The species diversity of the entire meta-community is made up of local pools of species of individual communities, including both the totality of actually observed taxonomic groups and species of “dark” diversity, which, by their ecological properties, are theoretically suitable for living in existing conditions and are potentially found during repeated studies. To assess the dark diversity, quantitative indices of suitability of the surveyed areas of the study area are calculated in relation to various taxa of the community under consideration. The study of the species composition of benthic communities was carried out on small and medium lowland rivers, tributaries of the Kuibyshev, Saratov and Volgograd reservoirs, including the rivers of the arid region of the Lake Elton basin. A total of 132 local communities were surveyed, from which 147 taxa of macrozoobenthos were selected for calculations. To highlight the dark diversity, an analysis of the joint occurrence of species was carried out and, using hypergeometric distribution formulas, estimates of the conditional probabilities of the statistical relationship of each of these species with individual sections of the rivers were calculated. Relationships between observed species richness and dark diversity are considered; the occurrence of latent species was tested in sections of rivers of a similar type. The concept of “gray” diversity is introduced, i.e., a subset of observed species, in which the indices of correspondence to the focal area are less than a given threshold.

The results of the analysis of studies of saine rivers of the arid region of the Elton region (the area of the Caspian lowland, the basin of the hyperhaline Lake Elton) based on the study of plankton and bottom communities in August 2013 and 2018 are presented. For multidimensional statistical analysis, we used the results of processing hydrobiological samples taken at 13 stations of five saline rivers. A matrix of the numbers of 136 species and taxa, representatives of zooplankton, macrozoobenthos and meiobenthos was formed. To process the data, the values of the numerical matrices were transformed into a single score scale from 0 to 6 using the algorithm for finding optimal boundaries. The stations were grouped according to the level of water mineralization:1 – >25 g/l, 2 – 10-25 g/l and 3 – <10 g/l.The use of statistical models of species distribution in the space of abiotic factors madeit possible to establish that the heterogeneity of the diversity of planktonic and bottom communities is due to biotopic differences and the level of mineralization of water masses. It is shown that for highly mineralized hydrosystems of arid regions, a clear separation of the life forms of plankton and bottom communities is not obvious.

The statistical background for the relationship between the taxonomic diversity of macrozoobenthos and water mineralization is presented in the example of the benthic communities of plain rivers in the Lower Volga River basin. Significant differences have been found for a complex of 35 indices of species and phylogenetic α- and β-diversity in the tributaries of the Saratov and Volgograd reservoirs compared to the saline rivers of the Elton Lake basin. The hypothesis of phylogenetic niche conservatism [5] is confirmed by a significant effect of phylogenetic overdispersion at low and medium salinity of watercourses and phylogenetic clustering at high water salinity. Mean salinity tolerance has been assessed for each of the 356 species considered; this index was interpreted as the statistical probability of inhabiting the waters of certain mineralization by particular species. A statistically significant phylogenetic signal corresponding to the species traits was revealed by Pagel’s lambda and Bloomberg’s K tests. Mean salinity tolerance for taxa of various systematic levels has been presented as a cladistic tree.

— The theoretical and practical aspects of building of joint species-distribution models, a modern tool for the analysis of ecological communities, are considered. It is shown that it is inappropriate to use the MaxEnt method or other methods based on the concept of “pseudo-absence” points when the observational data are quantitative indicators of the population density (in particular, the abundance of species in hydrobiological studies). Contemporary multidimensional models of the joint distribution of communities should include a set of parameters that assess the impact of the following groups of fixed and random factors on the species occurrence: (a) the covariates and categorical variables describing the environmental conditions and characteristics of biotopes, (b) the main indicators characterizing each species and the phylogenetic structure of communities, (c) the functions of spatial autocorrelation of the data at observation points, (d) the residual (i.e., not caused by external factors) associativity of species. Analysis of the published data and practical examples of implementation showed that the mentioned requirements, in general, are satisfied by the methodological platform and the R package Hierarchical Modeling of Species Communities (HMSC). They form the basis for the construction of multidimensional hierarchical generalized linear models with mixed parameters estimated by Bayesian procedure. The main concepts and blocks of the HMSC platform are described, and the results of models based on the authors’ data and long-term hydrobiological studies of benthic communities in 132 small and medium-sized rivers in the middle and lower Volga basin are discussed. The parameters of a set of one-dimensional candidate models for the abundance distribution of the subfamily Prodiamesinae (Diptera, Chironomidae) are analyzed, and a map of its forecast range within the region is constructed. To illustrate the multidimensional case, a model of the joint spatial distribution of 31 species of chironomids is constructed and its coefficients are analyzed. A residual correlation graph of statistically significant interspecies interactions has been built. It is concluded that the HMSC method and software package can be effectively used to solve fundamental problems of communities’ ecology: the ways in which the areas of individual populations, the structure of their communities, and the nature of interspecific interactions depend the on environmental conditions and methods to predict future trends of these processes in response to global changes.

