Clustering and canonical correspondence analysis of phytoplankton and environmental variables in Swedish lakes

Phytoplankton data consisting of 145 species from a limnological study of lakes from relatively undisturbed areas throughout Sweden were analysed in relation to 11 physical and chemical environmental variables. Three multivariate methods were applied: WPGMA clustering and TWINSPAN for classification, and detrended canonical correspondence analysis (DCCA), a recent technique which extracts ordination axes that can be related directly to variation in the environment. Three types of lakes were recognized consistently: acid humic lakes with Gonyostomum semen as the dominant species, very acid impoverished lakes with rather few, stress-tolerant species, and subarctic lakes with low total biomass but with a varied phytoplankton flora. DCCA allowed a straightforward display of the locations of lakes and species along environmental gradients (including the acidification gradient) reflected in phytoplankton composition. It is suggested that such analyses may be a useful tool for the early detection of environmental change.     

Modelling floristic species richness on a regional scale: a case study in Switzerland

In this paper a multivariate linear regression model is proposed for predicting and mapping regional species richness in areas below the timberline according to environmental variables. The data used in setting up the model were derived from a floristic inventory. Using a stepwise regression technique, five environmental variables were found to explain 48.9% of the variability in the total number of plant species: namely temperature range, proximity to a big river or lake, threshold of minimum annual precipitation, amount of calcareous rock outcrops and number of soil types. A considerable part of the unexplained variability is thought to have been influenced by variations in the quality of the botanical inventory. These results show the importance of systematic floristic sampling in addition to conventional inventories when using floristic data as a basis in nature conservation. Nevertheless it is still possible to interpret the resulting diversity patterns ecologically. Regional species richness in Switzerland appears to be a function of: (i) environmental heterogeneity; (ii) threshold values of minimum precipitation; and (iii) presence of calcareous rock outcrops. According to similar studies, environmental heterogeneity was the strongest determinant of total species richness. In contrast to some studies, high productivity decreased the number of species. Furthermore, the implications of this work for climate change scenarios are discussed.     

塔里木河流域荒漠河岸林群落的多元分析与环境解释

应用无偏对应分析（DCA）及二歧指示种分析（TWINSPAN）对塔里木河流域荒漠河岸林33个植物群落方资料进行了多元分析－排序和数量分类,并应用植物群落的排序值与环境参数的多元回归分析给出各群落类型的定量环境解释,探讨了该区植物群落的基本类型,生态梯度及其与环境因子的定量关系,结果表明,塔里木河流域漠河岸林的群落类型及其分布主要取决于土壤湿度和盐分含量,并可通过环境参数的数字表达式定量的确定。     

Relevance of abiotic criteria used in German lake typology for macroinvertebrate fauna

For lake characterisation, top-down typologies are mostly used throughout Europe, including type criteria such as climate, lake area, catchment geology and conductivity. In Germany, a lake typology was applied comprising ecoregion, calcium concentration, Schindler’s ratio, stratification type and residence time. However, the relevance of these criteria for the macroinvertebrate fauna has not been conclusively demonstrated till now. Benthic invertebrate community data and related environmental parameters of pristine or near-pristine lakes in Germany were analysed by multivariate analysis techniques to elucidate which environmental parameters are reflected by invertebrate composition. Moreover, benthic invertebrate data were transformed to metrics expressing ecological attributes and species richness (summarising functional composition, diversity and sensitivity measures). Multivariate statistics were used to test whether information relevant to ordination was lost and whether variation decreases using metrics which combine data with ecological attributes. Analysis of lake-type criteria revealed that ecoregions and prevailing substrates were characterized by different taxonomic compositions of macroinvertebrates. In addition, a relationship was found between community composition and lake size. Creating a novel bottom-up lake typology based on ecoregions, lake size and prevailing substrate gives better separation of distinct macroinvertebrate communities and a higher level of homogeneity within groups compared to top-down typology or single environmental parameters alone, both on species and metrics data. Despite some data variation due to methodological differences (e.g. different sampling and sorting techniques) and interannual and seasonal variation in the data set, NMDS ordination presented well-separated groups of bottom-up lake types. Lake types were more precisely separated by species data than by metric data in both top-down and bottom-up typology. However, as information loss from species lists to calculated metrics is marginal, type-specific benthic invertebrate assemblages are reflected both on the species level and on the metric level. Species and metric data are both suitable for data ordination, while single environmental parameters affecting macroinvertebrate composition can best be obtained using metrics.     

