Search

Factorial analyses are frequently used in ecological studies to identify different groups, which is a valid approach if those variables which show the highest variability also best differentiate among groups. Here we present VIDTAXA, an algorithm designed to identify statistically different groups in Principal Components and Correspondence analyses, without previous knowledge of the various potential groups present in the dataset. VIDTAXA is freely available as a function of the VARSEDIG package, which is available as an RWizard application and as an R package on CRAN. As a demonstration of VIDTAXA's potential, we used the algorithm in an example of phenetic taxonomy, for the identification of statistically different taxa in a number of marine Scorpaeniform species. This algorithm. however, it may be used with any kind of data, whether qualitative or quantitative, for the identification of statistically different groups in ecological studies.

There is no single diversity index that adequately summarises species diversity, since this is a multidimensional concept and hence should be quantified using a compound statistical measure. Here, we present the DER algorithm, available as an R package on CRAN and as an RWizard application on http://www.ipez.es/RWizard . This algorithm provides tools for differentiating assemblages on the basis of five compounds of diversity: rarity, heterogeneity, evenness, taxonomic/phylogenetic diversity and functional diversity. For all the samples, the algorithm calculates a total of 39 of the indices most often used. All indices of all samples are transformed to a scale range of between 0 and 1, and the algorithm calculates the polar coordinates of all samples with all possible combinations for all five groups of indices. Thus, for each combination, an index of rarity, heterogeneity (species richness is included in this group), evenness, taxonomic/phylogenetic diversity and functional diversity is used for each group to calculate the polar coordinates of all samples. When the polar coordinates of the samples are obtained for each combination, the convex hull and the mean Euclidean distance between samples are calculated. The algorithm selects the combination of indices with the highest value of the mean between convex hull and mean Euclidean distance between samples; priority is therefore given to maximising dispersion between the samples. The polar coordinates of the selected combination are depicted using a diagram from which it is possible to determine the differences in terms of rarity, heterogeneity, evenness, taxonomic/phylogenetic diversity and functional diversity between assemblages.

Here, we present SPEDInstabR, available as an R package on CRAN and as an RWizard application on http://www.ipez.es/RWizard, which provides tools for the identification of the environmental factors that better discriminate between the conditions prevailing in the area of a species and those existing in the geographical background over which the study is carried out. This could include the world, countries, regions, river basins, etc. or the extent of occurrence of the species estimated by using convex hull, α-shape or Kernel density distributions. The procedure consists of dividing each factor into a number of intervals or bins decided by the user, calculating the number of records in each bin, separately considering the cells where the species occur and those of the selected geographical background. A peak of instability is observed when there are important differences in the factor comparing the bins of presence with the corresponding ones of extent. We consider that those factors with a higher percentage contribution to the Instability index better discriminate between the cells of presence and the extent. We tested the algorithm using virtual species, comparing the generated selections with those produced by MaxEnt.

Understanding the factors shaping species’ distributions is a key longstanding topic in ecology with unresolved issues. The aims were to test whether the relative contribution of abiotic factors that set the geographical range of freshwater fish species may vary spatially and/or may depend on the geographical extent that is being considered. The relative contribution of factors, to discriminate between the conditions prevailing in the area where the species is present and those existing in the considered extent, was estimated with the instability index included in the R package SPEDInstabR. We used 3 different extent sizes: 1) each river basin where the species is present (local); 2) all river basins where the species is present (regional); and 3) the whole Earth (global). We used a data set of 16,543 freshwater fish species with a total of 845,764 geographical records, together with bioclimatic and topographic variables. Factors associated with temperature and altitude show the highest relative contribution to explain the distribution of freshwater fishes at the smaller considered extent. Altitude and a mix of factors associated with temperature and precipitation were more important when using the regional extent. Factors associated with precipitation show the highest contribution when using the global extent. There was also spatial variability in the importance of factors, both between species and within species and from region to region. Factors associated with precipitation show a clear latitudinal trend of decreasing in importance toward the equator.

