Random-effects ordination: describing and predicting multivariate correlations and co-occurrences

Ecology is inherently multivariate, but high-dimensional data are difficult to understand. Dimension reduction with ordination analysis helps with both data exploration and clarification of the meaning of inferences (e.g., randomization tests, variation partitioning) about a statistical population. Most such inferences are asymmetric, in that variables are classified as either response or explanatory (e.g., factors, predictors). But this asymmetric approach has limitations (e.g., abiotic variables may not entirely explain correlations between interacting species). We study symmetric population-level inferences by modeling correlations and co-occurrences, using these models for out-of-sample prediction. Such modeling requires a novel treatment of ordination axes as random effects, because fixed effects only allow within-sample predictions. We advocate an iterative methodology for random-effects ordination: (1) fit a set of candidate models differing in complexity (e.g., number of axes); (2) use information criteria to choose among models; (3) compare model predictions with data; (4) explore dimension-reduced graphs (e.g., biplots); (5) repeat 1–4 if model performance is poor. We describe and illustrate random-effects ordination models (with software) for two types of data: multivariate-normal (e.g., log morphometric data) and presence–absence community data. A large simulation experiment with multivariate-normal data demonstrates good performance of (1) a small-sample-corrected information criterion and (2) factor analysis relative to principal component analysis. Predictive comparisons of multiple alternative models is a powerful form of scientific reasoning: we have shown that unconstrained ordination can be based on such reasoning.     

Finding a common ordination for several data sets by individual differences scaling

Individual differences scaling is a multidimensional scaling method for finding a common ordination for several data sets. An individual ordination for each data set can then be derived from the common ordination by adjusting the axis lengths so as to maximize the correlations between observed proximities and individual ordination distances. The importance of the various axes for each data set and the mutual similarities and goodness of fit for the individual data sets are described by weight plots. As an example, 46 soft-water lakes in eastern Finland are ordinated on two dimensions according to 3 chemical data sets (water in summer and autumn, sediment) and 4 biological sets (major phytoplankton groups, phytoplankton, surface sediment diatom and cladoceran assemblages). The method seems to be effective as a means of ordination for obtaining the common ordination for the data sets. The major taxonomic groups gave the ordination which differed most clearly from the ordinations of the other data sets. Phytoplankton was most poorly ordinated in all the analyses. The other data sets were fairly coherent. When only biological data sets were ordinated, the diatoms and cladocerans showed rather different patterns. It seems that the cladocerans are best correlated with water chemistry, both according to weights in the joint analysis, and according to correlation between the axes from the biological data sets and the chemical variables.Abbreviations CCA = Canonical correspondence analysis - IDS = Individual differences scaling - MDS = multidimensional scaling - PCA = Principal components analysis     

Beta diversity as the variance of community data: dissimilarity coefficients and partitioning

Beta diversity can be measured in different ways. Among these, the total variance of the community data table Y can be used as an estimate of beta diversity. We show how the total variance of Y can be calculated either directly or through a dissimilarity matrix obtained using any dissimilarity index deemed appropriate for pairwise comparisons of community composition data. We addressed the question of which index to use by coding 16 indices using 14 properties that are necessary for beta assessment, comparability among data sets, sampling issues and ordination. Our comparison analysis classified the coefficients under study into five types, three of which are appropriate for beta diversity assessment. Our approach links the concept of beta diversity with the analysis of community data by commonly used methods like ordination and anova . Total beta can be partitioned into Species Contributions (SCBD: degree of variation of individual species across the study area) and Local Contributions (LCBD: comparative indicators of the ecological uniqueness of the sites) to Beta Diversity. Moreover, total beta can be broken up into within‐ and among‐group components by manova , into orthogonal axes by ordination, into spatial scales by eigenfunction analysis or among explanatory data sets by variation partitioning.     

Partitioning the variation in a plot‐by‐species data matrix that is related to n sets of explanatory variables

Abstract. Variation partitioning by (partial) constrained ordination is a popular method for exploratory data analysis, but applications are mostly restricted to simple ecological questions only involving two or three sets of explanatory variables, such as climate and soil, this because of the rapid increase in complexity of calculations and results with an increasing number of explanatory variable sets. The existence is demonstrated of a unique algorithm for partitioning the variation in a set of response variables on n sets of explanatory variables; it is shown how the 2n– 1 non‐overlapping components of variation can be calculated. Methods for evaluation and presentation of variation partitioning results are reviewed, and a recursive algorithm is proposed for distributing the many small components of variation over simpler components. Several issues related to the use and usefulness of variation partitioning with n sets of explanatory variables are discussed with reference to a worked example.     

