Exploring contingency tables with correspondence analysis

An algorithm for correspondence analysis is described and implementedin SAS/IML (SAS Institute, 1985a). The technique is shown, throughthe analysis of several biological examples, to supplement thelog-linear models approach to the analysis of contingency tables,both in the model identification and model interpretation stagesof analysis. A simple two-way contingency table of tumor datais analyzed using correspondence analysis. This example emphasisesthe relationships between the parameters of the log-linear modelfor the table and the graphical correspondence analysis results.The technqiue is also applied to a three-way table of surveydata concerning ulcer patients to demonstrate applications ofsimple correspondence analysis to higher dimensional tableswith fixed margins. Finally, the diets and foraging behaviorsof birds of the Hubbard Brook Forest are each analyzed and thena simultaneous display of the two separate but related tablesis constructed to highlight relationships between the tables. Received on August 29, 1988; accepted on April 25, 1989     

Factorial correspondence analysis of fear-related behaviour traits in Japanese quail

Factorial correspondence analysis was performed on 341 quails from a F2 cross between two lines divergently selected on the duration of tonic immobility over 29 generations. Several fear- or stress-related traits were recorded, i.e. tonic immobility duration, number of inductions needed to induce tonic immobility, open-field behaviour (time spent walking, latency before first movement and number of defecations), asymmetry of tibia lengths and corticosterone concentration after restraint stress. Variables were categorised in classes and analysed by factorial correspondence analysis. The first axis was mostly described by open-field behaviour, and the second by tonic immobility traits (duration of tonic immobility and number of inductions), which showed that these behaviours were almost independent. No relationship was found between axes of the factorial correspondence analysis and corticosterone concentration or asymmetry of tibia lengths, showing that these variables reflected other characteristics of stress susceptibility than those described by tonic immobility and open-field behaviour. These results show that reaction to stress of quails is a multidimensional trait and cannot be summarised by one trait.     

排序轴分类法及其应用

排序轴分类法及其应用张金屯（山西大学生物系,太原０３０００６）ＯｒｄｉｎａｔｉｏｎＡｘｅｓＰａｒｔｉｔｉｏｎｉｎｇａｎｄＩｔｓＡｐｐｌｉｃａｔｉｏｎ．　￥ＺｈａｎｇＪｉｎｔｕｎ（ＤｅｐｏｒｔｍｅｎｔｏｆＢｉｏｌｏｇｙ,ＳｈａｎｘｉＵｎｉｖｅｒｓｉ－ｔ...     

Analysis of cyclic nucleotide phosphodiesterase by isoelectric focusing coupled to a specific activity stain

The procedure described allowed a convenient analysis of cyclic nucleotide phosphodiesterase. The different phosphodiesterase forms present in a crude cytosolic preparation from rat heart were separated by isoelectric focusing on a polyacrylamide gel plate. Phosphodiesterase activity bands were rendered evident by a specific staining method. They were then characterized by means of their substrate specificity and their sensitivity to selective phosphodiesterase inhibitors. The correspondence between the stain bands and the previously described activity peaks, obtained by a preparative technique and detected by radioisotopic enzyme assay, was also investigated.     

Cryptogams on decaying wood in old-growth forests of southern coastal British Columbia

Abstract. We studied the floristic composition of lignicolous cryptogams (i.e. bryophytes and lichens inhabiting decaying wood) in the old-growth coniferous forests of southern coastal British Columbia. The composition of the cryptogams was related to forest communities (described by vegetation units using forest floor cryptogams and vascular plants) and regional climates (described by biogeoclimatic zones). The study is based on a total of 247 sample plots, each of 0.04 ha in size. The plots were located in three different biogeoclimatic zones and were classified into 12 alliances and four orders in a previous study. We used indicator species analysis to determine cryptogam indicator species for each vegetation unit and biogeoclimatic zone, and used similarity analysis and multi-variate analyses (discriminant analysis and detrended correspondence analysis) to detect differences in the floristic composition of the cryptogams among sample plots, vegetation units, and biogeoclimatic zones. Most of the cryptogams in this study had a narrow distribution, and only < 5% of the species were present across all the vegetation units and biogeoclimatic zones. The overall means of Jaccard coefficients between two sample plots from the same vegetation unit (alliance or order) or biogeoclimatic zone were significantly higher (P < 0.05) than those from different vegetation units or biogeoclimatic zones. The difference in the mean Jaccard coefficients within- and between-units was highest for zones. The results of detrended correspondence analysis and discriminant analysis suggest that the composition of lignicolous cryptogams changes with the change in the floristic composition of forest floor vegetation. When the first axes of detrended correspondence analysis were compared, the Pearson's correlation coefficients between the first axes of lignicolous cryptogams and forest floor vascular plants and between the first axes of lignicolous cryptogams and forest floor cryptogams were 0.78 and 0.87, respectively. The degree of correspondence in the composition of lignicolous cryptogams and forest floor vegetation increased from alliance to order to biogeoclimatic zone. This trend suggests that the floristic composition of lignicolous cryptogams is influenced at the community level mainly by edaphic conditions and at the regional level by climatic conditions.     