甘南玛曲植物群落的多元分析与环境解释

应用无偏对应分析（ＤＣＡ）及二岐指示种分析（ＴＷＩＮＳＰＡＮ）对玛曲１７８个植物群落样方资料进行了多斐邓和数量分类,并应用植物群落的排序值与环境参数的多元回归分析出各群类型的定量环境解释,探讨了该区植物群的基本类型生态梯度及其与环境因子的定量关系。结果表明,玛曲的植物群落类型及基分布主要取惟地热量和湿度,并可通过环境参数地数字表达式定量地确定。     

Quantitative paleo-estimation: hypothetical experiments with extrapolation and the no-analog problem

We experiment with artificial data to test the response of five numerical techniques in extrapolating paleo-environments for no-analog conditions. No-analog conditions are those beyond the technique calibration (modern) data set and will be encountered in applications to the geologic past, though they may not be easy to recognize. In the ideal, a numerical technique will correctly extrapolate to no-analog conditions. Failing this, the technique will have a consistent, predictable error response to increasing no-analog conditions, as these are measured by a reliable index. The no-analog conditions that we used are a natural extension of the calibration conditions we created. Thus we test techniques for their response to shifting environmental conditions rather than for factors unrelated to the ecology of the taxa (e.g. post-depositional fossil preservation). Five numerical techniques we test with our hypothetical data are (1) multivariate regression of species percents, (2) correlation-based principal components with linear regression, (3) covariance-based principal components with linear regression, (4) correlation-based principal components with non-linear regression, and (5) the Imbrie and Kipp technique. All the techniques show increasing estimation error as conditions depart from those of the calibration data set. There are two main causes of error in our estimates: (1) the distorting effects of matrix closure on taxon abundances; and (2) generation of ratio no-analogs among species abundances because of non-linear responses to conditions departing progressively from the calibration range. With all the techniques, the distribution of error for no-analog conditions is complex. Non-linear regression with factors shows the least predictable error response. We found that currently developed no-analog indicators do not have a good correlation to estimation error. This means that better indicators, more closely linked to the accuracy of estimates, need to be developed.     

Multivariate species boundaries and conservation of harlequin poison frogs

In this study, we present an iterative method for delimiting species under the general lineage concept (GLC) based on the multivariate clustering of morphological, ecological and genetic data. Our rationale is that distinct multivariate groups correspond to evolutionarily independent metapopulation lineages because they reflect the common signal of different secondary defining properties (environmental and genetic distinctiveness, phenotypic diagnosability, etc.) that imply the existence of barriers preventing or limiting gene exchange. We applied this method to study a group of endangered poison frogs, the Oophaga histrionica complex. In our study case, we used next‐generation targeted amplicon sequencing to obtain a robust genetic data set that we combined with patterns of morphological and ecological features. Our analyses revealed the existence of at least five different species in the histrionica complex (three, new to science), some of them, occurring in small isolated populations outside any protected areas. The lineage delimitation proposed here has important conservation implications as it revealed that some of the Oophaga species should be considered among the most vulnerable of the Neotropical frogs. More broadly, our study exemplifies how multiple‐amplicon and multivariate statistical techniques can be integrated to successfully identify species and their boundaries.     

Can patterns of spatial autocorrelation reveal population processes? An analysis with the fire salamander

