1 3.2 0.92 0.92 0.85 3.2 3.0 0.89 0.92 0.82 223.0 0.47 0.93 0.43 3.1 3.3 0.67 0.91 0.63 3.2 3.3 0.69 0.94 0.66 3.3 3.4 0.64 0.71 0.50 163.8 0.34 0.90 0.27 3.4 147.6 0.31 0.93 0.26 \down 4. Nilotic BR 4 4.1 0.13 0.96 0.13 10.9 0.02 1.00 0.01 4.1 81.0 0.17 0.91 0.16 5. North African BR 5.1 5.2 0.73 0.86 0.47 185.1 0.39 0.91 0.32 5.2 108.0 0.23 0.97 0.05 Note: BRs are named as in Figure 2. Open in new tab Table 3. IH values and independence G-tests (if applicable) for chorotypes and gradual patterns in Figure 5 Cluster . IH . G . Card. . Rel. card. . Height . Entropy . Max. FSR . No. species . Chorotypes C1 0.28 8.15*** 14.5 0.129 0.842 0.083 11.4 9 C2 0.55 13.61*** 20.3 0.181 0.831 0.149 11.6 10 C3 0.38 60.57*** 16.3 0.145 0.867 0.097 12.5 12 C4 0.5 14.38*** 21.0 0.187 0.746 0.167 11.7 13 C5 0.85 7.66** 8.8 0.078 0.866 0.056 7.3 3 C6 1.00 — 7.0 0.063 1.000 0.057 4.9 1 C7 1.00 — 4.2 0.037 1.000 0.029 4.2 1 C8 0.38 5.92* 14.5 0.130 0.777 0.109 7.6 7 C9 0.64 18.76*** 6.2 0.056 0.801 0.041 5.0 5 C10 0.97 11.72*** 6.0 0.053 0.979 0.029 5.8 3 C11 0.48 22.09*** 8.8 0.079 0.937 0.033 6.5 8 C12 0.69 3.89* 5.4 0.048 1.000 0.011 5.4 3 C13 1.00 28.67*** 4.5 0.040 0.910 0.014 4.3 4 C14 1 — 1.6 0.014 1.000 0.005 1.6 1 C15 1 23.94*** 3.4 0.030 0.986 0.005 3.3 3 C16 1 — 1.3 0.012 1.000 0.003 1.3 1 Gradual patterns C1′ 0.42 0.00 ns 11.2 0.100 0.852 0.079 8.7 2 C2′ 0.58 — 11.9 0.106 1.000 0.084 10.4 1 C(1-2)′ 0.91 1.23 ns 7.5 0.067 0.921 0.053 7.5 2 C4′ 0.82 — 9.2 0.082 1.000 0.067 7.4 1 C8′ 0.56 0.06 ns 22.9 0.205 0.863 0.221 10.0 2 C8″ 0.75 — 8.3 0.074 1.000 0.058 7.3 1 C(8-9-10)′ -0.15 32.84*** 4.5 0.040 0.714 0.037 3.0 7 C13′ -0.06 33.48*** 7.0 0.062 0.645 0.059 4.6 12 Cluster . IH . G . Card. . Rel. card. . Height . Entropy . Max. FSR . No. species . Chorotypes C1 0.28 8.15*** 14.5 0.129 0.842 0.083 11.4 9 C2 0.55 13.61*** 20.3 0.181 0.831 0.149 11.6 10 C3 0.38 60.57*** 16.3 0.145 0.867 0.097 12.5 12 C4 0.5 14.38*** 21.0 0.187 0.746 0.167 11.7 13 C5 0.85 7.66** 8.8 0.078 0.866 0.056 7.3 3 C6 1.00 — 7.0 0.063 1.000 0.057 4.9 1 C7 1.00 — 4.2 0.037 1.000 0.029 4.2 1 C8 0.38 5.92* 14.5 0.130 0.777 0.109 7.6 7 C9 0.64 18.76*** 6.2 0.056 0.801 0.041 5.0 5 C10 0.97 11.72*** 6.0 0.053 0.979 0.029 5.8 3 C11 0.48 22.09*** 8.8 0.079 0.937 0.033 6.5 8 C12 0.69 3.89* 5.4 0.048 1.000 0.011 5.4 3 C13 1.00 28.67*** 4.5 0.040 0.910 0.014 4.3 4 C14 1 — 1.6 0.014 1.000 0.005 1.6 1 C15 1 23.94*** 3.4 0.030 0.986 0.005 3.3 3 C16 1 — 1.3 0.012 1.000 0.003 1.3 1 Gradual patterns C1′ 0.42 0.00 ns 11.2 0.100 0.852 0.079 8.7 2 C2′ 0.58 — 11.9 0.106 1.000 0.084 10.4 1 C(1-2)′ 0.91 1.23 ns 7.5 0.067 0.921 0.053 7.5 2 C4′ 0.82 — 9.2 0.082 1.000 0.067 7.4 1 C8′ 0.56 0.06 ns 22.9 0.205 0.863 0.221 10.0 2 C8″ 0.75 — 8.3 0.074 1.000 0.058 7.3 1 C(8-9-10)′ -0.15 32.84*** 4.5 0.040 0.714 0.037 3.0 7 C13′ -0.06 33.48*** 7.0 0.062 0.645 0.059 4.6 12 Notes: Chorotypes are clusters for which IH was positive and higher than those of the other clusters including the distributions involved, and either IH was 1 or G was significant; gradual patterns are clusters that do not constitute chorotypes because at least one of the conditions described fails. Gradual pattern names indicate which chorotype/s they are associated with. Parameters that describe chorotypes and gradual patterns as fuzzy sets: cardinality, relative cardinality, height, entropy, and maximum FSR. The number of species constituting every chorotypical cluster is also listed. Statistical significance associated with the G-tests (degrees of freedom = 1): ns, P≥0.05; *P<0.05; **P<0.01; ***P<0.005; —, the cluster is constituted by only one species (and so similarity values to calculate G(IH) are nonexistent). Chrotypes and gradual patterns are named as in Figure 5. Open in new tab Table 3. IH values and independence G-tests (if applicable) for chorotypes and gradual patterns in Figure 5 Cluster . IH . G . Card. . Rel. card. . Height . Entropy . Max. FSR . No. species . Chorotypes C1 0.28 8.15*** 14.5 0.129 0.842 0.083 11.4 9 C2 0.55 13.61*** 20.3 0.181 0.831 0.149 11.6 10 C3 0.38 60.57*** 16.3 0.145 0.867 0.097 12.5 12 C4 0.5 14.38*** 21.0 0.187 0.746 0.167 11.7 13 C5 0.85 7.66** 8.8 0.078 0.866 0.056 7.3 3 C6 1.00 — 7.0 0.063 1.000 0.057 4.9 1 C7 1.00 — 4.2 0.037 1.000 0.029 4.2 1 C8 0.38 5.92* 14.5 0.130 0.777 0.109 7.6 7 C9 0.64 18.76*** 6.2 0.056 0.801 0.041 5.0 5 C10 0.97 11.72*** 6.0 0.053 0.979 0.029 5.8 3 C11 0.48 22.09*** 8.8 0.079 0.937 0.033 6.5 8 C12 0.69 3.89* 5.4 0.048 1.000 0.011 5.4 3 C13 1.00 28.67*** 4.5 0.040 0.910 0.014 4.3 4 C14 1 — 1.6 0.014 1.000 0.005 1.6 1 C15 1 23.94*** 3.4 0.030 0.986 0.005 3.3 3 C16 1 — 1.3 0.012 1.000 0.003 1.3 1 Gradual patterns C1′ 0.42 0.00 ns 11.2 0.100 0.852 0.079 8.7 2 C2′ 0.58 — 11.9 0.106 1.000 0.084 10.4 1 C(1-2)′ 0.91 1.23 ns 7.5 0.067 0.921 0.053 7.5 2 C4′ 0.82 — 9.2 0.082 1.000 0.067 7.4 1 C8′ 0.56 0.06 ns 22.9 0.205 0.863 0.221 10.0 2 C8″ 0.75 — 8.3 0.074 1.000 0.058 7.3 1 C(8-9-10)′ -0.15 32.84*** 4.5 0.040 0.714 0.037 3.0 7 C13′ -0.06 33.48*** 7.0 0.062 0.645 0.059 4.6 12 Cluster . IH . G . Card. . Rel. card. . Height . Entropy . Max. FSR . No. species . Chorotypes C1 0.28 8.15*** 14.5 0.129 0.842 0.083 11.4 9 C2 0.55 13.61*** 20.3 0.181 0.831 0.149 11.6 10 C3 0.38 60.57*** 16.3 0.145 0.867 0.097 12.5 12 C4 0.5 14.38*** 21.0 0.187 0.746 0.167 11.7 13 C5 0.85 7.66** 8.8 0.078 0.866 0.056 7.3 3 C6 1.00 — 7.0 0.063 1.000 0.057 4.9 1 C7 1.00 — 4.2 0.037 1.000 0.029 4.2 1 C8 0.38 5.92* 14.5 0.130 0.777 0.109 7.6 7 C9 0.64 18.76*** 6.2 0.056 0.801 0.041 5.0 5 C10 0.97 11.72*** 6.0 0.053 0.979 0.029 5.8 3 C11 0.48 22.09*** 8.8 0.079 0.937 0.033 6.5 8 C12 0.69 3.89* 5.4 0.048 1.000 0.011 5.4 3 C13 1.00 28.67*** 4.5 0.040 