Effects of detrending and rescaling on correspondence analysis: solution stability and accuracy

Detrending and non-linear axis rescaling potentially improve the accuracy of gradient recovery in correspondence analyses but also reduce the stability or consistency of solutions. Variation among bootstrapped ordination solutions was compared across methods in analyses of both field and simulated data. Solution accuracy, measured with mean squared errors from Procrustes analysis, was compared using simulated data with known structure.Standard detrending-by-segments combined with non-linear rescaling entailed some cost in solution stability, but could improve the accuracy of solutions for long gradients. Without non-linear rescaling these solutions were usually less stable and less accurate. Although detrending-by-polynomials might be preferable on other grounds, it did not produce more accurate or stable solutions than detrending-by-segments.Abbreviations CA = correspondence analysis - DCA = detrended correspondence analysis - MSE = Procrustes mean squared error statistic - SD = standard deviation units of species turnover - SRV = scaled variance in species ranks     

对应分析和去趋势分析在有蹄类取食模式研究中的应用

本研究将2009年1月和2010年1月小兴安岭大沾河湿地自然保护区二可河林场内驼鹿冬季食性作为原始数据,分别以对应分析（CA）、去趋势分析（DCA）,并将数据以样本为单位进行标准化后,再进行去趋势分析（DCA_std）3种排序方法,对驼鹿冬季取食模式进行了研究,后通过普鲁克分析,比较了不同排序方法对大型有蹄类取食模式研究的效果。结果表明,3种排序法的1轴和2轴均能涵盖绝大多数信息量,CA涵盖79.27%,DCA涵盖66.65%,DCA_std涵盖68.22%;3种方法均能够在1轴上区分针叶树和落叶乔木类食物,在2轴上,3种方法主要能够达到针叶树种与除落叶乔木外的其他植物类别的区分。虽三者均能够展现有蹄类取食模式,但在图形可视化后,仅DCA_std无明显的弓形效应。普鲁克分析结果表明,DCA_std样本位移平方和与CA和DCA均有很大差异,即将数据先进行标准化再进行DCA分析能够有效去除弓形效应。因此,在由多度组成的食性数据在进行标准DCA分析前,应对数据进行前期处理会得到更好的效果。同时,以样本为单位的标准化将使排序分析结果生态学意义更明确。     

卧龙自然保护区亚高山草甸的数量分类与排序

在野外植被调查的基础上,采用植被数量分析方法对岷江流域卧龙自然保护区亚高山草甸进行TWINSPAN分类和DCA排序,研究了植物种、植物群落与环境之间的关系.结果表明,该地区亚高山草甸共有植物139种,隶属于31科88属.应用数量分类方法将114个样方分为12个群落类型.在分析不同环境因子间的关系基础上,从定量的角度揭示了影响群落分布的主要因素是海拔梯度和土壤含水量.DCA排序图反映出排序轴的生态意义,第1轴反映了各群落类型所在环境的海拔梯度,从上到下,随着海拔的升高,植物群落或植物种的耐寒性越来越强;第2轴基本上反映了各群落类型所在环境的土壤含水量.排序结果与分类结果比较吻合,反映出植物群落类型和物种分布随环境因子梯度变化的趋势.     

Reconstructing community relationships: the impact of sampling error, ordination approach, and gradient length

Effectively summarizing complex community relationships is an important feature in studies such as biodiversity, global change, and invasion ecology. The reliability of such community summaries depends on the degree of sampling variability that is present in the data, the structure of the data, and the choice of ordination method, but the relative importance of these factors is not understood. We compared the validity of results from different ordination methods by applying five levels of sampling error to a simulated coenoplane model at two gradient lengths using two types of data (abundance and presence–absence). The multivariate methods we compared were correspondence analysis (CA), detrended correspondence analysis (DCA), non-metric multidimensional scaling (NMDS), principal component analysis (PCA) and principal coordinates analysis (PCoA). Our results showed CA and PCA using presence–absence data were the most successful methods regardless of sampling error and gradient length, closely followed by the other methods using presence–absence data. With abundance data, PCA and CA were the most successful approaches with the short and long gradients, respectively. Approaches based on PCoA and NMDS using abundance data did not perform well regardless of the choice of distance measure used in the analysis. Both of these methods, along with the PCA using abundance data, were strongly affected by the longer gradient, leading to more distorted results.     

