Introduction Biogeography is the discipline interested in documenting and understanding spatial biodiversity patterns [] and also in explaining the evolutionary history that led to this current spatial configuration [–]. Detailed data regarding how organisms are distributed, the basis of biogeographical studies, enable such distribution patterns to be identified, including natural biogeographical units [–]. These natural biogeographical regions are fundamental units of comparison in many broad-scale ecological and evolutionary studies [,] and provide an essential tool for conservation planning [,–]. There are several methods proposed to identify biogeographical units (e.g., [,–]). A well-known method is the parsimony analysis of endemicity that is used to detect natural biogeographical units in named areas of endemism [,,,]. According to some authors (e.g., [,,]), areas of endemism have a unique biota with similar historical processes and are the basis for postulating hypotheses regarding the processes that led to their origin.

However, the determination of natural biogeographical units based solely on strict endemism is effective only in cases of strict sympatry [,] that is not so common in natural conditions. Dispersal and extinction are natural events that can cause noise in the identification of areas of endemism and hinder the recognition of natural biogeographical units [,]. For this reason, biotic element analysis has been used in many studies as an alternative method to detect natural biogeographical units (e.g., [,,,,–]). The biotic element analysis identifies groups of taxa with geographic distributions significantly more similar to one another [,]. The advantage is that biotic elements may be recognized even when part of the taxa originated by vicariance has dispersed across barriers [,]. The biotic element analysis is based on the assumption of vicariance and postulates that diversification results from fragmentation of the ancestral biota by the emergence of barriers [,,,,].

Consequently, it is expected that the distributions of taxa with the same geographical origin are more similar to each other than to the distributions of taxa from distinct geographical origins, and the taxa that are closely related due to the vicariance process belong to distinct biotic elements [,]. The identification of natural biogeographical units is important to understand the evolutionary history of taxa and of the areas that encompass them, and such studies in natural environments are incipient [,], as in the case of the biota from the sandy plains of the coastal ridges of Brazil. The coastal sandplains are commonly known as Restingas and are included in the Tropical Atlantic Domain [], which also includes the Atlantic Forest, a global biodiversity hotspot []. Studies on different biological groups, especially those focused on forest habitats of the Atlantic Forest in Brazil, have been carried out to identify distributional patterns [,,].

Biogeographic studies have not yet addressed the distribution patterns of amphibian communities or the processes that have shaped these communities. Additionally, studies in the Restingas area of the Tropical Atlantic Domain is neglected, as most investigations have focused on the forested part of this domain [–]. For this reason, we assessed for the first time the amphibian distribution patterns in a biogeographical study of Restingas.

The aims of our study were: (1) to identify distribution patterns of anuran species occurring on sandy plains of beach ridges of the eastern Brazilian coast; (2) to detect natural biogeographical units throughout the study area and to identify groups of anuran species with non-random overlapping geographical distribution (biotic elements); and (3) to provide the first formal test of two predictions of the vicariance model to evaluate the hypothesis that the diversification of these species can be a result of fragmentation of the ancestral biota by emerging barriers. Study area The east coast of Brazil is located within the Tropical Atlantic Domain [] and is essentially covered by the Atlantic Forest, a global biodiversity hotspot []. The Restinga is a component of the Atlantic Forest habitat characterized by dunes and sandy plains covered by herbaceous and shrubby vegetation under direct sunlight (‘open Restinga’, ), having experienced extensive degradation over the past five centuries [].

The term Restinga has been used indiscriminately to refer to all types of vegetation that occur in quaternary coastal plains, including the forest vegetation of the lowlands and slopes of the Serra do Mar mountains. Thus, to avoid ambiguity, the term Restinga used in this study is based on topography and follows Rocha and collaborators [], Souza and collaborators [], and Franco and collaborators [] that stated: Restingas are quaternary habitats characterized by sandy soils with high salt concentration covered by predominantly herbaceous and shrubby xerophytic vegetation. Additionally, we also considered in the analysis non-forested sites represented by plains and wet lowlands adjacent to coastal sand ridges, as many amphibian species inhabiting the Restingas commonly use these areas for reproduction and foraging. Structure of the spatial distribution of anuran species We searched the main geographical variation patterns in anuran species composition along the eastern Brazilian coast using an indirect gradient analysis.

We used the non-metric multidimensional scaling method (NMDS) for reducing the anuran composition dataset (Matrix A) to one or more synthetic axes. Initially, we searched for the best dimensionality to represent the data set. Six dimensions were generated (6D solution) from the Matrix A, by the Bray-Curtis distance coefficient. To avoid the local minima problem [], we ran 40 starting configurations, using as stability criteria the instability value of 0.000010, 15 iterations to evaluate the stability of the solution and 400 as the maximum number of iterations (see []). The Monte Carlo test was used to evaluate whether NMDS extracted a stronger axis than expected by chance.