0.910 0.014 4.3 4 C14 1 — 1.6 0.014 1.000 0.005 1.6 1 C15 1 23.94*** 3.4 0.030 0.986 0.005 3.3 3 C16 1 — 1.3 0.012 1.000 0.003 1.3 1 Gradual patterns C1′ 0.42 0.00 ns 11.2 0.100 0.852 0.079 8.7 2 C2′ 0.58 — 11.9 0.106 1.000 0.084 10.4 1 C(1-2)′ 0.91 1.23 ns 7.5 0.067 0.921 0.053 7.5 2 C4′ 0.82 — 9.2 0.082 1.000 0.067 7.4 1 C8′ 0.56 0.06 ns 22.9 0.205 0.863 0.221 10.0 2 C8″ 0.75 — 8.3 0.074 1.000 0.058 7.3 1 C(8-9-10)′ -0.15 32.84*** 4.5 0.040 0.714 0.037 3.0 7 C13′ -0.06 33.48*** 7.0 0.062 0.645 0.059 4.6 12 Notes: Chorotypes are clusters for which IH was positive and higher than those of the other clusters including the distributions involved, and either IH was 1 or G was significant; gradual patterns are clusters that do not constitute chorotypes because at least one of the conditions described fails. Gradual pattern names indicate which chorotype/s they are associated with. Parameters that describe chorotypes and gradual patterns as fuzzy sets: cardinality, relative cardinality, height, entropy, and maximum FSR. The number of species constituting every chorotypical cluster is also listed. Statistical significance associated with the G-tests (degrees of freedom = 1): ns, P≥0.05; *P<0.05; **P<0.01; ***P<0.005; —, the cluster is constituted by only one species (and so similarity values to calculate G(IH) are nonexistent). Chrotypes and gradual patterns are named as in Figure 5. Open in new tab The Iberian, Italian–Balkan, and Eastern strong regions showed the highest entropy, that is, they were the fuzziest regions (Table 2), and the highest fuzzy cardinality, that is, they were the ones in which most OGUs had a high degree of membership. Each of these regions has more than 30 species—whereas none of the other regions has more than 15—and their neighbourhood involves very high fuzzy overlap and mutual inclusion values. A wide transition zone, including the French river basins and expanding throughout the north of the Iberian Peninsula, shapes the fuzzy boundary between the Iberian and the Italian–Balkan regions (Fig. 3b), which share 16 species, that is, 42% and 38% of their respective amphibian fauna (Fig. 5). On the other hand, the transition zone between the Italian–Balkan and the Eastern region spreads throughout both sides of the Bosphorus strait, the south and the east of Greece, the Aegean islands and the northern coasts of Turkey; 11 species are shared by these regions, that is, 26% of the Italian–Balkan species and 34% of the Eastern species. The Sicilian strong region also showed high entropy because of its high overlap with both the Italian–Balkan and the North African regions, in which their amphibian fauna is partly included; the Sicilian region shares 5 species, that is, 63% of its amphibian fauna, with the Italian–Balkan region, and 3 species, that is, 38% of its fauna, with the North African region. The least fuzzy strong region was the Western Islands, its entropy being lower than 0.05 out of 1 (Table 2); this region also had the lowest fuzzy cardinality. The limits between the Western Islands and North Africa are a clear example of a crisp boundary: no species are shared between both areas, and thus there is practically no fuzzy overlap and mutual inclusion. The species assemblages of the Western Islands region are mainly composed of endemics; 10 of its 14 species are endemic, and 2 more species could be considered endemic as Hyla sarda and Discoglossus sardus spread throughout less than 400 km2 outside the Western Islands region. Due to this, its biotic overlap with the Iberian, Italian–Balkan, and Sicilian regions is negligible; the species composition of the Western Islands region is fuzzily included in the Iberian, Italian–Balkan, and Sicilian regions because 1, 4, and 2 of its species are shared with these 3 regions, respectively. Africa shares only 8 out of its 20 northern species with the Mediterranean peninsulas and Near East (Figs. 2 and 5). Fifteen species occur in the North African region, 6 of which are endemic to BR 5.1, whereas 2 other species spread slightly southward; only the Nilotic species Amietophrynus regularis occurs in region 5.2 but not in region 5.1. Northern Algeria and northern Tunisia show the lowest membership degrees in the North African region (Fig. 4) because of the African species distributions that also occur outside this continent. The North African BR shows an almost crisp boundary with the Iberian Peninsula, which is denoted by an extremely low fuzzy overlap and by moderate mutual inclusion values (Table 2). Only 3 species are shared, that is, 20% and 8% of their amphibian fauna, respectively. In the east, there is a narrow transition zone between Northern Africa and the Nilotic region in the Qattara Depression; Pseudepidalea boulengeri and A. regularis alone are shared by these regions, but they represent the 33% of the Nilotic amphibian fauna. Finally, the Nilotic region shares 4 species with the Eastern regions: P. boulengeri, Pseudepidalea variabilis, P. bedriagae, and A. regularis, that is, 66% and 13% of their respective amphibian faunas, the latter species not spreading beyond Sinai. As a result, the boundary between these regions is a moderately fuzzy transition zone involving 2 OGUs to the north of Sinai. The Nilotic region was the least fuzzy continental region because 4 of its maximum of 7 species are restricted to this region within the context of our study area. Fuzzy membership in the Nilotic region is higher in the south (Fig. 4) because the northern half contains species that spread north-eastward outside Africa. Weak boundaries within strong BRs involved a high overlap (Table 2) that only showed values