Twenty years of numerical syntaxonomy

The development of numerical syntaxonomy during its first 20 yr is reviewed. The use of methods of numerical classification and ordination is the dominating feature of the development. National and local phytosociological data banks were established, large data sets handled and many important vegetation monographs were methodically based on multivariate data analysis. Particularly the development in Italy, the Netherlands, Czechoslovakia, and Sweden contributed to new theoretical elements of numerical syntaxonomy. Ordination became a common tool of searching for reticulate synsystematic relations between community types. The most popular ordination techniques have been Principal Components Analysis and Detrended Correspondence Analysis. Hierarchical agglomerative techniques of clustering still prevail in classification, although the divisive strategy of TWINSPAN has also become an effective tool for phytosociological clustering and table sorting. Extensive program packages, also for personal computers have now become standard equipment for many vegetation scientists.     

Pluralism and diversity: trends in the use and application of ordination methods 1990‐2007

Question: What are the trends and patterns in the application of ordination techniques in vegetation science since 1990? Location: Worldwide literature analysis. Methods: Evaluation of five major journals of vegetation science; search of all ISI‐listed ecological journals. Data were analysed with ANCOVAs, Spearman rank correlations, GLMs, biodiversity indices and simple graphs. Results: The ISI search retrieved fewer papers that used ordinations than the manual evaluation of five selected journals. Both retrieval methods revealed a clear trend in increasing frequency of ordination applications from 1990 to the present. Canonical Correspondence Analysis was far more frequently detected by the ISI search than any other method. Applications such as Correspondence Analysis/Reciprocal Averaging and Detrended Correspondence Analysis have increasingly been used in studies published in “applied” journals, while Canonical Correspondence Analysis, Redundancy Analysis and Non‐Metric Multidimensional Scaling were more frequently used in journals focusing on more “basic” research. Overall, Detrended Correspondence Analysis was the most commonly applied method within the five major journals, although the number of publications slightly decreased over time. Use of Non‐Metric Multidimensional Scaling has increased over the last 10 years. Conclusion: The availability of suitable software packages has facilitated the application of certain techniques such as Non‐Metric Multidimensional Scaling. However, choices of ordination techniques are currently less driven by the constraints imposed by the software; there is also limited evidence that the choice of methods follows social considerations such as the need to use fashionable methods. Methodological diversity has been maintained or has even increased over time and reflects the researcher's need for diverse analytical tools suitable to address a wide range of questions.     

Multiscale ordination: a method for detecting pattern at several seales

Multivariate analyses of vegetation data have been restricted to a single scale of sampling, or multiscale sampling has been restricted to a single species. However, vegetation scientists need to be able to explore spatial relationships of many species over many scales. We present a modification of Noy-Meir & Anderson's (1971) method of multiscale ordination by summing two-term local covariance matrices and smoothing the component profiles. The advantages of our method are: 1) results are less subject to the starting position of the transect, 2) matrices may be added at any block size, and 3) plots of factor scores are smoothed by a moving weighted average to better reveal patterns at a prescribed scale.This procedure provides statistical associations of species over a range of scales. The scales which exhibit the association to the maximum extent are then determined from multiscale ordination. The relationships of different associations and their scales can then be examined. The application of the method to fabricated data proved successful in recovering the structure built into the data. When used on real vegetation data, from a community and a landscape, the method revealed the details of species associations over a range of scales, and of the relationships among associations.Abbreviations PCA = Principal Components Analysis - DCA = Detrended Correspondence Analysis - TTLC = Two-Term Local Covariance     

Dissimilarity for partially ranked data and its application to cover-abundance data

Cover-abundance estimates are commonly employed in phytosociological investigations to record the performance of species. Because the coded values are on an ordinal scale of measure, various authors have suggested that some transformation is necessary before such values can be used for classification and ordination. However, it is not clear that transformation is a sufficient treatment, and it would seem preferable to use ordinal data directly. In this paper we examine such direct use of partial rankings and show that several dissimilarity measures can be defined for this case without invoking any transformations. They include dissimilarity measures associated with various rank correlation measures and with distances between strings; all the measure are variant forms of Hausdorf's interset distance. Certain other kinds of data, such as those employing dominant and subdominant species and the dry-weight-rank estimation of biomass, are also on an ordinal scale and could be analysed using similar techniques.To illustrate the approach, a string dissimilarity measure is used to analyse a set of data from Slovakian grasslands which appear to reflect a simple gradient. The original data were recorded with 10 classes of performance and are analysed using hierarchical and nondeterministic, overlapping, classifications.     

