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.     

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。     

A note on the occasional instability of detrending in correspondence analysis

When the two first eigenvalues of correspondence analysis are close to each other, their order can be reversed due to random variation in the data. The first axis can actually be in any direction in the plane defined by the two axes. However, the configuration of the points in the plane can remain unchanged but their projections onto any line in the plane can be very variable. The ordering in the first axis is preserved in detrending. The second axis is detrended with respect to the first one and therefore very variable configurations result when the orientation of the first axis in the plane is changed. This can lead to a situation where the detrended solutions are very unstable under random variation and therefore they can be only casually interpretable.     

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.     

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.     

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.     

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.     

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.     

Prairie plant guilds: a multivariate analysis of prairie species based on ecological and morphological traits

An ecomorphological analysis of the tallgrass prairie of central North America divided representative species of the native grassland flora into eight guilds or groups of species with similar life-form, phenology, and ecology. The guilds, segregated by multivariate analysis, are: (1) warm-season graminoids with Kranz anatomy and the Hatch-Slack photosynthetic pathway (C4 grasses); (2) cool-season graminoids without Kranz anatomy, but with the common Calvin or C3 photosynthetic pathway (C3 grasses and sedges); (3) annuals and biennial forbs; (4) ephemeral spring forbs; (5) spring forbs; (6) summer/fall forbs; (7) legumes; and (8) woody shrubs. The study was based on 158 plant species indigenous to three upland prairie sites in northeastern Kansas. Each species was scored for 32 traits which fall into five broad categories: plant habit, leaf characteristics, stem structures, root structures, and reproductive traits, including phenology. A multivariate, detrended correspondence analysis sorted the 158 species into the eight principal groups or guilds. These groups were further supported by a cluster analysis and discriminant function analysis of the same data set. The discriminant function analysis determined that 94.3% of the species were correctly classified in their respective guilds, and that the guilds were statistically different. Results indicate that guild analysis offers a basis for detailed classification of grassland vegetation that is more ecologically focused than species composition, as the myriad of species (about 1,000 prairie species on the central plains of North America) vary in presence, cover, and importance with their individualistic distribution.Abbreviations C3= C3 photosynthesis - C4= C4 photosynthesis - LSD= least significant difference     

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.     

Comparison of different treatments of rare species in canonical correspondence analysis

运用吕梁山南段植物群落及其环境调查数据,比较研究不同稀有种处理(剔除稀有种、稀有种不做处理与降低稀有种权重3种方法处理)对典范对应分析(CCA)排序结果的影响,并用Spearman秩相关系数检验对应排序轴的相关性。结果表明3种方法的分析效果基本一致,但它们对环境因子的解释趋势有差异。基于环境数据、物种数据和样方数据的排序轴相关分析结果显示:未处理稀有种的CCA与降低稀有种权重的CCA吻合度高于剔除稀有种的CCA与降低稀有种权重的CCA的吻合度,未处理稀有种的CCA与降低稀有种权重的CCA的前4轴呈极显著的一一对应关系;剔除稀有种的CCA和降低稀有种权重的CCA仅在基于环境数据和样方数据分析时前3轴呈极显著的一一对应关系,而在基于物种数据的相关分析时前4轴的对应相关性不显著。从物种-环境关系的解释量上来看,降低稀有种权重的CCA最优,剔除稀有种的CCA和未处理稀有种的CCA次之。结合对应排序轴的相关性分析和物种-环境关系累计解释量来看,这3种稀有种处理方法在准确地揭示物种与环境关系时的顺序依次为:降低稀有种权重>对稀有种不做处理>剔除稀有种。     

稀有种不同处理对典范对应分析排序结果影响的比较

运用吕梁山南段植物群落及其环境调查数据, 比较研究不同稀有种处理(剔除稀有种、稀有种不做处理与降低稀有种权重3种方法处理)对典范对应分析(CCA)排序结果的影响, 并用Spearman秩相关系数检验对应排序轴的相关性。结果表明3种方法的分析效果基本一致, 但它们对环境因子的解释趋势有差异。基于环境数据、物种数据和样方数据的排序轴相关分析结果显示: 未处理稀有种的CCA与降低稀有种权重的CCA吻合度高于剔除稀有种的CCA与降低稀有种权重的CCA的吻合度, 未处理稀有种的CCA与降低稀有种权重的CCA的前4轴呈极显著的一一对应关系; 剔除稀有种的CCA和降低稀有种权重的CCA仅在基于环境数据和样方数据分析时前3轴呈极显著的一一对应关系, 而在基于物种数据的相关分析时前4轴的对应相关性不显著。从物种-环境关系的解释量上来看, 降低稀有种权重的CCA最优, 剔除稀有种的CCA和未处理稀有种的CCA次之。结合对应排序轴的相关性分析和物种-环境关系累计解释量来看, 这3种稀有种处理方法在准确地揭示物种与环境关系时的顺序依次为: 降低稀有种权重>对稀有种不做处理>剔除稀有种。     

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.     

Ordination of vegetation change in Guadalupe Mountains,New Mexico,USA

Vegetation change over a nine-year period was studied in Guadalupe Mountains, New Mexico. Permanent transects in desert shrub vegetation were sampled in 1972 and 1980. Emphasis was given to shrubs because of their importance to big game diets. Univariate paired t-tests and reciprocal averaging ordination were used to detect and display coordinated changes in species composition over time. Despite apparently less browsing pressure in desert shrub vegetation in 1980 there were few significant changes in species composition. In addition, preferred forage species showed reduced reproduction while species of intermediate and poor forage value dis-played increased reproduction during this time. These data do not support traditional rangeland succession theory which states that enhanced reproduction of preferred species should follow grazing or browsing pressure reduction.     

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