below 0.75—out of 1—within the Eastern and the North African regions. Thus, very fuzzy transition zones are drawn along most of the weak boundaries (Fig. 3c). Sixteen chorotypes and 8 gradual patterns, fuzzily overlapping with chorotypes, were detected for the amphibian species in the Mediterranean area (Table 2 and Figs. 5 and 6). These chorotypes are involved in the configuration of the species composition of each BR (Fig. 7), and so the Iberian region was characterized mainly by chorotypes C1 and C2 and by the gradual patterns C1′ and C(1-2)′; the Italian–Balkan region by chorotypes C3, C4, C5, and C6, and by the gradual pattern C4′, whereas chorotype C7 was involved in the transition zone between both the Italian–Balkan and the Iberian regions; the Eastern region was characterized by chorotypes C8, C9, and C10 and by the gradual pattern C(8-9-10)′, and chorotype C8, together with the gradual patterns C8′ and C8″, characterizes the transition between the Eastern and the Italian–Balkan regions; the Western Islands region is characterized by chorotypes C11, C12, and C16; the Nilotic region by chorotype C13; the North African region by the gradual pattern C13′; and no chorotype specifically characterized the Sicilian region, although its fuzzy transition with their surrounding regions was mainly characterized by chorotype C3 and by the gradual pattern C13′. Figure 6. Open in new tabDownload slide Geographical representations of the chorotypes (C1–C16, outlined with rectangles) and gradual distribuion patterns (C1′−C13′) described for amphibians in the Mediterranean area. The FSR (Olivero et al. 2011) is mapped. Broken lines indicate that a gradual distribution pattern, from which an arrow is shot, is associated with a chorotype. Figure 6. Open in new tabDownload slide Geographical representations of the chorotypes (C1–C16, outlined with rectangles) and gradual distribuion patterns (C1′−C13′) described for amphibians in the Mediterranean area. The FSR (Olivero et al. 2011) is mapped. Broken lines indicate that a gradual distribution pattern, from which an arrow is shot, is associated with a chorotype. Figure 7. Open in new tabDownload slide Correlation between strong BRs (fuzzy difference between a region and the rest of the study area) and chorotypes (fuzzy species richness). Figure 7. Open in new tabDownload slide Correlation between strong BRs (fuzzy difference between a region and the rest of the study area) and chorotypes (fuzzy species richness). The 4 first DCA axes provided the following eigenvalues: 0.84, 0.64, 0.34, and 0.28. All OGUs were plotted on the first two ordination axes (Fig. 8). The 7 strong BRs and some of the weak BRs defined by our classification are easily recognizable as groups of nearby points in the plot. Figure 8. Open in new tabDownload slide The first two axes of a DCA of the OGUs shown in Figure 1 according to their amphibian species composition. Lines group dots—which symbolize OGUs—according to the biogeographic regionalization shown in Figure 3a: thick sharply bent lines surround strong regions; thin curved lines surround weak regions; broken lines surround areas that are not BRs but are gradually associated with regions. Areas shaded grey represent membership in transition zones, based on the fuzzy symmetric differences between neighbouring strong regions (see top-right map and Fig. 3b). Figure 8. Open in new tabDownload slide The first two axes of a DCA of the OGUs shown in Figure 1 according to their amphibian species composition. Lines group dots—which symbolize OGUs—according to the biogeographic regionalization shown in Figure 3a: thick sharply bent lines surround strong regions; thin curved lines surround weak regions; broken lines surround areas that are not BRs but are gradually associated with regions. Areas shaded grey represent membership in transition zones, based on the fuzzy symmetric differences between neighbouring strong regions (see top-right map and Fig. 3b). Discussion Mediterranean Biogeographic Regionalization Based on Amphibians Africa in the Mediterranean biogeographical area —According to our results, the continental Mediterranean areas are divided by a main biogeographic boundary between Eurasia and Africa. Vicariance in the Strait of Gibraltar can be generalized to most amphibian species for which a few kilometres of sea water appear to act as a biogeographic barrier (Pleguezuelos et al. 2008), whereas the amphibian need for moist habitats and water bodies for reproduction may be the reason for a steep north-to-south decrease of species richness (Fig. 9b) that coincides with a gradient of aridity (Lescure 1992; Blondel et al. 2010). A biogeographic boundary between Europe and Africa has been described for amphibians (Grabińska 1990) and mammals (Grabińska 1992; Vargas et al. 2003), but neither for reptiles (Grabińska 1990) nor for birds (Covas and Blondel 1998). Vicariance processes caused by the Strait of Gibraltar seem to have influenced current mammal distributions as much as amphibians (Steininger et al. 1985; Pleguezuelos et al. 2008), whereas dispersive processes across the strait are considered to be more important for reptiles (Carranza et al. 2004, 2006) and for birds (Blondel et al. 2010). Figure 9. Open in new tabDownload slide a) Species range limits of amphibians in the study area. b) Number of amphibian species. c) Number of amphibian species that are endemic to a single strong BR (Fig. 3); strong boundaries are outlined. Figure 9. Open in new tabDownload slide a) Species range limits of amphibians in the study area. b) Number of amphibian species. c) Number of amphibian species that are endemic to a single