Spatial autocorrelation (SAC) is often observed in species distribution data, and can be caused by exogenous, autocorrelated factors determining species distribution, or by endogenous population processes determining clustering such as dispersal. However, it remains debated whether SAC patterns can actually reveal endogenous processes. We reviewed studies measuring dispersal of the salamander Salamandra salamandra, to formulate a priori hypotheses on the scale at which dispersal is expected to determine population distribution. We then tested the hypotheses by analysing SAC in distribution data, and evaluating whether controlling for the effect of environmental variables can reveal endogenous processes. We surveyed 565 streams to obtain species distribution data; we also recorded landscape and microhabitat features known to affect the species. We used multiple approaches to tease apart endogenous and exogenous SAC: the analysis of residuals of logistic regression models considering different environmental variables; the analysis of eigenvectors extracted by several implementations of spatial eigenvector mapping. In capture–mark–recapture studies, 98% of individuals moved 500 m or less. Both species distribution and environmental features were strongly autocorrelated. The residuals of logistic regression relating species to environmental variables were autocorrelated at distances up to 500 m; analyses considering different sets of environmental variables, or assuming non‐linear species habitat relationships, yielded identical results. The results of spatial eigenvector mapping strongly depended on the matrix of distances used. Nevertheless, the eigenvectors of models with best fit were autocorrelated at distances up to 200–500 m. The concordance between multiple approaches suggests that 500 m is the scale at which dispersal connects breeding localities, increasing probability of occurrence. If exogenous variables are correctly identified, the analysis of SAC can provide important insights on endogenous population processes, such as the flow of individuals. SAC analysis can also provide important information for conservation, as the existence of metapopulations or population networks is essential for long term persistence of amphibians.     

Predicting species distributions from museum and herbarium records using multiresponse models fitted with multivariate adaptive regression splines

Current circumstances — that the majority of species distribution records exist as presence‐only data (e.g. from museums and herbaria), and that there is an established need for predictions of species distributions — mean that scientists and conservation managers seek to develop robust methods for using these data. Such methods must, in particular, accommodate the difficulties caused by lack of reliable information about sites where species are absent. Here we test two approaches for overcoming these difficulties, analysing a range of data sets using the technique of multivariate adaptive regression splines (MARS). MARS is closely related to regression techniques such as generalized additive models (GAMs) that are commonly and successfully used in modelling species distributions, but has particular advantages in its analytical speed and the ease of transfer of analysis results to other computational environments such as a Geographic Information System. MARS also has the advantage that it can model multiple responses, meaning that it can combine information from a set of species to determine the dominant environmental drivers of variation in species composition. We use data from 226 species from six regions of the world, and demonstrate the use of MARS for distribution modelling using presence‐only data. We test whether (1) the type of data used to represent absence or background and (2) the signal from multiple species affect predictive performance, by evaluating predictions at completely independent sites where genuine presence–absence data were recorded. Models developed with absences inferred from the total set of presence‐only sites for a biological group, and using simultaneous analysis of multiple species to inform the choice of predictor variables, performed better than models in which species were analysed singly, or in which pseudo‐absences were drawn randomly from the study area. The methods are fast, relatively simple to understand, and useful for situations where data are limited. A tutorial is included.     

Reconstructing paleoecology and paleoenvironmental variables using factor analysis and regression: some limitations

We test the success of Principal Components, Factor and Regression Analysis at recovering environmental signals using numerical experiments in which we control species environmental responses, the environmental conditions and the sampling scheme used for calibration. We use two general conditions, one in which sampling of a continental margin for benthic foraminiferal assemblages is done in a standard grid and the driving environmental variables are correlated to one another, and the other where sampling is done so that the environmental variables are uncorrelated. The first condition mimics many studies in the literature. We find that where the controlling environmental variables are correlated, Principal Components/Factor Analysis yield factors that reflect the common variance (correlation) of those variables. Since this common variance is largely a product of the sampling scheme, the factors extracted do not reliably present true species ecologic behavior. This behavior cannot be accurately diagnosed and faulty interpretations may lead to substantial error when using factor coefficients to reconstruct conditions in the past. When the sampling scheme is constructed so that the controlling environmental variables for the calibration data set are uncorrelated the factor patterns will reflect these variables more accurately. Species responses can be more successfully interpreted from the Principal Components/Factor Analysis structure matrices. Additionally, regression analysis can successfully extract the independent environmental signals from the biotic data set. However, matrix closure is a confounding effect in all our numerical results as it distorts species' abundances and spatial distribution in the calibration data set. Our results show clearly that a knowledge of the controlling environmental variables, and the correlations among these variables over a study area, is essential for the successful application of multivariate techniques for paleoenvironmental reconstruction.     

Are New Zealand's Nothofagus species in equilibrium with their environment?