Multivariate analysis of benthic invertebrate communities: the implication of choosing particular data standardizations,measures of association,and ordination methods

Benthic invertebrate data from thirty-nine lakes in south-central Ontario were analyzed to determine the effect of choosing particular data standardizations, resemblance measures, and ordination methods on the resultant multivariate summaries. Logarithmic-transformed, 0–1 scaled, and ranked data were used as standardized variables with resemblance measures of Bray-Curtis, Euclidean distance, cosine distance, correlation, covariance and chi-squared distance. Combinations of these measures and standardizations were used in principal components analysis, principal coordinates analysis, non-metric multidimensional scaling, correspondence analysis, and detrended correspondence analysis. Correspondence analysis and principal components analysis using a correlation coefficient provided the most consistent results irrespective of the choice in data standardization. Other approaches using detrended correspondence analysis, principal components analysis, principal coordinates analysis, and non-metric multidimensional scaling provided less consistent results. These latter three methods produced similar results when the abundance data were replaced with ranks or standardized to a 0–1 range. The log-transformed data produced the least consistent results, whereas ranked data were most consistent. Resemblance measures such as the Bray-Curtis and correlation coefficient provided more consistent solutions than measures such as Euclidean distance or the covariance matrix when different data standardizations were used. The cosine distance based on standardized data provided results comparable to the CA and DCA solutions. Overall, CA proved most robust as it demonstrated high consistency irrespective of the data standardizations. The strong influence of data standardization on the other ordination methods emphasizes the importance of this frequently neglected stage of data analysis.     

Compositional gradients in the forest vegetation of Finland

Abstract. Compositional gradients of forest vegetation in Finland were determined using detrended correspondence analysis, and ecologically interpreted with regression analysis. The data were collected in association with the 8th National Forest Inventory, and they comprised 1514 samples and 472 species, covering the whole forested land area of Finland. In the ordination space the first, very stable axis (DCA1) was much stronger than the following three, more unstable axes (DCA2 - 4). Site fertility (reflected by the forest site type series) and latitude had strongest covariation with the ordination space, followed by a number of variables primarily related to forest age or tree stand volume. Fertility variables were most closely parallel with DCA1, latitudinal ones with DCA1 and DCA2, and successional variables with DCA3. The results indicate that compositional overlap of sites classified into different Caj ander site types is considerable.     

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     

The impact on the Senjogahara ecosystem of extreme run-off events from the river Sakasagawa,Nikko National Park

Vegetational data from Senjogahara moor, Nikko National Park, Japan have been analysed using two contrasting but parallel multivariate approaches as a basis for future studies. The plant communities objectively defined using a divisive polythetic classificatory approach (TWINSPAN) have been successfully overlayed on an ordination of the same data using detrended correspondence analysis (DCA). The results reveal a vegetational mosaic reflecting differential levels of flood damage to the vegetation and its subsequent rates of recovery, in a space-time continuum. The results from the TWINSPAN classification show that 13 plant communities are present in the sample area and these correlate closely with complete absence, slight, or extremely heavy disturbance. The form of the disturbance as either channel erosion or alluvial depositional features is shown to also correspond quite closely with the vegetational types and is reflected in the ordination axes derived from DCA.     