A Comparative Study of Scores for Correspondence Analysis with Ordered Categories

Ordered categorical data can be analysed using correspondence analysis with the ordered categories taken into consideration. Such an analysis was proposed by Beh (1997) and uses orthogonal polynomials which require the input of a scoring scheme to reflect the ordered structure of the categories. This method of correspondence analysis visualises the relationship between the categories, in terms of the location, dispersion and higher order components. The impact of the scoring method on the orthogonal polynomials, and hence upon the correspondence plot and other output of the analysis should therefore be considered. This paper aims at identifying this impact by considering four scoring schemes: integer valued (natural) scores, midrank scores, Nishisato scores and singular vectors from the classical correspondence analysis of the data. It is shown that while the latter two maximise the location component, generally there is little difference when comparing them with the output of the former two scoring schemes. A simple comparative study of profile co-ordinates using different scoring schemes is also discussed.     

High-performance liquid chromatographic analysis of acylated lipids containing pyrene fatty acids

A high-performance liquid chromatographic method for the separation and quantification of acylated lipids containing pyrene fatty acids is described. The method is adapted from a procedure originally developed for the analysis of tissue lipids (Christie, W. W. (1985) J. Lipid Res. 26, 507-512). Pyrenyl lipid analogs ranging in polarity from cholesteryl ester to lysophosphatidylcholine are completely resolved on a silica column in 50 min by gradient elution with a ternary solvent system. Furthermore, pyrene-labeled triglycerides are resolved according to the number of pyrene fatty acid residues incorporated. Pyrenyl lipids are detected at levels of 10(-13) mol by high-sensitivity fluorescence detection. Accurate quantification of pyrenyl lipids is obtained by correcting peak areas for mobile-phase quenching effects. The close correspondence between chromatograms obtained for the separation of labeled lipids extracted from Hep-G2 cells incubated with either 12-(1-pyrenyl)dodecanoic acid (fluorescence detection) or [1-14C]oleic acid (radioactivity detection) indicates that this HPLC method is equally suitable for analysis of native lipids.     

The measurement of linguistic change

Summary Two methods for measuring the amount of linguistic change are described: 1. It is possible to measure the correspondence between two phoneme inventories of two periods in a language's development in the same way as in information theory between the inventories of the transmitted and received symbols (measure of correspondence B). 2. This first method, however, does not measure the development of a phonologic pattern. Therefore the correlation of similarity is computed (as applicated in the psychology of development).     

Co-inertia analysis: an alternative method for studying species–environment relationships