A comparison of reciprocal averaging and non-centred principal components analysis

Non-centred Principal Components Analysis (NPCA) ordinates sites and species simultaneously, and can be solved either by direct iteration or by eigenvector calculation. The weight of sites and species in the analysis is proportional to their overall abundance. Because of this, the method is not susceptible to distortion by rare species, as is the case with Reciprocal Averaging (RA). Detrending techniques can also be applied to this method to eliminate arch effects.When NPCA was tried with field data, it produced ordination axes that were significantly associated to independently measured environmental variables. In contrast, RA failed to produce axes related to environmental factors, even after the main rare species had been eliminated from the analysis.Abbreviations NPCA Non-centred Principal Components Analysis - RA Reciprocal Averaging     

Ordination and classification of operational geographic units in Southwest Sweden

The vascular plant distributions of Dalsland and northern Bohuslän (Southwest Sweden) were subjected to multivariate analyses in order to delimit geographically coherent floristic zones. 271 squares of 5×5 km were the Operational Geographic Units; the data matrix comprises presence/absence species records for each OGU. Different ordination and classification methods were tested and detailed results are presented for detrended correspondence analysis (DCA), UPGMA and ordination space partitioning (OSP). A weighting procedure, neighbour-weighting, which gives pseudo-frequency scores along the nominal scale 0–9 depending on the species' distribution patterns, is introduced. The superior method for delimiting geographically coherent floristic zones was judged to be ordination space partitioning, using DCA and neighbour-weighted species scores.Abbreviations DCA Detrended Correspondence Analysis - OGU Operational Geographical Unit - OSP Ordination Space Partitioning - UPGMA Unweighted Pair-Group Method using Arithmetic Averages     

Optimum-transformation of plant species cover-abundance values

Most of the methods used in the multivariate analysis of data on vegetation and environment, or transformations implied in such methods, put disproportionate emphasis on species with a relatively wide ecological amplitude occurring with relatively high cover-abundance values, and/or rare species. This problem can be overcome to some extent by reducing the cover-abundance values to presence-absence data, but this means a severe loss of information. A standardization of values by species maxima as is done automatically in some programs, may lead to an undesirable emphasis on species represented with low values only.In this paper a method is presented, by which relatively low cover-abundance values of species are upweighted to an arbitrarily chosen higher value, if these low values are considered to indicate an optimum response of that particular species. The method has been tested on a selection of 40 phytosociological relevés from dune slacks in the Voorne dunes, as well as on the Dune Meadow data set used in the textbook of Jongman et al. (1987). The cluster structure obtained with the optimum-transformation appears to be clearer and the contribution of typical dune slack species to the cluster structure increased significantly. Canonical correspondence analysis of the transformed data gave slightly more important main axes.Abbreviations CA = Correspondence Analysis - CCA = Canonical Correspondence Analysis - DOL = Detection of Optimality Level - SWOM = Standardized Weighted Optimality Measure - WPGMA = Weighted Pair Group Method Average linking clustering     