—The authors discuss the use of the Greenell concept of ecological niches to analyze the taxonomic structure of communities and their relationship with environmental factors. The modeling of ecological niches was carried out using the results of 30-year studies of macrozoobenthos communities on 90 small and 12 medium-sized plain rivers in the region of the Kuibyshev, Saratov, and Volgograd reservoirs. Geoclimatic indicators, relief characteristics, and hydrochemical assessments of the water quality at sampling points were considered as abiotic factors, where 11 variables with the least collinearity were selected. The multidimensional space of the initial abiotic factors was projected onto the orthogonal axes of the first two principal components; ordination diagrams with plotted points of the presence of species were constructed. The model of the potential ecological niche of each species was represented as an area in the space of latent variables, in which the habitat suitability index Z estimated by the probability density of occurrence corresponds to the given constraints. The authors used the Schoener and Hellinger indices to quantify the proportion of overlapping niches belonging to two different benthos taxa. The matrix of distances between overlapping niches was formed for all possible paired combinations of the 40 most ecologically significant macrozoobenthos species. Cluster analysis of the obtained distance matrix was carried out by the methods of hierarchical agglomeration and fuzzy k -means. In the general multidimensional space of abiotic variables of the region studied, four areas of collective niches for groups of species with maximum distances between their centroids were identified. The analysis of intergroup variation of environmental factors is given, and the characteristic features of each group are discussed: ecological strategy, biological traits, and tolerance level.

Considered are the theoretical and practical aspects of building joint species distribution models, which are a modern tool for the analysis of ecological communities. It is shown that in the case when observational data are quantitative indicators of population density (in particular, the number of species in hydrobiological studies), it is inappropriate to use the MaxEnt method and others based on the concept of "pseudo-absence" points. Contemporary multidimensional models of the joint distribution of communities should include a set of parameters that assess the impact of the following groups of fixed and random factors on the species occurrence: (a) covariates and categorical variables describing environmental conditions and characteristics of biotopes, (b) main indicators characterizing each species, and phylogenetic structure of communities, (c) functions of spatial autocorrelation of data at observation points, (d) residual (i.e., not caused by external factors) associativity of species. The analysis of published data and the practical examples of implementation showed that the mentioned requirements, in general, are satisfied by the methodological platform and Rpackage HMSC (Hierarchical Modelling of Species Communities), on the basis of which multidimensional hierarchical generalized linear models with mixed parameters, estimated by Bayesian procedure, are constructed. The main concepts and blocks of the HMSC platform are described and the results of models construction based on the authors' data long-term hydrobiological studies of benthic communities in 132 small and medium-sized rivers in the Middle and Lower Volga basin are discussed. The parameters of a set of one-dimensional candidate models for the abundance distribution of the subfamily Prodiamesinae (Diptera, Chironomidae) are analyzed and a forecast map of its range within the region is built. To illustrate the multidimensional case, a model of the joint spatial distribution of 31 species of chironomids is constructed and its coefficients are analyzed. A residual correlation graph of statistically significant interspecies interactions has been built. The conclusion is made that the HMSC method and software package can be effectively used to solve fundamental problems of communities ecology: how the areas of individual populations, the structure of their communities and the nature of interspecific interactions depend on environmental conditions, as well as to predict future trends of these processes in response to global changes.

