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。     

荒漠啮齿动物群落与植物群落的对应分析

动物与其生存环境变量之间的关系一直是生态学家们广泛关注的问题.啮齿动物作为荒漠生态系统中重要的功能群,其数量大小和生态功能对生态系统的平衡和稳定具有重要意义.生境中的植被为啮齿动物提供赖以生存的食物资源和栖息地,了解啮齿动物群落与植被特征之间的关系对于理解动物群落变动规律具有重要意义.不同植被条件下啮齿动物群落的结构不同,Hernández等(2005)研究发现北美Chihuahuan荒漠的灌木生境中啮齿动物密度高于草地生境.     

Problems of joint display of species and site scores in correspondence analysis

Joint plots of species and site scores in correspondence analysis can be interpreted so that points which are in the same direction from the origin are closely associated. Species and site scores can thus be compared. Within each set of scores the location of points is also meaningful. Owing to the unimodal species response model which can be recovered by the correspondence analysis, the location of the species points in respect to the site points indicates the location of the optimum when direct weighted averages are used. However, when the eigenvalue of the solution is low, very different joint plots are derived when the set which is used for computing the weighted averages for the other set is changed. This makes the interpretation of the between-set proximities in the joint plot vague. Generally, it is not possible to deduce the species composition of a site or sites where a species occurs from the joint plot, although for some pairs of species and sites this is justified. Although the proximity interpretation is not possible in every case, a joint plot display can greatly enhance the interpretation of results.     

环境因子对大亚湾人工鱼礁上附着生物分布的影响

通过对深圳大亚湾人工鱼礁区7个月(2008-04～2008-10)挂板实验,同时监测相应的环境因子指标.以附着生物丰度数据进行了除趋势对应分析(DCA),并根据附着生物丰度数据和7个环境因子进行了典范对应分析(CCA).共鉴定出附着生物54种,物种鉴定结果表明实验试板上的常见种有华美盘管虫 (Hydroides elegans)、三角藤壶( Balanus trigonus)、细肋肌蛤(Musculus mirandus)等.DCA种类排序图可明显地看出每种附着生物都有自己的分布中心和分布区域;CCA分析结果表明深度、透明度、溶解氧是影响附着生物群落变化的最主要环境因子,其次是盐度和温度.CCA排序图较好地反映了人工鱼礁上附着生物分布与各环境因子的相互关系.     

Species richness and distortion in reciprocal averaging and detrended correspondence analysis

Gradients in beta diversity and species richness cause different forms of distortion in reciprocal averaging ordinations. Detrended correspondence analysis largely removes the beta diversity effect and reduces, but does not eliminate, the influence of species richness.     

以林相图为基础的不同取样方式对植被排序分析结果的影响

以6种不同方式对林相图中同一样带取样,采用CA、DCA和CCA 3种排序方法,研究了取样方式对排序轴的解释效果、物种与环境因子、环境因子之间、环境因子与坐标轴之间关系的影响.结果表明,样方大小和形状的变化在不同程度上改变了排序结果.大样方和长方形样方都增强了排序轴的解释效果,并对双序图中稀有种、独特种的位置有较大的影响;环境因子中土壤因子对样方的大小和形状都很敏感,坡度、经纬度只对样方大小敏感,坡位、海拔、温度和降水则对样方形状敏感;随着样方面积的增加,海拔、温度和降水的作用降低,而坡向的作用增加.     

DCCA排序轴分类及其在关帝山八水沟植物群落生态梯度分析中的应用

首次在ＤＣＣＡ排序的基础上使用排序轴分类法（ＯＡＣ）,将其发展为一个新的典范分类方法,并应用这种方法对山西关帝山八水沟的植物群落进行了数量分类,共划分出５类,效果较好。方差分析与多重比较表明,环境与群落结构因子在不同群落之间存在较为显著的差异,表明ＤＣＣＡ排序轴分类法能较好地反映群落与环境的变异。因为ＤＣＣＡ排序轴分类同时结合了植被因子与环境因子,所以它能较好地表达植物群落的环境梯度和结构梯度,反     

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.     