Abstract. Past explanations of the large disjunctions in the distribution of New Zealand's four Nothofagus species have emphasized displacement during glacial cycles followed by slow re-occupation of suitable sites, or the effects of plate tectonics coupled with ecological and/or environmental limitations to further spread. In this study the degree of equilibrium between Nothofagus distribution and environment was compared with that of other widespread tree species by statistical analysis. Generalized additive regression models were used to relate species distribution data to estimates of temperature, solar radiation, soil water deficit, atmospheric humidity, lithology and drainage. For each species, the amount of spatial patterning remaining unexplained by environment was assessed by adding a variable describing species presence/absence on adjacent plots. Results indicate that Nothofagus species occur more frequently in environments suboptimal for tree growth, i.e. having various combinations of cool temperatures, low winter solar radiation, high root-zone water deficit, low humidity, and infertile granitic substrates. Despite these demonstrated preferences, they exhibit substantially more spatial clustering which is unexplained by environment, than most other widespread tree species. Predictions formed from regressions using environment alone confirm that several major Nothofagus disjunctions are not explicable in terms of the environmental factors used in this analysis, but more likely reflect the effects of historic displacement coupled with slowness to invade forest dominated by more rapidly dispersing endomycorrhizal species. The technique used in this study for detecting residual spatial autocorrelation after fitting explanatory variables has potentially wide application in other studies where either regression or ordination techniques are used for analysis of compositional data.     

Perspectives for the use of diatom assemblages in the water management policy of Overijssel (The Netherlands)

Diatoms have been sampled in several types of water bodies in the province of Overijssel for a period of five years. Samples from 333 sites were examined both in spring and autumn. Extensive analysis of physico-chemical variables was carried out.Data were processed by multivariate analysis for detecting correlations between species and environmental factors. Both ordination and clustering techniques were used. Statistical tests were performed to evaluate environmental relationships.The main factors in this study appear to be pH, nutrient pollution (saprobity and trophic degree) and alkalinity. Within the group of waters which is not influenced by extreme conditions of pH or pollution, there is a discrepancy between waters with low and high alkalinity.The present study confirms that diatoms are useful indicators of pollution and pH, as well documented by several authors. Diatoms are also suitable as biological indicators for alkalinity at least on a regional scale. This offers possibilities for the use of diatoms in monitoring studies, especially in waters that are still under relatively low environmental stress. It also offers opportunities for setting ecological standards, based on the characteristics of non-polluted water bodies. This aspect will be of interest to the water management policy in the province of Overijssel.     

Phylogenetic community structure in Minnesota oak savanna is influenced by spatial extent and environmental variation

The relative importance of environmental filtering, biotic interactions and neutral processes in community assembly remains an openly debated question and one that is increasingly addressed using phylogenetic approaches. Closely related species may occur together more frequently than expected (phylogenetic clustering) if environmental filtering operates on traits with significant phylogenetic signal. Recent studies show that phylogenetic clustering tends to increase with spatial scale, presumably because greater environmental variation is encompassed at larger spatial scales, providing opportunities for species to sort across environmental gradients. However, if environmental filtering is the cause of species sorting along environmental gradients, then environmental variation rather than spatial scale per se should drive the processes governing community assembly. Using species abundance and light availability data from a long‐term experiment in Minnesota oak savanna understory communities, we explicitly test the hypothesis that greater environmental variation results in greater phylogenetic clustering when spatial scale is held constant. Concordant with previous studies, we found that phylogenetic community structure varied with spatial extent. At the landscape scale (~1000 ha), communities were phylogenetically clustered. At the local scale (0.375ha), phylogenetic community structure varied among plots. As hypothesized, plots encompassing the greatest environmental variation in light availability exhibited the strongest phylogenetic clustering. We also found strong correlations between species functional traits, particularly specific leaf area (SLA) and perimeter per area (PA), and species light availability niche. There was also a phylogenetic signal in both functional traits and species light availability niche, providing a mechanistic explanation for phylogenetic clustering in relation to light availability. We conclude that the pattern of increased phylogenetic clustering with increased environmental variation is a consequence of environmental filtering acting on phylogenetically conserved functional traits. These results indicate that the importance of environmental filtering in community assembly depends not on spatial scale per se, but on the steepness of the environmental gradient.     

Comparison of five clustering algorithms to classify phytoplankton from flow cytometry data.