微生物生态研究中BIOLOG方法数据分析及R语言实现

微生物生态研究中,对微生物群落结构、群落特征以及其与环境因素的关系的揭示,一直受到广泛关注;适当的数据分析方法有助于更清晰地刻画微生物群落结构特征,明确其与环境因素的关系。结合实例,对微生物生态研究中基于BIOLOG微平板技术的数据分析方法进行梳理,分别介绍数据读取整理、特征指数计算、非限制性排序、限制性排序、聚类分析、环境向量拟合、蒙特尔检验等常用数据操作及生态分析方法;针对不同方法结论,结合研究目标和生态理论给出具有统计学意义的解释,并评价不同方法特点及适用场景;分析过程以R语言实现,并提供全部代码。结果表明,BIOLOG方法产生数据能从多个角度表征微生物群落功能特征,并结合环境指标梯度进行分析;但BIOLOG数据可能不满足正态性分布,在基于正态分布的分析前应提前进行检验;排序分析时应慎用主成分分析,可优先采用其他基于距离矩阵的排序方法;R语言能够简化BIOLOG数据读取及操作,易于完成各类统计分析。本研究能够对微生物生态研究者科学选择应用统计分析方法、提高数据处理效率提供直接参考。     

VEGAN,a package of R functions for community ecology

Abstract. VEGAN adds vegetation analysis functions to the general‐purpose statistical program R. Both R and VEGAN can be downloaded for free. VEGAN implements several ordination methods, including Canonical Correspondence Analysis and Non‐metric Multidimensional Scaling, vector fitting of environmental variables, randomization tests, and various other analyses of vegetation data. It can be used for large data. Graphical output can be customized using the R language's extensive graphics capabilities. VEGAN is appropriate for routine and research use, if you are willing to learn some R.     

Numerical analysis of vegetation complexes and community diversity of major coastal dinaric mountains

Abstract. This study includes 24 transects on slopes of the Velebit, Biokovo and Orjen mountains, the tallest coastal mountains along the Adriatic Sea, with a very high species richness according to European standards and having the largest regional concentrations of endemics. Within each transect the presence or absence of phytosociological alliances, according to the Zürich-Montpellier School, was interpreted from local studies. The alliance composition of the transects was compared with methods used in numerical syntaxonomy. Three types of vegetation complexes (N. Dinaric inland, transitional and S. Dinaric coastal) were derived from a numerical classification of the transects; they were defined on the basis of their characteristic alliances. The maritime impact affecting the mountains through the river canyons reduces the contrast in vegetation between inland and coastal slopes. The existence of a climatic macrogradient is indicated by seriation of the basic alliance/transect data matrix leading to a diagonal structure, by a gradual shift of the alliance composition within the same vegetational type, and by the distribution of the transects and alliances along the first axis of a Correspondence Analysis ordination. Transect scores on the second ordination axis are negatively correlated with transect vegetational diversity (number of alliances per transect); this axis may reflect a decrease in humidity and temperature range. This interpretation is supported by the result of a comparison of the total mountain vegetational diversity (Mann-Whitney test), which showed that Orjen is the most diverse mountain ridge. The expected correlation between plant community diversity and altitude of the transects is blurred, probably due to the impact of the cold Bora wind and subsequent compression of vegetational zones.     

Parallel Analysis: a method for determining significant principal components

Abstract. Numerous ecological studies use Principal Components Analysis (PCA) for exploratory analysis and data reduction. Determination of the number of components to retain is the most crucial problem confronting the researcher when using PCA. An incorrect choice may lead to the underextraction of components, but commonly results in overextraction. Of several methods proposed to determine the significance of principal components, Parallel Analysis (PA) has proven consistently accurate in determining the threshold for significant components, variable loadings, and analytical statistics when decomposing a correlation matrix. In this procedure, eigenvalues from a data set prior to rotation are compared with those from a matrix of random values of the same dimensionality (p variables and n samples). PCA eigenvalues from the data greater than PA eigenvalues from the corresponding random data can be retained. All components with eigenvalues below this threshold value should be considered spurious. We illustrate Parallel Analysis on an environmental data set. We reviewed all articles utilizing PCA or Factor Analysis (FA) from 1987 to 1993 from Ecology, Ecological Monographs, Journal of Vegetation Science and Journal of Ecology. Analyses were first separated into those PCA which decomposed a correlation matrix and those PCA which decomposed a covariance matrix. Parallel Analysis (PA) was applied for each PCA/FA found in the literature. Of 39 analy ses (in 22 articles), 29 (74.4 %) considered no threshold rule, presumably retaining interpretable components. According to the PA results, 26 (66.7 %) overextracted components. This overextraction may have resulted in potentially misleading interpretation of spurious components. It is suggested that the routine use of PA in multivariate ordination will increase confidence in the results and reduce the subjective interpretation of supposedly objective methods.     