• 1 Methods used for the study of species–environment relationships can be grouped into: (i) simple indirect and direct gradient analysis and multivariate direct gradient analysis (e.g. canonical correspondence analysis), all of which search for non-symmetric patterns between environmental data sets and species data sets; and (ii) analysis of juxtaposed tables, canonical correlation analysis, and intertable ordination, which examine species–environment relationships by considering each data set equally. Different analytical techniques are appropriate for fulfilling different objectives.
• 2 We propose a method, co-inertia analysis, that can synthesize various approaches encountered in the ecological literature. Co-inertia analysis is based on the mathematically coherent Euclidean model and can be universally reproduced (i.e. independently of software) because of its numerical stability. The method performs simultaneous analysis of two tables. The optimizing criterion in co-inertia analysis is that the resulting sample scores (environmental scores and faunistic scores) are the most covariant. Such analysis is particularly suitable for the simultaneous detection of faunistic and environmental features in studies of ecosystem structure.
• 3 The method was demonstrated using faunistic and environmental data from Friday (Freshwater Biology 18, 87-104, 1987). In this example, non-symmetric analyses is inappropriate because of the large number of variables (species and environmental variables) compared with the small number of samples.
• 4 Co-inertia analysis is an extension of the analysis of cross tables previously attempted by others. It serves as a general method to relate any kinds of data set, using any kinds of standard analysis (e.g. principal components analysis, correspondence analysis, multiple correspondence analysis) or between-class and within-class analyses.

     

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。     

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．     

A method for investigating hepatocyte polyploidization kinetics during postnatal development in mammals.

A method for investigating weakly-proliferating cell populations of liver parenchyma on the basis of a quantitative analysis of hepatocyte polyploidization during postnatal development is described. The method uses a mathematical model which characterizes the hepatocyte polyploidization process, and incorporates data concerning the time course for relative frequencies of hepatocytes in different ploidy classes. As a result of these measurements and calculations for rat liver, transition rates of hepatocytes (the relative number of cells during a given time unit) from one ploidy class to another, and a coefficient for the reduction of hepatocyte mitotic activity with an increase in its ploidy class were obtained. Calculated curves show a good correspondence with the real process of hepatocyte frequency changes as they relate to changes in the age of the animals. To check this method, experiments investigating time changes of autoradiographic label content in the different ploidy classes of hepatocytes were carried out. By mathematically modeling the label diluting process resulting from cell proliferation and polyploidization, transition rates of hepatocytes were calculated, and they reflect values calculated from the model according to changes in occurrence frequencies.     

Sampling of solid spent agar media for gas chromatography of diffused acidic fermentation products

Abstract Sampling and processing of solid agar media for gas chromatographic analysis is described. Small pieces of agar are cut from a 'sterile' area of the plate leaving the actual bacterial growth undisturbed for further tests. It is shown that diffused fermentation acids are adequately represented in these samples to permit their use for phenotypic and taxonomic characterization of isolates. Because of the established qualitative and quantitative correspondence of fermentation patterns from agar-grown and from broth-grown bacteria, respectively, the method is offered as a rapid alternative for the sampling of spent culture broths. In addition, the sampling of spent agar plugs seems to hold promise for the study of defined mixed cultures and of mixed growth from primary plates.     

Higher order structure in ribosomal RNA.

The only reliable general method currently available for determining precise higher order structure in the large ribosomal RNAs is comparative sequence analysis. The method is here applied to reveal 'tertiary' structure in the 16S-like rRNAs, i.e. structure more complex than simple double-helical, secondary structure. From a list of computer-generated potential higher order interactions within 16S rRNA one such interaction considered likely was selected for experimental test. The putative interaction involves a Watson-Crick one to one correspondence between positions 570 and 866 in the molecule (E. coli numbering). Using existing oligonucleotide catalog information several organisms were selected whose 16S rRNA sequences might test the proposed co-variation. In all of the (phylogenetically independent) cases selected, full sequence evidence confirms the predicted one to one (Watson-Crick) correspondence. An interaction between positions 570 and 866 is, therefore, considered proven phylogenetically.     

Principal component and normal mode analysis of proteins; a quantitative comparison using the GroEL subunit

Principal component analysis (PCA) and normal mode analysis (NMA) have emerged as two invaluable tools for studying conformational changes in proteins. To compare these approaches for studying protein dynamics, we have used a subunit of the GroEL chaperone, whose dynamics is well characterized. We first show that both PCA on trajectories from molecular dynamics (MD) simulations and NMA reveal a general dynamical behavior in agreement with what has previously been described for GroEL. We thus compare the reproducibility of PCA on independent MD runs and subsequently investigate the influence of the length of the MD simulations. We show that there is a relatively poor one-to-one correspondence between eigenvectors obtained from two independent runs and conclude that caution should be taken when analyzing principal components individually. We also observe that increasing the simulation length does not improve the agreement with the experimental structural difference. In fact, relatively short MD simulations are sufficient for this purpose. We observe a rapid convergence of the eigenvectors (after ca. 6 ns). Although there is not always a clear one-to-one correspondence, there is a qualitatively good agreement between the movements described by the first five modes obtained with the three different approaches; PCA, all-atoms NMA, and coarse-grained NMA. It is particularly interesting to relate this to the computational cost of the three methods. The results we obtain on the GroEL subunit contribute to the generalization of robust and reproducible strategies for the study of protein dynamics, using either NMA or PCA of trajectories from MD simulations.     

