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.     

典范分析在江苏海岸带盐土植物排序中的应用

本文应用典范分析,对取自江苏海岸带一珍禽保护区盐土植被的样方进行排序,根据前人已作的江苏海岸带植被的研究结果,分析比较了以各类典型变量排序样方对揭示植物群落分布连续性及环境梯度变化的有效性。     

Performance of four ordination techniques assuming three different non-linear species response models

Summary The performances of four ordination techniques (reciprocal averaging, parametric mapping, gaussian ordination and non-metric multidimensional scaling) are evaluated using artificial data based on three vegetation models: the gaussian response curve, -function curves, and an ecological response model. No technique performs well with the artificial data not based on a gaussian model. Non-metric multidimensional scaling seemed marginally better than other techniques. Some of the implications of this failure are discussed.     

Applying Canonical Analysis to a Kind of Generalized Regression

This paper is concerned with the generalized model E(φ(Y)! X) =φ(X) involving the transformations on both the predictor vector X and the response variable Y. For this purpose, Taylor expansions and canonical analysis are applied. For optimizing the expansions, it is shown by a simulation study that not only prediction error, the combination of model error and noise error, is an important index, but the distribution of the residuals and the t-values of the coefficients also must be considered. Furthermore, the results of penicillin titrition show that the practical situations often need to be considered in selecting an appropriate model for a real-life problem.     

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     

Ordination as a tool for analyzing complex data sets

Summary Ordination has proven to be a useful tool for examining relationships between environment and vegetation in data sets with a simple underlying environmental strueture. Complex data sets have proven much less tractable. A strategy is offered for dealing with complex data sets based on progressive removal of sets of stands along identified gradients, and subsequent reordination. This strategy is demonstrated using forests of the North Carolina piedmont.The author gratefully acknowledges the continuing collaboration of Dr. Norman L. Christensen of Duke University. This research was supported by National Science Foundation grants DEB-7708743 and DEB-7804043 to R.K.P. and DEB-7707532 and DEB-7804041 to N.L.C.     

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     

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.     

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.     

Sparse canonical correlation analysis from a predictive point of view

Canonical correlation analysis (CCA) describes the associations between two sets of variables by maximizing the correlation between linear combinations of the variables in each dataset. However, in high‐dimensional settings where the number of variables exceeds the sample size or when the variables are highly correlated, traditional CCA is no longer appropriate. This paper proposes a method for sparse CCA. Sparse estimation produces linear combinations of only a subset of variables from each dataset, thereby increasing the interpretability of the canonical variates. We consider the CCA problem from a predictive point of view and recast it into a regression framework. By combining an alternating regression approach together with a lasso penalty, we induce sparsity in the canonical vectors. We compare the performance with other sparse CCA techniques in different simulation settings and illustrate its usefulness on a genomic dataset.     

Cranial capacity/cranial base relationships and prediction of vault form: A canonical correlation analysis

Canonical correlation analysis was used to test an hypothesized morphological relationship between vault form and cranial capacity relative to length of the chondrocranium. Ninety-five adult male Czech skulls were measured for vault form expressed as length, width and height of the brain case; the chondrocranium was represented by nasion-basion and basion-opisthion lengths. In terms of explained variation, the first and most important dimension of covariation between vault and chondrocranial variables was size. The second most significant dimension of covariation expressed the hypothesized shape relationships—i.e., overall size being equal, the shorter the chondrocranial base relative to cranial capacity, the shorter and wider the vault. Furthermore, the competing hypothesis that vault form is determined by facial length proved untenable since facial length was predictive of vault shape only when measured as prosthion-basion, a measure that incorporates basal length. When corrected for basal length, facial length is unrelated to vault form. The results are consistent with the assumption that phylogenetic and microevolutionary trends toward brachycephaly in man stem from changes in the relationship between two components of skull growth, the chondrocranial base and the brain.     

Estimating a multivariate familial correlation using joint models for canonical correlations: application to memory score analysis from familial Hispanic Alzheimer's disease study

Summary .  Analysis of multiple traits can provide additional information beyond analysis of a single trait, allowing better understanding of the underlying genetic mechanism of a common disease. To accommodate multiple traits in familial correlation analysis adjusting for confounders, we develop a regression model for canonical correlation parameters and propose joint modeling along with mean and scale parameters. The proposed method is more powerful than the regression method modeling pairwise correlations because it captures familial aggregation manifested in multiple traits through maximum canonical correlation.