A biogeographical analysis of the European Atlantic lowland heathlands

Questions: What is the climatic envelope of European Atlantic heathlands and the relationship between their floristic geographical variability and climatic parameters? Are the biogeographic patterns extracted from genuine heath plants comparable to those extracted from the accompanying flora? To what extent does the species composition extracted from phytosociological data support the current theory of refuge areas of heath vegetation in southern Atlantic Europe during the Pleistocene ice ages? Location: Atlantic Europe and NW Morocco. Methods: The geographical territory in which Atlantic heathlands occur was divided into 23 sectors following geographic and chorological criteria. A presence–absence table with 333 taxa was then constructed with the available phytosociological data. The taxa were classified into different groups according to their phytosociological affinity. Several types of numerical analysis were performed with this matrix and the climatic data obtained from meteorological sources. Results: Heathlands require a humid and oceanic climate and are limited by cold temperatures in the north and by summer droughts in the south. The highest floristic richness of this vegetation type is found in NW Iberia. Ordinations indicate a strong correlation between floristic composition of biogeographic sector and summer drought (Ios) and thermicity (It). Conclusions: The main climatic factors determining lowland heathland floristic distribution are thermicity and summer drought. The current optimal conditions for heath flora in NW Iberia suggest that there were southern refuges during the Pleistocene ice ages from which northward expansion has taken place.     

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.     

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.     

基于典范对应分析的滨海湿地土壤季节性盐渍化特征

为了更好地开发利用黄河三角洲湿地土壤资源和生态环境建设,运用单因素方差分析(One-way ANOVA)和典范对应分析方法(CCA),对黄河口湿地0—10 cm土壤全盐量(TS)、盐分离子组成、pH、钠吸附比(SAR)、电导率(EC)的季节性变化特征及数量关系进行了分析。结果表明:该区土壤属于盐土类型,春季(5月)、夏季(8月)、秋季(10月)全盐含量均高于17.9 g/kg,且春季、秋季的含盐量高于夏季,造成春、秋季积盐,夏季脱盐。盐分阳离子以Na~+为主,阴离子以Cl~-为主,除Mg~(2+)在夏季、秋季和Cl~-在秋季表现出强烈的变异性外,其余离子在不同季节均表现出中等强度的变异性。春季,Cl~-与Na~+、Mg~(2+),SO■与K~+;夏季,Cl~-与HCO~-_3,SO■与Mg~(2+)、Ca~(2+),Ca~(2+)与Mg~(2+);秋季,Cl~-与SO■,SO■与Mg~(2+),Ca~(2+)与Mg~(2+),均有很好的关联性。pH值均介于7.7—8.1之间,各个季节受盐分离子的影响较小,分布较为均匀。SAR介于3.08—5.29之间,春季受控于HCO~-_3;夏季受控于K~+;秋季受各离子的影响均较小,分布较为均匀。EC介于7.16—13.04 mS/cm,春季受各离子的影响均较小,其空间分布较为均匀;夏季受控于SO■、Ca~(2+)、Mg~(2+);秋季受控于Na~+。TS与Cl~-、Na~+、Mg~(2+)在季节变化上的差异性一致,且各个季节均受控于Cl~-。故通过合理的措施控制或减少Cl~-来源是一条减轻黄河口湿地土壤盐渍化的合适途径。     

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.     

Interrelatedness of 5S RNA sequences investigated by correspondence analysis

Summary Correspondence analysis (a form of multivariate statistics) applied to 74 5S ribosomal RNA sequences indicates that the sequences are interrelated in a systematic, nonrandom fashion. Aligned sequences are represented as vectors in a 5N-dimensional space, where N is the number of base positions in the 5S RNA molecule. Mutually orthogonal directions (called factor axes) along which intersequence variance is greatest are defined in this hyperspace. Projection of the sequences onto planes defined by these factorial directions reveals clustering of species that is suggestive of phylogenetic relationships. For each factorial direction, correspondence analysis points to regions of importance, i.e., those base positions at which the systematic changes occur that define that particular direction. In effect, the technique provides a rapid determination of group-specific signatures. In several instances, similarities between sequences are indicated that have only recently been inferred from visual base-to-base comparisons. These results suggest that correspondence analysis may provide a valuable starting point from which to uncover the patterns of change underlying the evolution of a macromolecule, such as 5S RNA.