strong BR (Fig. 3); strong boundaries are outlined. A gradient of aridity may explain the strong eastward decrease in species richness that gives rise to a fuzzy transition zone between north-western and north-central Africa (Pleguezuelos et al. 2008; Fig. 3a,c). In the north east of Africa, the proximity of the river Nile encourages the existence of a different region that may spread southward beyond the study area. Mediterranean peninsulas —The continental biotic boundaries north of Africa indicate a regionalization based on differences between the Mediterranean peninsulas through very fuzzy transition zones. This regionalization is consistent with Rueda et al.'s (2010) patterns for European amphibians, and to a lesser extent with Grabińska's (1990) patterns. According to Rueda et al. (2010), the Italian and Balkan peninsulas constitute a single BR, whereas Iberia remains biotically linked to southern France. Although the Iberian and Italian peninsulas have very similar numbers of amphibian species, the frequency of endemics in Iberia is higher (Crnobrnja-Isalovic 2007; cf. Fig. 9b,c). Grabińska (1990) also recognized Iberia and Anatolia as biogeographic regions for amphibians, whereas this author considered France, Italy, and the Balkan Peninsula transitional areas between the Mediterranean area and central Europe. The biogeographical separation between Iberia and the Italian–Balkan peninsulas has been proposed in regionalizations based on other taxa: all vertebrates (Grabińska 1994), forest birds (Covas and Blondel 1998), mammals (Grabińska 1992; Heikinheimo et al. 2007), and butterflies and trees (Rueda et al. 2010). The transitional role of southern France is reflected by the fact that, for several taxa, this area has been linked to either Iberia (Grabińska 1994; Heikinheimo et al. 2007; Rueda et al. 2010), to Italy (Covas and Blondel 1998) and to both areas (Grabińska 1993; Myklestad and Birks 1993; Olivero et al. 1998; Vargas et al. 2003; Heikinheimo et al. 2007; Rueda et al. 2010), probably because it contains northern extra-Mediterranean biotic elements (Grabińska 1990). On the other hand, Anatolia and the Italian–Balkan regions have been considered biogeographically different from each other also for both scrubland and steppe birds (Covas and Blondel 1998), but similar for other taxa (Grabińska 1992, 1994; Covas and Blondel 1998), which is consistent with the existence of a wide and highly fuzzy transition zone between the Anatolian and the Balkan peninsulas. The number of European amphibian species inhabiting the 3 Mediterranean peninsulas is extraordinarily high compared with the number of species shared between them (Gasc 1997). Crnobrnja-Isalovic (2007) suggests that this represents the uniqueness and importance of each of the Iberian, Italian, Balkan, and Anatolian peninsulas as refugia during the Pleistocene glaciations (see also Taberlet et al. 1998; Hewitt 1999; Médail and Diadema 2009). However, the role of Pleistocene refugia in speciation is controversial because some of sister taxa appear to have preglacial origins (Arntzen et al. 2007; Hofman et al. 2007). Nonetheless, the Mediterranean Pleistocene refugia certainly had an important role in remodelling the distributions of pre-existing lineages during the glacial climatic fluctuations (Hofman et al. 2007). Moreover, refugia within refugia seem to have been essential in shaping the current biogeographic patterns within the Mediterranean peninsulas (see Alexandrino et al. 2000; Martínez-Solano 2004; Crnobrnja-Isalovic 2007; Gómez and Lunt 2007; Sotiropoulos et al. 2007; Médail and Diadema 2009). Within strong BRs, the fuzzy interpretation of weak boundaries (Fig. 3c) provided higher consistency than the initially crisp regionalization (Fig. 3a) when compared with other proposals in the literature. For example, our fuzzy regionalization for amphibians within Iberia absorbed most of the existing discrepancies between the regionalizations proposed by Doadrio (1988), Vargas et al. (1998), Márquez et al. (2001), and García-Barros et al. (2002). The north-central area of Iberia, a transition between all the Iberian regions in our pattern, has been recognized in the literature as biogeographically confusing (see Márquez et al. 2001; García-Barros et al. 2002). Insular regions —Compared with the mainland, the Mediterranean insular fauna shows species impoverishment probably mediated by human disruption, whereas there are few endemic amphibian species, especially in the islands of the eastern half of the Mediterranean Sea (Blondel et al. 2010; see also Fig. 9). Our results reflect this trend: the crispest Western Islands region shows the highest number of endemics; the fuzzily bounded Sicilian region, Crete, Rhodes, and the Karpathos archipelago have only one endemic species each; and Cyprus and the Aegean islands show no endemics whatsoever. Contextualizing our Method for Fuzzy Biogeographic Regionalization Transition zones: hovering between the discrete and the continuous —Characterizing biogeographic boundaries as either crisp or fuzzy entities is framed within the debate on whether fauna and vegetation can be described in terms of continuous or discrete communities (see Austin 1985, Austin and Smith 1989). In Mayr's (1965) opinion, biogeographic units do not constitute physical entities, and so can neither be observed nor be clearly delimited. However, Austin and Smith (1989) suggested that the concept of biota with a continuously varying composition could form the basis for a predictive theory providing there was an explicit link between biota and environment; abrupt changes or gradual transitions would