Predicting patterns of vascular plant species richness with composite variables: a meso-scale study in Finnish Lapland

This paper is an attempt, using statistical modelling techniques, to understand the patterns of vascular plant species richness at the poorly studied meso-scale within a relatively unexplored subarctic zone. Species richness is related to floristic-environmental composite variables, using occurrence data of vascular plants and environmental and spatial predictor variables in 362 1 km² grid squares in the Kevo Nature Reserve. Species richness is modelled in two different way. First, by detecting the major floristic-environmental gradients with the ordination procedure of canonical correspondence analysis, and subsequently relating these ordination axes to species richness by generalized linear modelling. Second, species richness is directly related to the composite environmental factors of explanatory variables, using partial least squares regression. The most important explanatory variables, as suggested by both approaches, are relatively similar, and largely reflect the influence of altitude or altitudinally related variables in the models. The most prominent floristic gradient in the data runs from alpine habitats to river valleys, and this gradient is the main source of variation in species richness. Some local environmental variables are also relatively important predictors; the grid squares rich in vascular plant taxa are mainly located in the lowlands of the reserve and are characterised by rivers and brooks, as well as by abundant cliff walls. The two statistical models account for approximately the same amount of variation in the species richness, with more than half of the variation unexplained. Potential reasons for the relatively modest fit are discussed, and the results are compared to the characteristics of the diversity-environment relationships at both broader- and finer-scales.     

Bootstrapped ordination: a method for estimating sampling effects in indirect gradient analysis

Indirect gradient analysis, or ordination, is primarily a method of exploratory data analysis. However, to support biological interpretations of resulting axes as vegetation gradients, or later confirmatory analyses and statistical tests, these axes need to be stable or at least robust into minor sampling effects. We develop a computer-intensive bootstrap (resampling) approach to estimate sampling effects on solutions from nonlinear ordination.We apply this approach to simulated data and to three forest data sets from North Carolina, USA and examine the resulting patterns of local and global instability in detrended correspondence analysis (DCA) solutions. We propose a bootstrap coefficient, scaled rank variance (SRV), to estimate remaining instability in species ranks after rotating axes to a common global orientation. In analysis of simulated data, bootstrap SRV was generally consistent with an equivalent estimate from repeated sampling. In an example using field data SRV, bootstrapped DCA showed good recovery of the order of common species along the first two axes, but poor recovery of later axes. We also suggest some criteria to use with the SRV to decide how many axes to retain and attempt to interpret.Abbreviations DCA= detrended correspondence analysis - SRV= scaled rank variance     

Detrended correspondence analysis: An improved ordination technique

Summary Detrended correspondence analysis (DCA) is an improvement upon the reciprocal averaging (RA) ordination technique. RA has two main faults: the second axis is often an arch or horseshoe distortion of the first axis, and distances in the ordination space do not have a consistent meaning in terms of compositional change (in particular, distances at the ends of the first RA axis are compressed relative to the middle). DCA corrects these two faults. Tests with simulated and field data show DCA superior to RA and to nonmetric multidimensional sealing in giving clear, interpretable results. DCA has several advantages. (a) Its performance is the best of the ordination techniques tested, and both species and sample ordinations are produced simultaneously. (b) The axes are scaled in standard deviation units with a definite meaning, (c) As implemented in a FORTRAN program called DECORANA, computing time rises only linearly with the amount of data analyzed, and only positive entries in the data matrix are stored in memory, so very large data sets present no difficulty. However, DCA has limitations, making it best to remove extreme outliers and discontinuities prior to analysis. DCA consistently gives the most interpretable ordination results, but as always the interpretation of results remains a matter of ecological insight and is improved by field experience and by integration of supplementary environmental data for the vegetation sample sites.This research was supported by the Institute of Terrestrial Ecology, Bangor, Wales, and by a grant from the National Science Foundation to R.H. Whittaker. We thank R.H. Whittaker for encouragement and comments, S.B. Singer for assistance with the Cornell computer, and H.J.B. Birks, S.R. Sabo, T.C.E. Wells, and R.H. Whittaker for data sets used for ordination tests.     