Centres of diversity quantified—A maximum variance approach to a biogeographic problem

Summary A quantitative method that optimizes the mapping of species diversity in phytogeographic studies is described. Diversity is computed on the basis of species number per unit area. The optimal size of unit area for which diversity is computed is held to be that which maximises the diversity difference between species-rich and species-poor regions. An example is given using Turkish Papaver. A very high correspondence is found between intuitive insights based on long study and the computer-generated diversity maps. Phytogeographic elements were also determined by computer after gridding Turkey at the scale discovered to be optimal for diversity and scoring the grid squares for presence-absence of each species. In this case, too, quite high correspondence was found between the computer and intuitive results.Nomenclature follows Cullen (1965).The authors express their thanks to Mr. K. Roberts, University of Western Ontario Computing Centre of writing the original maximum variance program and to the National Research Council of Canada for supporting the computing side of the project.     

Model-free methods of analyzing domain motions in proteins from simulation: A comparison of normal mode analysis and molecular dynamics simulation of lysozyme

Model-free methods are introduced to determine quantities pertaining to protein domain motions from normal mode analyses and molecular dynamics simulations. For the normal mode analysis, the methods are based on the assumption that in low frequency modes, domain motions can be well approximated by modes of motion external to the domains. To analyze the molecular dynamics trajectory, a principal component analysis tailored specifically to analyze interdomain motions is applied. A method based on the curl of the atomic displacements is described, which yields a sharp discrimination of domains, and which defines a unique interdomain screw-axis. Hinge axes are defined and classified as twist or closure axes depending on their direction. The methods have been tested on lysozyme. A remarkable correspondence was found between the first normal mode axis and the first principal mode axis, with both axes passing within 3 Å of the alpha-carbon atoms of residues 2, 39, and 56 of human lysozyme, and near the interdomain helix. The axes of the first modes are overwhelmingly closure axes. A lesser degree of correspondence is found for the second modes, but in both cases they are more twist axes than closure axes. Both analyses reveal that the interdomain connections allow only these two degrees of freedom, one more than provided by a pure mechanical hinge. Proteins 27:425–437, 1997. © 1997 Wiley-Liss, Inc.     

Subclass mapping: identifying common subtypes in independent disease data sets

Whole genome expression profiles are widely used to discover molecular subtypes of diseases. A remaining challenge is to identify the correspondence or commonality of subtypes found in multiple, independent data sets generated on various platforms. While model-based supervised learning is often used to make these connections, the models can be biased to the training data set and thus miss inherent, relevant substructure in the test data. Here we describe an unsupervised subclass mapping method (SubMap), which reveals common subtypes between independent data sets. The subtypes within a data set can be determined by unsupervised clustering or given by predetermined phenotypes before applying SubMap. We define a measure of correspondence for subtypes and evaluate its significance building on our previous work on gene set enrichment analysis. The strength of the SubMap method is that it does not impose the structure of one data set upon another, but rather uses a bi-directional approach to highlight the common substructures in both. We show how this method can reveal the correspondence between several cancer-related data sets. Notably, it identifies common subtypes of breast cancer associated with estrogen receptor status, and a subgroup of lymphoma patients who share similar survival patterns, thus improving the accuracy of a clinical outcome predictor.     

Comparison of super-secondary structures in proteins

A method of comparing the conformations of different, but structurally related proteins is described. Local variations, such as the systematic translation of a helix, or the position of deletions and insertions can be detected, and the correspondence of only marginally similar structures can be measured. The occurrence of larger continuous folds (“super-secondary structures”) has been detected in the comparison of lactate dehydrogenase with itself and with other protein structures.