then occur depending on the landscape pattern, and co-occurring groups of species could be recognized within particular regions with recurrent patterns of landscape. Thus, variations in the composition of species assemblages appear to hover between the discrete and the continuous (Leung 1987; Hengeveld 1990; Williams 1996), but this is only reflected in a biogeographical regionalization if sharp and precise boundaries can be combined with gradual transition zones. Fuzzy sets provide an efficient summarization of the continuum concept while allowing for the recognition of discrete communities (Roberts 1989). The method described in this study enabled us to consider a gradual spatial replacement of species in the absence of evidence that species form discrete aggregations—as suggested by Hengeveld (1990)—and to distinguish between crisp boundaries and highly fuzzy transition zones. More or less gradual transition zones were distinguished in northern Africa, probably derived from spatial changes in the environment as proposed by Peters (1955), and the gradualness of these transitions depended on the degree of sharpness of these changes; they were sharper around the Nile basin and more gradual in the transition between the Atlas highlands and the Sahara Desert. The other transition zones could have responded to prior ecological changes combined with physiographic barriers, as suggested by Morrone (2004), and were fuzzier in the limits between the Mediterranean peninsulas, where they were closely connected to each other but with different biotic histories, and with physiographical barriers such as the Alps and the Bosphorus Strait; they were sharper around the Western Islands and in the Strait of Gibraltar. Biogeographic homology versus quantitative similarity —Our methodological approach is framed within Kreft and Jetz's (2010) classification of methods for delineating biogeographical regions based on biotic similarities, within the quantitative clustering approach. Defenders of the use of biogeographical homology suggest that raw or global similarity, as a criterion to define biogeographic units, does not reflect natural patterns (Escalante 2009); methods based on similarity are considered to be a heritage of numerical taxonomy—the phenetic school—that lacks theoretical support within the discipline of biogeography (Murguia and Llorente-Bousquets 2003). Biogeographical homology is a conjecture regarding a common biogeographical history, which means that different plant and animal taxa are spatiotemporally integrated in a biota (Morrone 2001, 2004). According to this, most of the taxa inhabiting throughout a BR share a common geobiotical history—just like, in cladistic taxonomy, the morphological characteristics considered to classify different organisms share a common evolutionary history—and so the identification of patterns of biogeographic homology is a basic requirement for proposing schemes of natural regionalizations (Morrone 2001; Escalante 2009). Endemic species distributions are treated as character states of areas that are classified into biogeographic units, that is, areas of endemism, by using methods such as generalized track analysis (panbiogeography: Croizat 1958, 1964), parsimony analysis of endemicity (Rosen 1988; Morrone 1994) and optimization analysis (Szumik et al. 2002). Although the occurrence of dispersal is not doubted by modern historical biogeographers (Grehan 1991; Morrone 2004), some authors believe that areas of endemism are suitable for use as biogeographic units only under the assumption that biotas evolved according to the vicariance model and without dispersal. Hausdorf (2002) stated that the reasons for using parsimony algorithms to reconstruct a dichotomous split sequence that delimits areas of endemism are unclear, because if dispersal were taken into account the distribution of taxa would not be the result of such a split sequence between the OGUs. Without dispersal, each biota would consist of a single chorotype, chorotypes would not overlap, and all species would be endemic to a region without any blending of fauna or flora into other regions (Hausdorf 2002; Kreft and Jetz 2010). From the perspective of fuzzy logic, such an extreme position would generate a regionalization in which every OGU would have a maximum degree of membership in a single BR; chorotypes and BRs would then converge and so every BR would correspond to the distribution pattern defined by a single chorotype, which is far from being the case according to our results (Figs. 3–5). The debate between defenders of biogeographic homology and supporters of quantitative biogeography remains unresolved. The former group argues that similarity should either be used for exploratory purposes alone, constrained to ecological biogeography analyses or simply abandoned (Murguia and Llorente-Bousquets 2003); on the other hand, the latter group suggests that species assemblages can be distinct in composition without necessarily having high proportions of endemic species (Kreft and Jetz 2010). This study does not contribute to solving this scientific debate, but is based on the assumption that whole-assemblage similarities need to be considered when comparing regional biotic compositions; whether biogeographic units have a historical origin and how far they are influenced by ecological factors should not be assumed a priori but investigated by further analyses (Hausdorf 2002), and whether endemic species have or have not been responsible for the existence of some BRs can also be searched a posteriori (cf. Figs. 3 and 9c). For example, in our regionalization, amphibian endemics were important