Instability of ordination results under changes in input data order: explanations and remedies

Abstract. Correspondence analysis (CA) and its Detrended form (DCA) produced by the program CANOCO are unstable under reordering of the species and sites in the input data matrix. In CA, the main cause of the instability is the use of insufficiently stringent convergence criteria in the power algorithm used to estimate the eigenvalues. The use of stricter criteria gives results that are acceptably stable. The divisive classification program TWINSPAN uses CA based on a similar algorithm, but with extremely lax convergence criteria, and is thus susceptible to extreme instability. We detected an order-dependent programming error in the non-linear rescaling procedure that forms part of DCA. When this bug is corrected, much of the instability in DCA disappears. The stability of DCA solutions is further enhanced by the use of strict convergence criteria. In our trials, much of the instability occurred on axes 3 and 4, but one should not assume that published two-dimensional ordinations are sufficiently accurate. Data sets which have pairs of almost equal eigenvalues among the first three axes could suffer from marked instability in the first two dimensions. We recommend that a debugged, strict version of CANOCO be released. Meanwhile, users can check the stability of their CA and DCA ordinations using the software that we have made available on the World Wide Web ( http://www.helsinki.fi/jhoksane/ ). An accurate program for CA, a debugged, strict version of DECORANA (for DCA) and a strict version of TWINSPAN are also available at our site.     

The bootstrapped ordination re-examined

Abstract. A method is described to determine the number of significant dimensions in metric ordination of a sample. The method is probabilistic, based on bootstrap resampling. An iterative algorithm takes bootstrap samples with replacement from the sample. It finds in each bootstrap sample ordination coordinates and computes, after Procrustean adjustments, the correlation between observed and bootstrap ordination scores. It compares this correlation to the same parameter generated in a parallel bootstrapped ordination of randomly permuted data, which upon many iterations will generate a probability. The method is assessed in principal coordinates analysis of simulated data sets that have varying number of variables and correlation levels, uniform or patterned correlation structure. The results suggest the method is more reliable than other available methods in recovering the true intrinsic dimensionality. Examples with grassland data illustrate utility.     

Species response curves along environmental gradients. A case study from SE Norwegian swamp forests

Abstract. Vegetation science has relied on untested paradigms relating to the shape of species response curves along environmental gradients. To advance in this field, we used the HOF approach to model response curves for 112 plant species along six environmental gradients and three ecoclines (as represented by DCA ordination axes) in SE Norwegian swamp forests. Response curve properties were summarized in three binary response variables: (1) model unimodal or monotonous (determinate) vs. indeterminate; (2) for determinate models, unimodal vs. monotonous and (3) for unimodal models, skewed vs. symmetric. We used logistic regression to test the influence, singly and jointly, of seven predictor variables on each of three response variables. Predictor variables included gradient type (environmental or ecocline) and length (compositional turnover); species category (vascular plant, moss, Sphagnum or hepatic), species frequency and richness, tolerance (the fraction of the gradient along which the species occurs) and position of species along each gradient. The probability for fitting a determinate model increased as the main occurrence of species approached gradient extremes and with increasing species tolerance and frequency and gradient length. Appearance of unimodal models was favoured by low species tolerance and disfavoured by closeness of species to gradient extremes. Appearance of skewed models was weakly related to predictors but was slightly favoured by species optima near gradient extremes. Contrary to the results of previous studies, species category, gradient type and variation in species richness along gradients did not contribute independently to model prediction. The overall best predictors of response curve shape were position along the gradient (relative to extremes) and tolerance; the latter also expressing gradient length in units of compositional turnover. This helps predicting species responses to gradients from gradient specific species properties. The low proportion of skewed response curves and the large variation of species response curves along all gradients indicate that skewed response curves is a smaller problem for the performance of ordination methods than often claimed. We find no evidence that DCA ordination increases the unimodality, or symmetry, of species response curves more than expected from the higher compositional turnover along ordination axes. Thus ordination axes may be appropriate proxies for ecoclines, applicable for use in species response modelling.     