Global data sets are essential in macroecological studies. File formats of the few available data sets of freshwater ecosystems, however, are either incompatible with most macroecological software packages, incomplete, or of coarse spatial resolutions. We integrated more than 460 million geographical coordinates for freshwater habitats in the FRWater data set, partitioned into seven different habitats (lentic, wetlands, reservoirs, small rivers, large rivers, small ditches, large ditches, small channels, large channels, small drains and large drains) in ModestR (http://www.ipez.es/ModestR). A comprehensive collection of geospatial rasters was assembled, one for each of the seven freshwater habitats, with the area in km2 occupied by each habitat presented in cells of 5 arc-minute resolution. The utility of FRWater was evaluated using hierarchical partitioning via the identification of the contribution of the seven different freshwater habitats to both species richness and rarity. To this end, we used a data set of 836,123 geographical records of the 16,216 species of freshwater fishes recognized as valid by systematists at the end of 2014. Areas in North America and Europe are the most detailed in the FRWater data set, evidencing the higher quality of data sources in those regions. The number of geographical coordinates is much lower for Africa, Asia, Australia, and South America where many water bodies remain unmapped. In light of the variation in information quality at continental levels, we performed and present comparative analyses for Europe versus South America at local (5ʹ × 5ʹ grid cells) and regional (5° × 5° grid cells) scales. The relative contribution of small rivers to both species richness and rarity was highest under almost all analyses, followed by lentic habitats and large rivers. The areas of different habitats moreover explained a relatively high proportion of the observed variance in geographic rarity. Our findings corroborate previous findings that the greater contribution of small rivers to species richness is probably due to these habitats promoting geographical rarity. Hence, species richness is favored by the isolation resultant from, and the refuges associated with, small river basins and via the diversification processes promoted by such isolation., his work was supported by the ENDESA [110/02168].

Patricia Pelayo-Villamil [et al.], Aim: To examine the pattern and cumulative curve of descriptions of freshwater fishes world-wide, the geographical biases in the available information on that fauna, the relationship between species richness and geographical rarity of such fishes, as well as to assess the relative contributions of different environmental factors on these variables., Location: Global., Methods: ModestR was used to summarize the geographical distribution of freshwater fish species using information available from data-based geographical records. The first-order jackknife richness estimator was used to estimate the completeness of such data in all terrestrial 1-degree cells world-wide. An α-shape procedure was used to build range maps capable of providing relatively accurate species richness and geographical rarity values for each grid cell. We also examined the explanatory capacity of a high number of environmental variables using multiple regressions and Support Vector Machine., Results: Cumulative species description curves show that a high number of species of freshwater fishes remain to be discovered. Completeness values indicate that only 199 one-degree grid cells, mainly located in eastern North America and Europe, could be considered as having relatively accurate inventories. Range maps provide species richness values that are positively and significantly related to those resulting from the first-order jackknife richness estimator. The relationship between species richness and geographical rarity is triangular, so that these species-rich cells are those with a higher proportion of distributionally rare species. Species richness is predicted by climatic and/or productivity variables but geographical rarity is not., Main conclusions: In general, species-rich tropical areas harbour a higher number of narrowly distributed species although comparatively species-poor subtropical cells may also contain narrowly distributed species. Historical factors may help to explain the faunistic composition of these latter areas; a supposition also supported by the low predictive capacity of climatic and productivity variables on geographical rarity values.