in the south-western Iberian quarter (region 1.3), in the Western Islands region, mostly in Corsica, and to a lesser extent in central and southern Italy (region 2.1), whereas other areas, such as the Balkan and Anatolian peninsulas, lack a great number of regional endemics, which could be biogeographically interpreted by the apparently immense dispersal of amphibian species from and to these regions after the Pleistocene ice retreat (Taberlet et al. 1998; Hewitt 1999; Crnobrnja-Isalovic 2007). Inside the Iberian region, the observed pattern of weak boundaries delimits some of the largest Iberian areas of endemism described in García-Barros et al. (2002), while the areas described as transitional in the analysis concentrate the highest density of Iberian microendemic species. Methodological context within quantitative biogeography —Kreft and Jetz (2010) distinguished 3 main quantitative methodological approaches that can complement each other in biogeographical studies: ordination, geographical visualization of turnover, and classification. Alternatives to these methods include visually inspecting the density of species range limits (McAllister et al. 1986) and gradients in species richness (Rabinovich and Rapoport 1975; Ruggiero and Ezcurra 2003). In our case study, range limits strongly coincide mainly in transition zones defined by weak boundaries (cf. Figs. 3 and 9a), such as those inside the Iberian Peninsula and between northern and southern Italy; some of these boundaries are also characterized by notable gradients in species richness (cf. Figs. 3 and 9b). However, neither range limits nor gradients in species richness would have led to an accurate regionalization. Ordination is able to show continuous biogeographic transitions and also to mark discontinuous changes in biotic composition, intuitively allowing inferences about biotic distances between and within regions (Kreft and Jetz 2010). However, the recognition of transition zones by ordination is indirect, because they only become apparent as vague rates of change due to comparisons with neighbouring OGU scores (Williams et al. 1999); that is, they appear as part of a continuous theoretic landscape of gradual change in which limits—either gradual or sharp—between regions cannot be objectively determined unless ordination is combined with classification. Our biogeographical regionalization seems to be outlined by the location of points in a DCA plot where our Mediterranean OGUs were ordered on the basis of the amphibian species distributions (Fig. 8). The almost-crisp boundaries between northern Africa and Iberia, and also around the Western Islands region, are shown in that plot by long distances between areas that are, however, geographic neighbours; apart from these boundaries, it is difficult to intuitively recognize, without the help of a classification, which points constitute the core of regions and which ones are transitional OGUs, despite the fact that points belonging to transition zones were frequently located between the regions of which they are fuzzy boundaries. According to Williams et al. (1999), classification methods can differentiate the relative strengths of entire boundaries through the hierarchy, but cannot reveal any variation in strength or breadth along these boundaries. However, this information could be obtained by mapping the rates of species turnover throughout the study area, for which some indices based on β-diversity have been proposed (see examples in Williams 1996; Williams et al. 1999). Thus, the turnover approach was conceived as supplementing the analytical power of classification in biogeographical regionalization (Williams et al. 1999) because of its high potential for the analysis of biogeographic transitions. Our proposal involves the description of areas with high species turnover. However, we opted to define transition zones as areas where different biotas overlap (Halffter 1976), for which regions with characteristic biotas need to be detected before analysing their limits. The contribution of our methodological approach is that the characterization of boundaries as more or less fuzzy transition zones constitutes an extension of the classification method itself, based on the same relationships between OGUs that were used to define the BRs, that is, the similarities matrix. Thus, by creating a fuzzy classification from an initially crisp classification, we obtained information on variations in strength, breadth, and gradualness along the length of each boundary. Cluster analyses can be divided into 2 main families according to whether objects are classified hierarchically or not (Kreft and Jetz 2010). Our classification method belongs to the hierarchical family, but nonhierarchical—or partitioning—algorithms have also contributed to the use of fuzzy logic in ecological and biogeographical classifications. The most representative example of this is the Fuzzy-C-Means clustering algorithm (FCM; Bezdeck et al. 1984), which derives from the K-means algorithms (MacQueen 1967). Like our method, FCM provides a fuzzy partition starting from a collection of crisp data—presences and absences—based on the perception that relationships between species ranges are not crisp. However, with the exception of researchers such as Brown (1998), this partition has been very rarely presented in the form of regions delimited by fuzzy transitions; instead, fuzzy membership has been used to draw crisp limits between clusters as the final output (e.g., see Eyre et al. 2003). Our methodological approach to mapping a fuzzy regionalization is fully applicable to the results of FCM, as it is to any