BACKGROUND: Artificial neural networks (ANNs) have been shown to be valuable in the analysis of analytical flow cytometric (AFC) data in aquatic ecology. Automated extraction of clusters is an important first stage in deriving ANN training data from field samples, but AFC data pose a number of challenges for many types of clustering algorithm. The fuzzy k-means algorithm recently has been extended to address nonspherical clusters with the use of scatter matrices. Four variants were proposed, each optimizing a different measure of clustering "goodness." METHODS: With AFC data obtained from marine phytoplankton species in culture, the four fuzzy k-means algorithm variants were compared with each other and with another multivariate clustering algorithm based on critical distances currently used in flow cytometry. RESULTS: One of the algorithm variants (adaptive distances, also known as the Gustafson--Kessel algorithm) was found to be robust and reliable, whereas the others showed various problems. CONCLUSIONS: The adaptive distances algorithm was superior in use to the clustering algorithms against which it was tested, but the problem of automatic determination of the number of clusters remains to be addressed.     

Statistical methods for temporal and space–time analysis of community composition data

This review focuses on the analysis of temporal beta diversity, which is the variation in community composition along time in a study area. Temporal beta diversity is measured by the variance of the multivariate community composition time series and that variance can be partitioned using appropriate statistical methods. Some of these methods are classical, such as simple or canonical ordination, whereas others are recent, including the methods of temporal eigenfunction analysis developed for multiscale exploration (i.e. addressing several scales of variation) of univariate or multivariate response data, reviewed, to our knowledge for the first time in this review. These methods are illustrated with ecological data from 13 years of benthic surveys in Chesapeake Bay, USA. The following methods are applied to the Chesapeake data: distance-based Moran''s eigenvector maps, asymmetric eigenvector maps, scalogram, variation partitioning, multivariate correlogram, multivariate regression tree, and two-way MANOVA to study temporal and space–time variability. Local (temporal) contributions to beta diversity (LCBD indices) are computed and analysed graphically and by regression against environmental variables, and the role of species in determining the LCBD values is analysed by correlation analysis. A tutorial detailing the analyses in the R language is provided in an appendix.     

Non-parametric multivariate analyses of changes in community structure

Abstract In the early 1980s, a strategy for graphical representation of multivariate (multi-species) abundance data was introduced into marine ecology by, among others, Field, et al. (1982). A decade on, it is instructive to: (i) identify which elements of this often-quoted strategy have proved most useful in practical assessment of community change resulting from pollution impact; and (ii) ask to what extent evolution of techniques in the intervening years has added self-consistency and comprehensiveness to the approach. The pivotal concept has proved to be that of a biologically-relevant definition of similarity of two samples, and its utilization mainly in simple rank form, for example ‘sample A is more similar to sample B than it is to sample C’. Statistical assumptions about the data are thus minimized and the resulting non-parametric techniques will be of very general applicability. From such a starting point, a unified framework needs to encompass: (i) the display of community patterns through clustering and ordination of samples; (ii) identification of species principally responsible for determining sample groupings; (iii) statistical tests for differences in space and time (multivariate analogues of analysis of variance, based on rank similarities); and (iv) the linking of community differences to patterns in the physical and chemical environment (the latter also dictated by rank similarities between samples). Techniques are described that bring such a framework into place, and areas in which problems remain are identified. Accumulated practical experience with these methods is discussed, in particular applications to marine benthos, and it is concluded that they have much to offer practitioners of environmental impact studies on communities.     

Co-inertia analysis: an alternative method for studying species–environment relationships

• 1 Methods used for the study of species–environment relationships can be grouped into: (i) simple indirect and direct gradient analysis and multivariate direct gradient analysis (e.g. canonical correspondence analysis), all of which search for non-symmetric patterns between environmental data sets and species data sets; and (ii) analysis of juxtaposed tables, canonical correlation analysis, and intertable ordination, which examine species–environment relationships by considering each data set equally. Different analytical techniques are appropriate for fulfilling different objectives.
• 2 We propose a method, co-inertia analysis, that can synthesize various approaches encountered in the ecological literature. Co-inertia analysis is based on the mathematically coherent Euclidean model and can be universally reproduced (i.e. independently of software) because of its numerical stability. The method performs simultaneous analysis of two tables. The optimizing criterion in co-inertia analysis is that the resulting sample scores (environmental scores and faunistic scores) are the most covariant. Such analysis is particularly suitable for the simultaneous detection of faunistic and environmental features in studies of ecosystem structure.
• 3 The method was demonstrated using faunistic and environmental data from Friday (Freshwater Biology 18, 87-104, 1987). In this example, non-symmetric analyses is inappropriate because of the large number of variables (species and environmental variables) compared with the small number of samples.
• 4 Co-inertia analysis is an extension of the analysis of cross tables previously attempted by others. It serves as a general method to relate any kinds of data set, using any kinds of standard analysis (e.g. principal components analysis, correspondence analysis, multiple correspondence analysis) or between-class and within-class analyses.