This paper presents results of comprehensive studies of saline rivers in the arid Elton Lake region based on hydrobiological surveys of planktonic and bottom communities. Two tables representing the species structure of communities and produced on the basis of survey data collected on 13 river sites in 2013 and 2018, including data on the abundance of hydrobionts belonging to 94 different taxonomic groups of macrozoobenthos, meiobenthos, and zooplankton, have been compared. The co-inertia analysis has identified a high statistical consistency of the data matrices determined by objective spatial distribution patterns of aquatic organisms. A randomization test was applied to the Procrustean correlation coefficient, and it showed that the conjugacy of the two species structures in the space of latent variables is statistically significant (p = 0.00026). Concurrently, a change trend was noted for the taxonomic composition of some surveyed communities affected by dynamic abiotic factors. The relationship between the taxonomic structure of hydrobionts and the combination of 30 abiotic environmental factors measured in the course of the hydrobiological and hydrochemical monitoring of the studied river sites was analyzed. Using canonical correlation analysis and the technique of projection to latent structures, a complex of ordination diagrams has been produced permitting the identification of specific “environmental niches” for each species group, including certain sets of biotope characteristics. A significant mutual correlation between the planktonic and bottom communities has been established. This correlation indicates close interrelations between these communities determined both by biotic interactions and by mutually consistent reactions to changes in aquatic environmental factors.

The dynamics of benthic communities of various reaches of the Kuibyshev Reservoir over a long-term observation period 1966 to 2016 has been statistically analyzed. The results of a comparison of the spatial-temporal distribution of structural indicators of chironomid (Chironomidae) communities, including the species diversity and abundance of 48 taxa based on hydrobiological survey data in nine large parts of the reservoir for different years, are presented. Nonparametric analysis of variance revealed a high statistical significance of the variability of the species composition of benthic communities under the influence of temporal and spatial factors. Using multidimensional ordination and generalized Procrustes analysis, the dynamics of the distribution of ecosystem objects (individual species and areas) in the coordinates of two latent axes of maximum variation is shown. A geometric analysis of the multidimensional trajectories of changes in the community of aquatic organisms in individual reaches for different periods of time is carried out. Similar developmental processes of chironomid communities were revealed in a longitudinal succession of reaches on the former channel and sunken floodplain, while the analogous structural characteristics of the Kamskiy reach and eutrophic Cheremshanskiy Bay are specific. The priority role of chironomids as the most important indicator group necessary for biotic assessment of long-term (50 years) changes in the ecological state of a large reservoir is considered.

A statistical analysis was performed on hydrochemical and hydrobiological data obtained from samples of macrozoobenthos, meiobenthos, and zooplankton in 2013 and 2018 from different biotopes of the five highly mineralized rivers of the basin of the hyperhaline Lake Elton. The general trends in the formation of the species structure of the metacommunity of aquatic organisms are considered based on the Lybold-Mikkelson concepts. Randomized null models are used to test hypotheses on the consistent occurrence of species (coherence), the formation of compact species associations (boundary clumping), and the regular change in the species composition along environmental gradients (turnover). The nature of changes in biotic diversity were determined to be nonstationary and intermittent, and the taxonomic structure was highly mosaic, which is characteristic of stochastic-type ecosystems. A close correlation was established within individual mixed associations of benthic and planktonic species due to biotic interactions and the coordinated response of organisms to environmental factors. Statistical models Random Forest and subsequent multivariate analysis were used to identify groups of species by the degree of tolerance to external abiotic influences, and the sets of factors having a significant impact were established.

We present the results of a comprehensive study of five saline rivers in the arid region of Lake Elton, including hydrobiological surveys of plankton and benthic communities. The DIABLO method was used for a statistical analysis of the associative links between the species structures of the macrozoobenthos, meiobenthos, and zooplankton communities. This method combines multidimensional ordinations based on n blocks of observations and uses special algorithms of canonical correlation. It is shown that a significant portion of the cumulative variation in the data can be explained by a consensus configuration based on information common for all the three groups of observations. The diagrams, constructed and analyzed with the use of the cluster and Generalized Procrustes analysis, enable us to isolate stable associations of taxa typical for particular biotopes with homogeneous environmental conditions. We have constructed graphs of correlation pleiades and calculated indicator significance for particular species of macrozoobenthos, meiobenthos, and zooplankton. It is shown that highly mineralized systems of arid regions are not always characterized by a pronounced specification of life forms of plankton and benthic communities. The interpenetration between benthic and plankton animals results in a high portion of mixed ecological groups. Plankton and benthic communities correlate well enough with each other, which testifies to a close relationship between them due to both biotic interactions and a mutually agreed response to changes in aquatic environment factors. These data enable us to consider the plankton and benthic communities of highly mineralized rivers a nonequilibrium dynamically changing consortia of species.