classification based on degrees of membership in clusters. However, just like the K-means algorithm, FCM has limitations as a method for regionalization (Kreft and Jetz 2010; Olivero et al. 2011): the need to specify a priori a number of BRs, the inability to keep unclassified OGUs, and the need to decide a degree of fuzziness for partitioning. An approach to the optimal number of regions can be attempted by comparing different classifications obtained with different numbers of clusters by means of partition efficiency indicators, such as the Non-Fuzzyness Index (Roubens 1982) and ν-fold cross-validation, which was applied in Rueda et al.'s (2010),K-means-based biogeographic regionalizations (another interesting method for an objective selection of the number of clusters was proposed by Fraley and Raftery [2002]). However, in our approach, the decision regarding how many clusters should be considered BRs is not derived from an overall evaluation of the optimum number of clusters, but from the individual assessment of each cluster potentially considered to represent a biographic entity. Methodological innovations such as the Possibilistic C-Means algorithm (Krishnapuram and Keller 1993) not only avoid the need to specify the number of clusters but also accept unclassified elements; however, it still requires a priori decisions about the degree of overlap that is acceptable for distinguishing different regions. Compared with previous studies in which the statistical basis of our method was used, the fuzzy approach provides a more heuristic way to analyse the complexity of the biota within an area and goes beyond the simple characterization of biotic boundaries as permeable, semipermeable, or impermeable, as proposed in Olivero et al. (1998) following Hernández and Sainz (1984). Compared with other classification procedures based on fuzzy sets, the novelty of our methodological proposal is that both fuzzy logic and statistics are used in combination to avoid arbitrary decisions, providing a synergy that can improve reliability in the definition of biogeographic regions and transition zones. Supplementary Material Supplementary material, including data files, can be found online in the Dryad data repository at http://datadryad.org, doi:10.5061/dryad.1cq8n52h. Funding This work was supported by Ministerio de Ciencia e Innovación, Spain, and European Regional Development Fund, European Union [project CGL2009-11316]. Acknowledgements We thank Dr. A.M. Barbosa for her useful methodological contributions; Dr. J.H.B. Birks, Dr. J. Morrone, and anonymous reviewers for their useful comments; and Mr. S. Coxon for his help in revising the language used in this article. Appendix Identification of Biogeographic Regions and Boundaries The method used for biogeographical regionalization was cluster analysis based on a matrix of biotic similarities between OGUs (see Kreft and Jetz 2010). An optimum number of regions is determined by information extracted from both the structure of the classification tree and the significance of similarity values. Note that we use the terms “BR” and “biotic boundary” in the following, without alluding to any established nomenclatural system for biogeographical regionalizations (e.g., Brown and Lomolino 1998, p. 302). Biotic pair-wise similarities between OGUs were calculated using Baroni-Urbani and Buser's (1976) index: where A is the number of species that occur in OGU a, B is the number of species that occur in OGU b, C is the number of species that occur in both a and b, and D is the number of species in the study area that are absent from both a and b. Completely coinciding species compositions produce a similarity value 1, while having nothing in common is represented by value 0. Shared absences were taken into account in order to make similarities be a characteristic of the relation between OGUs in the context of the Mediterranean basin (Real et al. 1992). According to Baroni-Urbani and Buser (1976), considering common absences is valuable because they highlight differences that are biogeographically informative; for example, locations within the study area where some species cannot live because of the environmental conditions, and locations where some species do not live because of historical reasons. Shared absences are, however, multiplied by shared presences in their index to give more importance to shared presences and to prevent the possibility that 2 OGUs would show high similarity because of shared absences alone. This index has a table of critical values, which is key to our proposed methodology. On the basis of the resulting similarity matrix, we classified the OGUs using the Unweighted Pair-Group Method using Arithmetic Averages (UPGMA). This agglomerative classification algorithm produces less distortion in relation to the original similarities than complete, single, and other average linkages such as WPGMA and UPGMC (Sneath and Sokal 1973) and has shown to provide better performance for biogeographical regionalization—using the cophenetic correlation coefficient, which represents a direct measure of how much of the original information is retained in the dendrogram (Sneath and Sokal 1973)—than UPGMC, WPGMA, WPGMC, Ward's method, single linkage, complete linkage, neighbour-joining trees, and the DIANA algorithm (Kreft and Jetz 2010). The following description, and that presented by Olivero et al. (2011) for chorotype analysis, represents generally equivalent procedures. However, for the aims of the study, we define new parameters and reinterpret and combine in a different way to those described in Olivero et al. (2011). The null model that similarities