协惯量分析与典范对应分析在植物群落排序中的应用比较

采用协惯量分析(PCA-CA COIA)和典范对应分析(CCA)两种排序方法, 对北京小龙门林场的黄檗 (Phellodendron amurense)群落进行了分析, 并用Spearman秩相关系数检验了对应排序轴的相关性。两种排序方法得出的结果基本一致, 两者的第一排序轴都反映了海拔高度和坡向对群落分布的影响, 而各自第二、第三排序轴所代表的环境意义有所差异, 并出现了交叉, 但是两者的前3个排序轴均反映了海拔、坡位、土壤厚度和凋落物层厚度的变化趋势, 说明在环境因子个数较少或共线性效应不明显的情况下, 协惯量分析也能达到CCA的分析效果, 并且在排序轴特征值解释量上高于典范对应分析。     

Canonical Correspondence Analysis with variation partitioning: some comments and an application

Abstract. This study presents an alternative treatment of data from a comprehensive vegetation study in which the main gradient structure of boreal coniferous forest vegetation in southern Norway was investigated by ordination techniques. The data sets include vegetation samples of different plot sizes, supplied with measurements of 33 environmental explanatory variables (classified in four groups) and nine spatial explanatory variables derived from geographical coordinates. Partitioning the variation of the species-sample plot matrices on different sets of explanatory variables is performed by use of (partial) Canonical Correspondence Analysis. Several aspects of vegetation-environment relationships in the investigation area are discussed on the basis of results obtained by the new method. Generally, ca. 35% of the variation in species abundances are explained by environmental and spatial variables. The results indicate support for the hypothesis of macro-scale topographic control over the differentiation of the vegetation, more strongly so in pine than in spruce forest where soil nutrients play a major role. Towards finer scales, the primary topographical and topographically dependent factors lose importance, and vegetational differentiation is more strongly affected by the accumulated effects of the vegetation (including the tree stand) on soils, shading, litter fall, etc. The fraction of variation in species abundance explained by significant environmental variables was found to be ca. twice as large as the fraction explained by spatial variables. The fraction of variation explained by the supplied variables differed between data sets; it was lower for cryptogams than for vascular plants, and lower for smaller than for larger sample plots. Possible reasons for these patterns are discussed. Some methodological aspects of CCA with variation partitioning are discussed: improvements, necessary precautions, and the advantages over alternative methods.     

Elements of metacommunity structure of Paraguayan bats: multiple gradients require analysis of multiple ordination axes

Techniques to evaluate elements of metacommunity structure (EMS; coherence, species turnover and range boundary clumping) have been available for several years. Such approaches are capable of determining which idealized pattern of species distribution best describes distributions in a metacommunity. Nonetheless, this approach rarely is employed and such aspects of metacommunity structure remain poorly understood. We expanded an extant method to better investigate metacommunity structure for systems that respond to multiple environmental gradients. We used data obtained from 26 sites throughout Paraguay as a model system to demonstrate application of this methodology. Using presence–absence data for bats, we evaluated coherence, species turnover and boundary clumping to distinguish among six idealized patterns of species distribution. Analyses were conducted for all bats as well as for each of three feeding ensembles (aerial insectivores, frugivores and molossid insectivores). For each group of bats, analyses were conducted separately for primary and secondary axes of ordination as defined by reciprocal averaging. The Paraguayan bat metacommunity evinced Clementsian distributions for primary and secondary ordination axes. Patterns of species distribution for aerial insectivores were dependent on ordination axis, showing Gleasonian distributions when ordinated according to the primary axis and Clementsian distributions when ordinated according to the secondary axis. Distribution patterns for frugivores and molossid insectivores were best described as random. Analysis of metacommunities using multiple ordination axes can provide a more complete picture of environmental variables that mold patterns of species distribution. Moreover, analysis of EMS along defined gradients (e.g., latitude, elevation and depth) or based on alternative ordination techniques may complement insights based on reciprocal averaging because the fundamental questions addressed in analyses are contingent on the ordination technique that is employed.     

Plant composition associated with environmental gradients in tropical montane forests (Cueva de Los Guacharos National Park,Huila, Colombia)

Niche differentiation among tropical forest plants can generate species turnover along gradients of soil, topography, climate, and land use history. In this study we explore the relative importance of these variables as drivers of floristic composition in Cueva de Los Guacharos National Park. We established twenty 0.1‐ha plots, within which trees, lianas, and shrubs (diameter ≥ 2.5 cm) were censused. We selected plot locations in primary and disturbed forests, and we measured topography and soil variables. Despite their structural similarity, primary and disturbed forests differed floristically, and also differed in environmental variables measured. A NMDS ordination showed that variation in the floristic composition across plots is highly correlated to the exchangeable acidity, elevation, temperature, and magnesium availability. Variance partitioning analysis shows that together spatial and environmental variables explain 24.2 percent of the variation in species composition. ‘Pure environmental’ variables were more important in explaining compositional variability than ‘pure spatial’ processes (9.8% and 1.4%, respectively). Residual variance may be attributed to stochastic process or non‐measured biotic effects.     