中条山中段植物群落数量分类与排序研究

在群落样方调查基础上,采用双向指示种分析法（TWINSPAN）和除趋势对应分析（DCA）对中条山中段植物群落进行了数量分类和排序。TWINSPAN将53个样方分为14组,根据植被分类的原则划分为14个群丛,论述了各群丛的群落学特征。53个样方的DCA排序结果反映了植物群落类型与环境梯度之间的关系,表明影响群丛分布格局的主导生态因子为海拔高度、水分和热量。DCA排序将65个种分为5个种组,各种组在排序轴上的位置反映了种组成员的生态适应性及其在群落中的重要性和更新生态位。     

Effects of sample distribution along gradients on eigenvector ordination

In general, disproportionately heavy sampling of the ends of a gradient increases the interpretability of eigenvector ordinations. More specifically, correspondence analysis (CA) and detrended correspondence analysis (DCA) best reproduce the original positions of samples in simulated coenoclines when samples are clustered toward the ends of the axis. Principal components analysis (PCA) reproduces the original sample positions less well than either CA or DCA and shows no improvement as samples are increasingly clustered toward the ends of the axis. PCA and CA show less curvature of one dimensional data into the second axis when sampling favors the ends of the axis.     

A comparative study of hourly and daily relationships between selected meteorological parameters and airborne fungal spore composition

Air sampling was conducted in Szczecin (Poland) throughout April–September 2013. The final data set included 177 daily and 4248 hourly samples. The total of 21 types of spores, which occurred in a number >10 in the season, were taken into account. The following meteorological parameters were analyzed: air temperature, relative humidity, precipitation and wind speed. Effects of individual weather parameters on hourly and daily concentrations of different fungal spore types were examined using Spearman’s rank association test, whereas effects of complex of meteorological factors on hourly and daily compositions of spore were assessed using detrended correspondence analysis (DCA) and redundancy analysis (RDA). Airborne fungal spore distribution patterns in relation to meteorological variables were determined by RDA, after DCA results detected a linear structure of the spore data. The RDA results obtained indicated that all the applied variables accounted for 20 and 22% of the total variance in the hourly and daily spore data, respectively. The results of stepwise forward selection of variables revealed all included hourly and daily meteorological variables were statistically significant. The largest amount of the total variance in the spore composition was explained by the air temperature in both cases (16%). Multivariate ordination did not show large differences between the hourly and daily relationships (with exception of wind speed impact), while the differences between simple hourly and daily correlations were more clear. Correlations between daily values of variables were in most cases higher than between hourly values of variables.     

A comparison of detrended correspondence analysis and principal co-ordinates analysis using four sets of Tasmanian vegetation data

Indirect gradient analysis, which entails the elucidation of relationships between trends in community composition and underlying environmental or successional gradients, is a major objective of ordination in plant ecology. Two ordination techniques, detrended correspondence analysis (DCA) and principal co-ordinates analysis (PCOA), were compared using three sets of Tasmanian vegetation data having known gradients and one set where the vegetation was expected to respond to diverse environmental variables. In every case, the results obtained by DCA were considered superior to, or at least as good as, those of PCOA. Hence, DCA appears to be the more suitable of the two methods for indirect gradient analysis.     

山西北部地区沙棘群落的数量分类和排序研究

采用双向指示种分析法对山西北部地区沙棘群落进行分类和排序研究,结果将山西北部地区沙棘群落划分为14个群系,并论述了各群系的特征。DCA排序进一步说明了群系的分布格局与水分和土壤的密切关系,结果表明组成沙棘灌丛的种群对群落生境具有指示作用,能客观反映群落的生境特征．     

桂林岩溶石山青冈栎群落的数量分析

应用双向指示种分析(TWINSPAN)和除趋势对应分析(DCA)方法对桂林岩溶石山青冈栎群落进行数量分类与排序。通过TWINSPAN分类,将青冈栎群落60个样方划分为8个群丛类型,探讨了各群丛类型的基本特征。结果表明:DCA排序与TWINSPAN分类结果较一致,DCA排序较好地体现了各群丛类型与环境因子的相互关系,DCA第一排序轴主要反映了坡度的变化梯度;DCA排序图的对角线基本体现了坡向的变化梯度。坡度的变化是影响岩溶石山青冈栎群落物种组成与分布的重要生态因子。     