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The result indicated that the best solution would be reached by a two dimensional analysis. Sega Saturn Mpeg Rom File. A new analysis was performed using a two-dimensional (2D) solution with the following settings: 1000 starting configurations, using as stability criteria the instability value of 0,0005, 999 iterations to evaluate the stability of the solution and 500 as the maximum number of iterations. The Monte Carlo test (999 randomizations) was used to evaluate whether NMDS extracted a stronger axis than expected by chance. The NMDS axes were rotated to a new varimax solution []. The proportion of variance represented by the NMDS axis, based on the correlation between distance in the ordination space (Euclidian distance) and distance in the original space (Bray-Curtis distance), was obtained by the standardized Mantel test (r). As a last step, a new NMDS analysis was performed with only one dimension (1D solution), using the same 2D configuration settings, to verify whether the 1D solution would be able to synthesize the main pattern of variation in anuran species composition along the eastern Brazilian coast.

We tested the presence of monotonic variation of anuran composition (quadrats; dependent variable) along the latitudinal gradient (independent variable) by single linear regression analysis. The assumption of normal distribution was tested by the Shapiro-Wilk W test and also by the projection of the normal distribution curve over a histogram distribution (observed frequencies); the assumption of linearity was checked by the projection of the variables of interest on a scatter diagram, followed by the ‘runs test’ performed in Prism software version 3.0. The level of significance was set at P ≤ 0.05. Biotic element analyses The predictions of the vicariance model regarding distribution patterns of amphibians were tested using the biotic element analysis [,], which searches for biogeographical units under the vicariance model perspective. Biotic elements (BE) are groups of taxa in which the distributions are significantly more similar to one another than to those of taxa from another group. This analysis was carried out with prabclus package in the statistical software R [] using Matrix A (see ).

Biotic element analysis is based on tests of two predictions of the vicariance model. The first prediction states that division of the ancestral biota should produce groups of taxa that are significantly regionalized [,,]. The second prediction states that closely related species must be found within distinct biotic elements [,,]. Three measures are required to test the null hypothesis that the species distribution ranges are not significantly regionalized (first prediction): a distance measure between the distribution limits of the taxa examined, a statistical test, and a null model to generate sets of random ranges []. We chose the geco distance coefficient instead of the Kulczynski distance (default in prabclus) because it considers not only the percentage of geographical units shared by taxa, but also the geographical relationships of the occupied units [–]. For the required geco coefficient, we used f = 0.2.

The T test was used based on the assumption that given a significant clustering of scales, the distances between the distribution ranges of the same group will be smaller than those between the ranges of different groups []. The distribution of the test statistic under the null model was estimated by a Monte Carlo test. To test the second prediction of the vicariance model, which states that closely related species must be distributed among distinct biotic elements [,], the chi-square test ( X 2) was used to analyze the distribution of congeneric species among biotic elements (see [,]). Once it was found that amphibians in the study area are divided into groups of species with significantly regionalized ranges, the next step was to identify the biotic elements.

Non-metric multidimensional scaling (NMDS) was applied to the geco distance matrix generated in the previous step. Model-based Gaussian clustering (MBGC) was used on the same geco distance matrix to identify the biotic elements (BE). The percentage of a species distribution in each grid was calculated based on the total species distributed among the different biotic elements. The region with the highest (greater than 75%) percentage of species distribution was defined as the “core area” of each biotic element (see [,]).

Structure of the spatial distribution of anuran species The NMDS axes obtained using two dimensions (2D) reflected the structuring in the distribution of the sampling units (SUs) (). The 2D NMDS solution resulted in a stress value of 11.7 and the extracted axes were stronger than expected by chance (Monte Carlo test, P. Projection of individual scores resulting from the non-metric multidimensional scaling method (NMDS) for 22 quadrats (sample units). The one-dimensional (1D) NMDS solution expressed a linear structure in the distribution of anuran species SUs (), but with a high stress value (30.5). Even so, NMDS extracted a stronger axis than expected by chance (Monte Carlo test, P. Biotic elements in the Restinga Biotic element analysis carried out for 63 anuran species corroborated the main vicariance model predictions: (i) the distribution was found to be significantly clustered, forming a regionalized biota along the sandy plains of the beach ridges of the eastern coast of Brazil.

The T statistic obtained was 0.146, significantly smaller (P. S1 Appendix Matrix A. Anuran species (n = 63) per sample quadrat (Q1–Q22) used in the analyses. Sample units were ordered following the. Window Xp Black Edition 2009 Nba. Geographic regions of biotic elements are indicated by the following abbreviations: NE—Northeastern, SE—Southeastern, and S—Southern. Biotic elements (BE) are numbered from BE1 to BE4, and N represents model-based clustering with noise.

Cells with number one indicate species presence; blank cells, species absence. Anuran families are also indicated: Bu, Bufonidae; Cr, Craugastoridae; Hy, Hylidae; Le, Leptodactylidae; Mi, Microhylidae; Od, Odontophrynidae.