The influence of seasonal and taxonomic factors on the ordination and classification of running-water sites in Great Britain and on the prediction of their macro-invertebrate communities

SUMMARY. 1. Macro-invertebrate samples were collected from 268 running-water sites in Great Britain in each of three seasons (spring, summer and autumn). A combined seasons’treatment was generated by amalgamating the individual seasons’data. These four seasonal options were each subjected to four distinct taxonomic analyses differing in level of identification and whether the data were quantitative or qualitative. Thus sixteen data-sets were available for analysis. Environmental data on physical and chemical variables, macrophyte cover and date of sampling were also recorded for each site. 2. All sixteen data-sets were ordinated by detrended correspondence analysis and classified by two-way indicator species analysis. There were strong correlations between the sixteen ordinations and significant concordance between classifications. 3. The relationships between ordination scores and single environmental variables were investigated. Muhiple discriminant analysis was used to fit environmental data to eight selected classifications covering the full range of seasonal and taxonomic treatments. The environmental variables most useful in distinguishing between rivers were substratum characteristics, alkalinity and total oxidized nitrogen. Within-river differences were often highly correlated with discharge, distance from source, width and depth. Slope and altitude contributed strongly to both between-river and within-river distinctions. 4. Between-site variation (beta diversity), eigenvalues of ordination, the reliability of classifications, the proportion of sites correctly assigned to their biological group using environmental data and the standardized similarity between observed and predicted fauna were all higher when identifications were taken to species level, rather than one of three family treatments. Qualitative data on a reduced list of families gave comparable or better results than more detailed family treatments. 5. Combined seasons’data enabled better categorization and prediction than single season's. 6. The values of the Czekanowski Index of Similarity between the observed and predicted fauna of test sites were close to realistic maximum values. 7. Recommendations are made concerning potential usages of the various classifications. The species level classification has uses in the field of conservation and in the prediction of biological response to environmental change. The family level classifications have value in developing local site inventories and in the interpretation of pollution surveillance programmes.     

Effects of species partition on explanatory variables in direct gradient analysis - a case study from Senegal

Abstract. Species-environment data from Senegal, West Africa, are used to study the effects of partition of a large species data set into subsets corresponding to rare and common species respectively. The original data set contains 129 woody plant species from 909 plots and 60 explanatory variables. By applying Canonical Correspondence Analysis to data subsets, marked differences in the forward-selected variables were detected. The highest resemblance was found between the complete species set and the common species subset. Only one of eight selected variables was common to all species and the rare species groups. These findings were tested with partial ordination, applying the selected variables from the original species group (Vb), as variables and covariables to the analyses of common and rare species. For the common species this application resulted in a constrained ordination with higher eigenvalues as compared to the set of variables selected with reference to the common species group. Using the rare species group, the application of Vb gave a much lower sum of eigenvalues than did the ordination with selected variables based on the rare species group only. Evidently, the set of variables selected on the basis of the rare species data were more significant. Hence, the resulting gradients depend on the frequency of the species. Gradient analysis is apparently only valid for groups of species with closely resembling characteristics. This implies that different functional types of species, with different distributions and abundances, respond individually to environmental variation. Extrapolating deduced gradients from one species group to another maybe risky, particularly when used in vegetation modelling.     

稀有种处理对RDA排序结果影响的比较研究

为了解稀有种对RDA排序结果的影响,该研究以北京东灵山华北落叶松林调查数据为例,在RDA排序的基础上,对比分析了未处理稀有种RDA与剔除频度5%、盖度5%的稀有种后RDA排序结果的差异,并用蒙特-卡罗拟合检验分析了二者物种变量和环境变量之间的相关关系,以及用Spearman秩相关系数检验了对应排序轴的相关性。结果表明:(1)蒙特-卡罗拟合检验结果显示未处理稀有种RDA与剔除稀有种RDA各自对应的物种变量和环境变量之间均呈极显著相关关系;(2)从排序轴特征值对物种数据方差以及物种—环境关系解释量来看,剔除稀有种RDA前两排序轴与前四排序轴均有较高的物种-环境关系累积解释量;(3)剔除稀有种前后对应排序轴的Spearman秩相关分析结果表明,尽管未处理稀有种RDA和剔除稀有种RDA在第三轴和第四轴间存在一定的交叉,但二者对应的前四排序轴均呈极显著的一一对应关系(P0.001),相似性极高。总之,结合物种-环境关系的累积解释量及对应排序轴的相关性可知,在环境因子个数较少、研究尺度较小时,使用RDA排序揭示植物种、植物群落和环境因子之间相互作用的生态关系时,剔除稀有种前后RDA排序具有较高吻合性,只是对环境因子的解释趋势稍有差异。     