小陇山国家级自然保护区次生林分类、排序及演替

在野外调查基础上,采用TWINSPAN和DCA对小陇山林区次生林群落进行了数量分类和排序,从植物群系组成、植物群落与环境的生态关系方面,研究小陇山植被群落的分布格局,用以确定该区次生林演替,并给予合理的环境解释。结果表明:采用TWINSPAN数量分类方法,将植被划分为12个群落类型;DCA排序图明显反映出排序轴的生态意义,第一轴基本上突出反映了湿度变化,沿第一轴从左到右,湿度逐渐增大;第二轴主要表现了温度梯度,沿第二轴从下到上,温度逐渐降低;次生林的演替序列为山杨林→山杨+白桦林→锐齿栎混交林及锐齿栎纯林,其自然恢复演替以锐齿栎林为顶极群落。     

长江故道湿地植被的数量分类与排序

采用双向指示种分析法（TWINSPAN）和除趋势对应分析法（DCA）对长江故道湿地植被做分类和排序研究。TWINSPAN分类将湿地植被234个样方分为28个群丛,论述了各群丛的群落学特征。DCA排序结果反映了植物群落类型与环境梯度之间的关系,表明影响群丛分布格局的主导生态因子为生境的水分条件。TWINSPAN数量分类在DCA排序图中有较为明确的分布范围和界限,两者的结合使用,能很好地反映群落与环境因子间的生态关系。     

Ordination methods and chironomid species in stony bottom streams

Stony bottom streams in Italy were sampled in 369 sites in different years, and 174 chironomid species (or species groups) were identified.The species by sites matrix was submitted to different ordination methods, with the aim of outlining the major factors that are responsible of the observed species composition.The methods considered were principal component analysis (PCA), detrended correspondence analysis (DCA) and non-metric multidimensional scaling (MDSCAL). These methods assume different models describing the species-responses to the environmental gradients.PCA gave poor results, the best species ordination was given by MDSCAL. DCA gave results in agreement with MDSCAL. DCA results were useful as a starting point to perform MDSCAL. MDSCAL was performed with different options. At last Procrustean analysis was carried out to have a single fitted configuration, that summarized the results given by the different MDSCAL methods.All multivariate analyses emphasized that the first ordination axis can be interpreted as a crenonrithron-potamon gradient, probably an oxygen availability and/or a water temperature gradient, whereas the second axis can be considered a water speed gradient, separating lotic from lentic sites.The 3rd and 4th ordination axes had apparently no ecological meaning.Separated clusters of species were never evident, so well defined chironomid species assemblages could not be outlined in this analysis.     

Coastal plant and soil relationships along the southwestern coast of South Korea

We studied how plant species distribution was regulated by the relationships between vegetation and soil factors on the southwestern coast of South Korea. Vegetation was classified using two-way indicator species analysis (TWINSPAN), thereby producing four vegetation groups that were linked to three habitat types. Two ordination techniques —; detrended correspondence analysis (DCA) and canonical correspondence analysis (CCA) —; were applied to examine the relationships between vegetation and 12 edaphic factors, including soil pH, water and osmotic potentials, moisture content, electrical conductivity, Cl and Na⁺ contents, total Kjeldahl nitrogen, and contents of organic matter, sand, silt, and clay. Results were similar for both types of evaluations. According to DCA and CCA, the 23 communities tended to cluster into three types: salt swamp, salt marsh, and sand dune. The first two canonical axes accounted for 14.9% of the community-soil factor relationship among communities. As identified via CCA, the main gradients were soil-water relations and soil texture.     

汾河河口湿地植被数量分类与排序

在群落样方调查基础上,采用双向指示种分析（TWINSPAN）和除趋势对应分析（DCA）对汾河入河口湿地植被群落进行了数量分类和排序。TWINSPAN将78个样方分为18个群丛,并论述了各群丛的群落学特征。DCA排序结果反映了植物群落类型与环境梯度水分之间的关系,表明影响群丛分布格局的主导生态因子为土壤水分。     

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