     

Biodiversity of soft-sediment benthic communities from Italian transitional waters

Aim For conservation purposes, it is important to understand the forces that shape biodiversity in transitional waters (TWs) and to evaluate the effects of small‐scale latitudinal changes. To this end, we analysed data on soft‐sediment macroinvertebrates from nine Italian TWs in order to (1) investigate the structure and distribution of the benthic fauna and their relationships with environmental and geographical variables, and (2) examine species richness and β‐diversity at various spatial scales. Location European Transition Waters Ecoregion 6. Methods Using a data set collected along a 7° latitudinal cline between 45°28′ N and 39°56′ N, we used Spearman’s rank correlation analysis to evaluate the relationships between species richness and both environmental and geographical variables, and linear regression analysis to show the relationships between α‐, β‐ and γ‐diversity. Three measures were used to assess β‐diversity: Whittaker’s β_W, and two similarity indices, namely the Bray‐Curtis similarity index and Δ_s. Using multivariate analyses, we determined the similarity in composition of the benthic community between sites and compared the biotic ordination with abiotic (geographical and environmental) characteristics. Results Two hundred and sixty‐eight species were recorded from 46 sites. Of these, 53.4% were restricted to one TW. Annelida was the dominant taxonomic group, followed by Crustacea and Mollusca. The α‐diversity was highly variable (5–87 species) and was correlated with latitude. The γ‐diversity, measured at the TW scale, was correlated significantly with α‐diversity. The β‐diversity increased with spatial scale and habitat heterogeneity. In the community pattern identified by multivariate analysis, TWs were segregated by latitude and biogeography, and this reflected different climatic conditions. Main conclusions We found that α‐diversity increased when moving from higher to lower latitudes, and that it depended on both regional and local factors. In addition, we detected latitudinal variations in the extent of regional influence on local species richness. The observed distribution pattern of TW faunas depended mostly on climate type. We suggest that the distribution of annelidan species could be used as a proxy for assessing general community patterns for Italian TWs.     

Α comparison of alternative techniques for prediction of the fauna of running-water sites in Great Britain

1. Early versions of the river invertebrate prediction and classification system (RIVPACS) used TWINSPAN to classify reference sites based on the macro-invertebrate fauna, followed by multiple discriminant analysis (MDA) for prediction of the fauna to be expected at new sites from environmental variables. This paper examines some alternative methods for the initial site classification and a different technique for prediction. 2. A data set of 410 sites from RIVPACS II was used for initial screening of seventeen alternative methods of site classification. Multiple discriminant analysis was used to predict classification group from environmental variables. 3. Five of the classification–prediction systems which showed promise were developed further to facilitate prediction of taxa at species and at Biological Monitoring Working Party (BMWP) family level. 4. The predictive capability of these new systems, plus RIVPACS II, was tested on an independent data set of 101 sites from locations throughout Great Britain. 5. Differences between the methods were often marginal but two gave the most consistently reliable outputs: the original TWINSPAN method, and the ordination method semi-strong hybrid multidimensional scaling (SSH) followed by K-means clustering. 6. Logistic regression, an alternative approach to prediction which does not require the prior development of a classification system, was also examined. Although its performance fell within the range offered by the other five systems tested, it conveyed no advantages over them. 7. This study demonstrated that several different multivariate methods were suitable for developing a reliable system for predicting expected probability of occurrence of taxa. This is because the prediction system involves a weighted average smoothing across site groupings. 8. Hence, the two most promising procedures for site classification, coupled to MDA, were both used in the exploratory analyses for RIVPACS III development, which utilized over 600 reference sites.