The aim of the SINENVAP algorithm is to facilitate the estimation of spatial interpolations within polygons, by using simple, ordinary, and universal kriging. This algorithm is available as a function of the EcoIndR package, which is available as an RWizard application and an R package on CRAN. The main strengths of this algorithm include: the possibility of using different file formats for polygon variable and coordinate inputs (CSV, EXCEL, RData, shape or ASC), compatibility with UTM or decimal coordinates, estimation of optimal grid cell size, the possibility of selecting only points inside polygons from the entire dataset, the application of a jitter function or to estimate the mean value of the variable for duplicated coordinates, reservation a percentage of data for validation, selection of those grid coordinates nearest the data coordinates reserved for validation, the possibility of fitting 13 different models into the semivariogram, automatic selection of the model that best predicts the data reserved for validation through the use of seven accuracy measures, the possibility of using countries, regions, departments, river basins, or even alpha shape distribution as polygons, and finally, depiction of contour plots with the spatial interpolation of the variable and the error within polygons. The spatial interpolation of the temperature in North America and the distribution of a virtual species are used as examples of this algorithm's potential to perform spatial interpolations on both large and small scales.

Many studies on elasmobranchs, sharks and batoids (rays, skates and guitarfishes), have focused on the factors responsible for biomass decline, but little attention has been paid to the factors that affect species richness. We used the software package ModestR to determine the geographical distribution of all valid marine elasmobranch species (512 species of sharks and 619 species of batoids), thereby making it possible to determine the species composition of the elasmobranch community in any area worldwide. The primary aim of this study was to identify the factors associated with the species richness of elasmobranchs. The data were analyzed using multiple regressions and Support Vector Machine (SVM) in cells of 1A(0)xA 1A(0) with the analyzed abiotic variables being bathymetry, chlorophyll a, sea surface temperature, photosynthetically available radiation, pH, cloud cover, the concentrations of calcite, silicate, phosphate and nitrate, salinity, particulate organic carbon, diffuse attenuation and dissolved oxygen. The mean area of occupancy of the species was used as an indicator of niche occupancy. The model performed with SVM explained 97 and 99 % of the variance observed in the species richness of batoids and sharks, respectively. Mean area of occupancy, temperature and bathymetry were the variables with a higher contribution to the variance observed in both sharks and batoids. The negative residuals of the model performed with SVM indicated areas with lower than predicted species richness. These may be potential areas with undiscovered and/or unregistered species, or areas with decreased species richness due to the negative effect of anthropogenic factors, i.e. overfishing.

We present and discuss VARSEDIG, an algorithm which identifies the morphometric features that significantly discriminate two taxa and validates the morphological distinctness between them via a Monte-Carlo test. VARSEDIG is freely available as a function of the RWizard application PlotsR (http://www.ipez.es/RWizard) and as R package on CRAN. The variables selected by VARSEDIG with the overlap method were very similar to those selected by logistic regression and discriminant analysis, but overcomes some shortcomings of these methods. VARSEDIG is, therefore, a good alternative by comparison to current classical classification methods for identifying morphometric features that significantly discriminate a taxon and for validating its morphological distinctness from other taxa. As a demonstration of the potential of VARSEDIG for this purpose, we analyze morphological discrimination among some species of the Neotropical freshwater family Characidae.

Die elementare Einfuhrung in die Allgemeine Topologie, Lebesgue-Integrationstheorie und Funktionalanalysis in einheitlicher Darstellung auf der Basis der Reellen Analysis und Linearen Algebra. Mit Anwendung unter anderem auf Differential- und Integralgleichungen, Optimierung und numerische Verfahren. Ausgehend von bekannten Begriffen wie Metrik, Konvergenz, Vektorraum oder Skalarprodukt werden topologische, speziell pseudometrische Raume mit ihren fundamentalen Eigenschaften behandelt, wie sie in der modernen Mathematik Verwendung finden. Im Anschlus an eine klassische Darstellung der abstrakten Lebesgue-Integration von Funktionen einer Variablen folgen funf Grundsatze der Linearen Funktionalanalysis, Banach-Hahn-Mazur-Trennungssatze sowie Untersuchungen uber Extrempunkte, Dualitat und Hilbertraum-Operatoren. Durch uber 150 Beispiele und 428 Aufgaben mit vollstandigen Losungsvorschlagen eignet sich das Buch auch hervorragend als Begleittext zu Vorlesungen und Ubungen sowie zum Selbststudium.