between OGUs are not different from those expected at random was tested using the table of critical similarity values presented in Baroni-Urbani and Buser (1976). This table is based on exact randomization tests where the observed similarity values are compared with all the possible outcomes (Sokal and Rohlf 1981, p. 788; Real and Vargas 1996). In this way, similarity values higher than 95% and lower than 95% of outcomes were, respectively, considered “significant similarities” (+) and “significant dissimilarities” (−), and the rest were considered as values expected at random (0). These significances reflect the exact mathematic probability of finding a lower or higher similarity value, and not the statistical probability of committing a Type II error. By examining the classification tree from the lowest to the highest similarity node, we searched for 2 types of biotic boundaries: “weak boundaries,” defined by significant similarities within the bounded regions; and “strong boundaries,” defined by significant between-region dissimilarities (McCoy et al. 1986). Thus, we operationally defined what is the main aim of biogeographical regionalizations: to maximize homogeneity in taxonomic composition within regions while maximizing the differences between regions (Kreft and Jetz 2010). For each node in the dendrogram let A be the set of OGUs in the left branch and let B be the set of OGUs in the right branch. The Cartesian product A × A represents the pair-wise comparison of every OGU in set A with every other OGU in set A; for set B, the product B × B compares every OGU in set B with every other OGU in set B; finally, let the product A × B represents the comparison of every OGU in set A with every OGU in set B. Should set A represent a BR, we would expect to find primarily significant similarities in the product A×A, with relatively few significant dissimilarities. If set A were distinct from set B, we would expect to find primarily significant dissimilarities or similarities expected at random in product A×B, with relatively few significant similarities. The following set of parameters—see Olivero et al. (2011) for their mathematical formulations—is defined as follows: Pp: proportion of pair-wise comparisons A×A that are significant similarities. Psp: proportion of OGUs in set A that have at least one significant similarity to another OGU in set A. Pm: proportion of pair-wise comparisons in A×A that are significant dissimilarities. Psm: proportion of OGUs in set A that have at least one significant dissimilarity to another OGU in set A. P′p: proportion of pair-wise comparisons in the product A×B that are significant similarities. P′sp: proportion of OGUs in set A or B that have at least one significant similarity to another OGU in the other set. Based on these values, the extent to which significant similarities and dissimilarities predominate where expected is calculated in the following way: the predominance of significant similarities within set A; the predominance of significant dissimilarities in set A; ⁠, the predominance of significant similarities in product A × B; ⁠, the predominance of significant dissimilarities in product A × B. These are used to calculate the index of internal homogeneity and distinctness (IH), a rescaled to [−1, 1] version of DW (A×A) presented in Olivero et al. (1998), that represents the degree to which set A meets a criterion that is basic for representing a BR: On the other hand, the degree to which there is a weak boundary between sets A and B is measured by DW: where IHA and IHB are the indices of internal homogeneity and distinctness for both sets A and B, respectively. The nomenclature for DW was taken from McCoy et al. (1986), where D denotes “distance” and W means “weak.” Finally, the following rules were followed to identify significant weak boundaries and significant regions: A weak boundary was considered to exist between sets A and B if: 1) DW = 1, that is, all the criteria were completely met; or else 2) DW was positive and statistically significant. Our statistical approach was based on testing the null hypothesis that “+” similarities between the OGUs grouped in set A and between the OGUs grouped in set B are not more frequent than “+” similarities between these 2 sets, which was measured using a G-test of independence (Sokal and Rohlf 1981); in this case, the G parameter was named G(W). In every branch of the classification tree, the examination ended as soon as a node between sets of OGUs was identified as not being a biotic boundary. A BR was considered to exist at side A of a weak boundary if: 1) IHA=1, that is, all the criteria were completely met; or else 2) IHA was positive and statistically significant. In this case, our statistical approach was based on testing the null hypothesis that “+” similarities between the OGUs grouped in set A are not more frequent than “+” similarities between sets A and B, which was measured using a G-test of independence; in this case, the G parameter was named G(IHA). The degree to which there is a strong boundary between sets A and B is measured by DS (from D= “distance” and S= “strong”; McCoy et al. 1986): where dmA and dmB are the respective dm values for sets A and B. 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TI - Integrating Fuzzy Logic and Statistics to Improve the Reliable Delimitation of Biogeographic Regions and Transition Zones
JF - Systematic Biology
DO - 10.1093/sysbio/sys061
DA - 2013-01-01
UR - https://www.deepdyve.com/lp/oxford-university-press/integrating-fuzzy-logic-and-statistics-to-improve-the-reliable-uYWjCLbHFo
SP - 1
EP - 21
VL - 62
IS - 1
DP - DeepDyve
ER -