Variation in wetland invertebrate communities in lowland acidic fens and swamps

1. Invertebrates were collected semi‐quantitatively from four relatively undisturbed wetlands in the west coast of New Zealand’s South Island: two acidic fens and two swamps. Samples were collected from up to four discrete habitats within each wetland: large open‐water channels, small leads (small, ill‐defined channels with emergent vegetation in them) and large (>10 m diameter) or small (<10 m diameter) ponds. Samples were also collected from different plant species within each wetland, each with different morphology, and from areas without vegetation. This was done to determine whether invertebrate communities varied more between‐wetlands than within‐wetlands, as the results had implications for future wetland monitoring programmes. 2. Principal components analysis of water chemistry data revealed striking differences in pH, conductivity and nutrients between the four wetlands. Not surprisingly, pH was lowest in one of the acidic fens, and highest in one of the swamps, where conductivity was also high. Midges (Tanytarsus, Tanypodinae, Orthocladiinae and Ceratopogonidae), nematodes, harpactacoid copepods and the damselfly Xanthocnemis dominated the invertebrate fauna. Orthoclad midges and mites were the most widespread taxa, found in 91 of 94 samples. Diptera were the most diverse invertebrate group, followed by Trichoptera and Crustacea. 3. Ordination analysis of the invertebrate data showed that the four wetlands supported different invertebrate communities. However, species composition did not change completely along the ordination axes, suggesting that a relatively species‐poor invertebrate fauna was found in the wetlands. Taxa such as molluscs were restricted to wetlands with high pH. Multi‐response permutation procedures (MRPP) was used to analyse resultant ordination scores to see how they differed according to five terms: ‘Wetland’, ‘Habitat’, ‘Growth Form’, ‘Morphology’ and ‘Plant’. Most of the sample separation along ordination axes reflected differences between wetland, although the ‘Habitat’ and ‘Plant’ terms also explained some of the variation. The ‘Growth Form’ and ‘Morphology’ terms had only minor effects on community composition. 4. A multivariate regression tree modelled invertebrate assemblages according to the five predictor terms. The resultant model explained 54.8% of the species variance. The ‘Wetland’ term contributed most to the explanatory power, followed by ‘Habitat’. ‘Growth type’ and ‘Morphology’ explained only a small amount of variance to the regression tree, while the different plant species explained none of the variation. 5. Variation in these New Zealand wetland invertebrate communities appears to be controlled most by large‐scale factors operating at the level of individual wetlands, although different habitats within individual wetlands contributed slightly to this variation. Based on these results, sampling programmes to describe wetland invertebrate communities do not need to sample specific habitats or plant types within a wetland. Instead, samples can be collected from a wide range of habitats within individual wetlands, and pooled. Within each habitat, it is unnecessary to collect individual samples from different macrophytes or un‐vegetated areas. Our results suggest that collecting replicate pooled samples from different habitats within each wetland will be sufficient to characterize the invertebrate assemblage of each wetland.     

Fine-scale patterns of vegetation and environmental factors on an ombrotrophic mire expanse: a numerical approach

The vegetation within an ombrotrophic mire expanse in SE Norway is studied in detail. Percentage cover of 45 species in 436 sample plots (16 ×16 cm), dispersed on 26 transects, are recorded. In addition, species abundance in 6976 subplots (4×4 cm) are recorded. 14 variables are recorded for each of the sample plots, while only distance to the water-table is estimated for the subplots. Spatial co-ordinates are supplied for all sample- and subplots. DCA ordination of a data-set consisting of 412 sample plots reveals two ecologically interpretable vegetational gradients: the hummock-hollow gradient (DCA 1), and a gradient associated with the peat-production of the bottom layer (DCA 2). Passive DCA of subplots is used to get an impression of within sample plot heterogeneity, and shows that the fine-scale compositional turnover may be considerable. Partitioning of the variation in species abundance data is done by use of (partial) CCA. The fraction of unexplained variation is rather large for all the tested data-sets, but within the total variation explained, both distance to the water-table and spatial structure explain large parts.