A generalized standardization procedure in ecological ordination: Tests with Principal Components Analysis

Abstract. Standardization by norms of sample position vectors as well as by sample totals has been used frequently in vegetation ecology. Both standardizations are only special cases of the Generalized Standardization Procedure (GSP) described in this paper. The general procedure allows a wide choice of data transformations simply by varying values of a single standardization parameter. Principal Components Analysis (PCA) often involutes opposite ends of a coenospace, producing results that may be difficult to interpret. Experiments with simulated as well as field data sets revealed that involuted gradients can be unfolded if GSP is applied prior to PCA. Compared to Correspondence Analysis, GSP-PCA was superior in recovering the structure of analysed coenoclines.     

Quantitative studies of modern wet-ground molluscan faunas from Bossington, Hampshire

There have been few quantitative studies of modern Mollusca in Britain, especially from wet-ground areas. This is particularly true of the English chalklands, which is surprising given the focus of sub-fossil molluscan research in that area. Those studies that are available highlight the difficulty of separating molluscan faunas from structurally complex habitats such as fen and carr. Quantitative molluscan data from a variety of wet-ground habitats situated within the chalklands of southern England were analysed using an indirect ordination technique, Principal Components Analysis. This demonstrated that the separation of faunas from structurally complex wet-ground habitats is possible. The numerical separation does not rely on indicator species, but is a function of variation of the predominant species. It is suggested that further studies of this type might aid the interpretation of sub-fossil Mollusca from wet-ground contexts.     

On the evaluation of ordinal data with conventional multivariate procedures

In a recent Forum paper, it is argued that, in most studies, ordinal data such as the Braun‐Blanquet abundance/dominance scale are not properly treated by multivariate methods. This is because conventional multivariate methods are generally adequate for ratio‐scale variables only, while for ordinal variables differences between states and their ratios are not interpreted. Conversely, in this paper it is shown that using conventional multivariate procedures for evaluating ordinal data should imply a shift from a metric space to a topological data space; as such the use of ordinal data does not represent a serious methodological error, provided that results are interpreted accordingly.     

Representing species in reserves from patterns of assemblage diversity

Aim A positive relationship between assemblage diversity (AD) – equivalent to the biotic version of the environment diversity, ED, method – and species diversity has been reported. This being true, reserve networks with many different assemblages would be expected to represent more species than reserve networks including fewer and less different assemblages. This idea was tested using European species atlas distributions of terrestrial vertebrates and plants. It is asked whether: (1) maximizing AD within one group would represent species diversity of this group better than expected by chance; and (2) maximizing AD within one group would represent species diversity of other groups better than expected by chance. Location Europe. Methods Three ordination techniques (non‐metric multidimensional scaling, detrended correspondence analysis and correspondence analysis) are used to summarize patterns of compositional turnover within assemblages. p‐Median location‐allocation models are then calculated from ordination space to measure the degree of expected species representation within the group being sampled as well as the expected representation within other groups. Results are compared with near‐optimal solutions obtained with complementarity‐based algorithms and to a null model obtained by simulating selection of areas at random. Matrix correlation analysis was also performed to investigate broad patterns of covariation in compositional turnover of assemblages of species belonging to different taxonomic groups and these values were compared with correlation in species richness scores between groups. Results The AD model did not always represent more species of the group being sampled than expected by chance (P < 0.05). Results were independent of the method and taxonomic group considered. Effectiveness of AD within one group to represent species of other groups varied, but in most cases it was worse than using complementarity‐based algorithms as a surrogate strategy. Even when correlations indicated high coincidence between assemblages, taxonomic‐based surrogates did not always recover more species than expected by chance (P < 0.05). Main conclusions Results are discussed in the light of two possible explanations: (1) the AD model is based on unrealistic assumptions, namely that species have equal probability of having the centre of their distributions anywhere in ordination space and that species display unimodal, symmetrical, bell‐shaped response curves to gradients; (2) particular implementation of methods may be inadequate to summarize useful complementarity among assemblages, especially for restricted‐range species. We conclude that both arguments are likely to play a role in explaining results, but that opportunities exist to improve performance of existing surrogate strategies.     