The modern approach to the study of communities' ecology involves the integration and joint processing of large arrays of observations. This usually involves a variety of indicators (population, phenotypic, genetic, environmental, chemical, landscape and geographical) which are characterized by significant temporal and spatial variability. The purpose of the analysis is to identify significant statistical relationships of the taxonomic structure with the characteristics of biotopes and environmental factors. It is based on multivariate methods that allow optimal projection of data with a large number of variables into low-dimensional spaces. The article focuses on the evolution of algorithms for multivariate analysis, starting with the classic unconstrained ordination based on principal components (PCA) up to modern integrated symmetric methods used in omics technologies. A class of algorithms, such as metric (PCoA) and non-metric (NMDS) multidimensional scaling, based on the calculation of distance matrices, is distinguished and the advantages and disadvantages of their use are considered. The dependence of the results of redundancy analysis (RDA) and canonical correspondence analysis (CCA) on the distribution law of the empirical data is discussed and recommendations for their preliminary transformation are given. It is shown the role of such symmetric methods as the two-block algorithm of partial least squares (2B-PLS) and the co-inertia analysis (CIA), which allow to establish by decomposition on axes of multidimensional covariations what species from different complexes of observations are most associated among themselves. Procrustean analysis (PCIA) can be widely used to identify changes in the species composition of the study region before and after some event (e.g., anthropogenic impact). Generalized Procrustean algorithms and canonical analysis (GPA, RGCCA, DIABLO) allow you to work with a large number of tables and explore the dynamics of community structure for several sequential periods of time or to form a consensus configuration by the best way. References to numerous examples of the use of ordination methods in domestic and foreign literature are given. The main prospects and directions of development of multidimensional methods in relation to the ecology of communities are shown.

A comparative analysis of the variability of the species structure of macrozoobenthos communities in small and medium rivers of the Middle and Lower Volga river basin has been carried out. The statistically significant influence of the natural climatic zone, where the watercourse is located, and manifestation of the latitudinal gradient of biodiversity are shown. A list of indicator species has been made for each geographical zone identified using different criteria of biotopical distribution. Based on the analysis, the indicator value (IndVal) index, which takes into account the zonal distribution of both the occurrence frequencies of a species and its abundance ratios, was recognized as the most adequate. Association rules that contain combinations of species that most frequently occur together in hydrobiological tests have been formulated using the Apriory algorithm.

A rapid assessment of Environmental Quality Criteria and probability of Ecological Risk without special toxicometric experimenting is an actual problem in environmental science. The article presents a statistical prediction methodology of approximated no-effect concentrations (NOEC) and modelling of Species Sensitivity Distribution (SSD) based on the field observation data. We use values of species abundance of tested community, which were located on a set of sites of region under study with wide variation range of polluting substances concentration. Statistical processing includes the following sequence stages: (1) calculation of distances matrix in multidimensional species’ space between each pair sites; (2) nonmetric multidimensional scaling (NMDS) is applied to reduce a 2-dimensional plot matrix of sites and species projections; (3) the analyzed contamination mediafactors are interpreted as an ecological gradient in species compositions and construction of the additional ordination axes; (4) generalized additive models (GAM) are build and 3D smoothing surfaces of spatial distribution of pollutant’s concentration on ordination plot are fitted; (5) using the fitted models predicted values of PV ecological maxima and the upper boundary values of TV confidence intervals of each species for each single compounds are found; (6) obtained data are used for SSDs modelling. The methodology has been supported by results of bioindication for communities of microscopic fungi of soil samples from the former uranium mining province (Kyrgyzstan). Threshold values of six soil contamination indicators that ensure a pre-given admissible probability of environmental risk have been determined.