Sequence clustering threshold has little effect on the recovery of microbial community structure

Analysis of microbial community structure by multivariate ordination methods, using data obtained by high‐throughput sequencing of amplified markers (i.e., DNA metabarcoding), often requires clustering of DNA sequences into operational taxonomic units (OTUs). Parameters for the clustering procedure tend not to be justified but are set by tradition rather than being based on explicit knowledge. In this study, we explore the extent to which ordination results are affected by variation in parameter settings for the clustering procedure. Amplicon sequence data from nine microbial community studies, representing different sampling designs, spatial scales and ecosystems, were subjected to clustering into OTUs at seven different similarity thresholds (clustering thresholds) ranging from 87% to 99% sequence similarity. The 63 data sets thus obtained were subjected to parallel DCA and GNMDS ordinations. The resulting community structures were highly similar across all clustering thresholds. We explain this pattern by the existence of strong ecological structuring gradients and phylogenetically diverse sets of abundant OTUs that are highly stable across clustering thresholds. Removing low‐abundance, rare OTUs had negligible effects on community patterns. Our results indicate that microbial data sets with a clear gradient structure are highly robust to choice of sequence clustering threshold.     

甘肃马衔山林区植被的数量分类与排序

 本文用目前各国学者广泛使用的一些数量分类和排序方法对黄土高原区的马衔山植物群落进行了分类和排序。所用方法包括多元等级分划分类(TWINSPAN程序)、PCA排序(ORDINA程序)、RA和DCA排序(DECORANA程序)。研究结果表明可以把32个样地分为两大类共7个群落类型：山地森林 (1)山杨+白桦群落,(2)青杆群落,(3)青杆+白桦+山杨群落,(4)山杨+康定柳+糙皮桦群落;山地灌丛 (1)康定柳+糙皮桦群落,(2)糙皮桦+黄毛杜鹃+裂香杜鹃群落,(3)黄毛杜鹃+裂香杜鹃群落。它们的分布格局与海拔梯度密切相关。此外,本文还对所用方法的比较进行了讨论。     

稻田田埂昆虫群落与田埂杂草关系的研究

为探索稻田田埂昆虫群落与田埂类型的关系,本文对田埂昆虫群落进行主分量分析和模糊聚类分析,结果表明:田埂昆虫群落类型与田埂类型有一定的联系。经典范分析,从定量上明确田埂昆虫群落与田埂类型的关系程度(r_1=0.8232),并得出田埂杂草高度是影响田埂昆虫群落的关键因子。     

Plant-environment relationships on the Montlake wildlife area,Seattle, Washington,USA

Grassland vegetation on the Montlake fill was analyzed using TWINSPAN. Eight herb communities were recognized. Moisture, proximity to gas vents, and disturbance are the main factors that control species and community distributions. Binary discriminant analysis (BDA) and detrended correspondence analysis (DCA) were used to study species-environment relationships. BDA revealed complex species response patterns and the resultant indicator values were used to interpret the ordination axes. Species distributions are controlled primarily by moisture, but also influenced by soil pH. Multiple regressions revealed little about plant-environment relationships not discovered by BDA. Before robust nonlinear methods are available, BDA, metric ordination with data stratification and nonmetric ordination are methods that can yield satisfactory results in exploratory plant-environment studies. BDA alone is an efficient, useful first approach where response patterns of species are initially unknown.Abbreviations BDA Binary Discriminant Analysis - DCA Detrended Correspondence Analysis