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     

Numerical studies of compositional gradients in oreophilous vegetation (northern Apennines,Italy)

Summary A numerical study of a set of phytosociological data from oreophilous vegetation in the Apennines (Italy) has been performed. Ranking, classification and ordination methods have been used. The advantages of the joint use of the different methods is diseussed. The results confirm a compositional gradient related to degradation due to grazing, and another, related to base-richness in the soil. Compositional variation does not appear strongly disjointed.Nomenclature follows Zangheri (1976)This work was supported by a grant from the Italian CNR, Pfoject Environment Quality. We wish to thank Professor L. Orlóci for discussions and facllities, and Drs. D. Ubaldi and C. Ferrari for participation in the fieldwork.     

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.     

Book reviews

John B. Boles (ed.), MASTERS AND SLAVES IN THE HOUSE OF THE LORD: RACE AND RELIGION IN THE AMERICAN SOUTH, 1740–1870, Lexington, KY: The University of Kentucky Press, 1988, 257 pp.

David E. Swift, BLACK PROPHETS OF JUSTICE: ACTIVIST CLERGY BEFORE THE CIVIL WAR, Baton Rouge, Louisiana, LA: Louisiana State University Press, 1989, xv + 384 pp., £31.50.

Alexander B. Murphy, THE REGIONAL DYNAMICS OF LANGUAGE DIFFERENTIATION IN BELGIUM: A STUDY IN CULTURAL‐POLITICAL GEOGRAPHY, Chicago, IL: University of Chicago, Geography Research Paper No. 227, 1988, xiii + 249 pp., $12.00.

Pierre L. van den Berghe, STRANGER IN THEIR MIDST, Denver, CO: University Press of Colorado, 1989, xvii + 300 pp., $24.95.     

Ordination and classification in the upland Rugege forest (Rwanda,Central Africa)

Summary Quantitative data on habitat and vegetation from 42 releves of the Rugege forest have been submitted to different ordination and classification methods.The habitat factors which have an important effect upon vegetation are: hydromorphy, abundance of tree layer and depth of soil.The different ordination (principal components analysis and reciprocal averaging) and numerical classification methods applied to the same set of data lead to consistent results. The numerical classification seems better than the Braun-Blanquet's method.Four groupings have been defined.The future developments of ecological studies in the Rugege forest are discussed in relation to the forest conservation.All data presented in this work were collected during my stay in the National Institute of Scientific Research of Rwanda, 1971 – 1972. Part of the computations (numerical analysis and principal components analysis) was carried out at the Nijmegen University's IBM 370/155; I am happy to thank Dr. E. van der Maarel and Dr. J.G.M. Janssen for their welcome and assistance. The reciprocal averaging ordinations and the principal components analysis on the basis of correlation between relevés were performed on the Louvain-La-Neuve University's IBM 370/158; I am very grateful to Professeur Berthet for this important assistance.This paper corresponds to part of a thesis presented at the Liège University on 7th November 1973.     

On the manipulation and editing of phytosociological and ecological data

Editing and other manipulations of phytosociological data are considered parts of a more comprehensive data management program. The topic is reviewed against the background of an increasing number of presentations in Vegetatio. It is observed that the newer editing programs do not add anything new to the already existing battery of programs. Yet, there is a need for further discussions of some risks in data manipulations, notably a priori deletion of relevés and species transformation of field scores, and incorporation of suitable devices in the packages available. Also, the evaluation of classification results and the allocation of new material to existing classification systems need more attention. So do the problems concerning the production of structured phytosociological tables, as outcomes of multivariate data treatments.     

Gradient structure of forest vegetation in the central Washington cascades

Summary Forest vegetation located in three areas of the central Washington Cascades, arrayed along a gradient of increasing continentality and decreasing rainfall, were compared using ordination methods. Within each region, lower and upper elevation sites were analyzed separately and for each set of sites, trees and ground story vegetation were analyzed independently. Principal components analysis, reciprocal averaging, weighted averaging, and polar ordination were applied to each set. The characteristics of the data determined which method gave the most readily interpretable results, but RA and WA usually best ordered the stands along a complex, combined coenocline, while PO often decomposed the gradient into moisture and temperature components. PCA was of little use, even with relatively low beta diversity.Results are presented in the form of stand by species tables for each data set and the most appropriate two dimensional ordination. Both are correlated to the classification. A mosaic diagram for each region is synthesized from these analyses and habitat data. These diagrams indicate that community types occupy a smaller portion of the habitat as continentality increases.The ordination results were in close agreement with our earlier classification of these stands. The maritime (west) region contains stands of low richness and with relatively little coenocline differentiation. In contrast, the continental (east) region has high alpha and beta diversity. Species in the west tend to occupy a broad portion of the available habitat range, while species in the east do not. The analyses reveal that ordinations by different strata may produce similar stand sequences if both strata are responding directly to the same factors, but that the correspondence degenerates where the understory responds primarily to the nature of the canopy dominant species. Thus stand sequence correlations are highest in the lowland eastern region and lowest in the lowland western region.This study demonstrates that none of these metric ordination methods is fool-proof and that none should be used exclusively or in isolation. RA and PO are demonstrated to be useful general methods; WA gave results similar to those of RA. PCA never produced uniquely superior results. Analyses with too few species and moderate beta diversity often produce distortions as pronounced as those with many species and high beta diversity.Nomenclature follows Hitchcock & Conquist (1973).Funds provided by the Graduate School Research Fund, University of Washington and by grants GB-20963 and GB-36810X to the Coniferous Forest Biome, U.S.I.B.P. This is contribution # 318 to the Coniferous Forest Biome. M.F. Denton, R.S. Fleming, A.R. Kruckeberg, and R.H. Whittaker each made significant suggestions. We thank R.S. Fleming, S.G. Fleming, C. Brewer, B.C. Cannon, K.E. Wade, K. Loughney, and J.E. Canfield for their assistance with field work and data analysis.     

Coastal sand dune vegetation of Tabasco and Campeche,Mexico

Abstract. Sand dune vegetation along the coast of the Mexican states of Tabasco and Campeche was sampled by means of 1501 releves and the data were analyzed with classification and ordination programs. 36 community types were distinguished, which were grouped into 10 higher-order groups. The communities are described in a sequence reflecting the main vegetation zonation. Beach, embryo dune and foredune community groups include 12 community types, the sheltered zone includes 16 types and the fixed dunes 8 types. The ordination results reveal one main vegetation gradient corresponding to the increase in mean distance from the shoreline and elevation, and being covariant with species richness, mean vegetation cover and mean vegetation height. Additional differences are related to the geographical transition between the Gulf and Caribbean coastal vegetation and environmental conditions, mainly type of sand, occurring in the study area. Siliceous sand and a Gulf climate are characteristic for most of Tabasco, and calcareous sand and a Caribbean-type climate are characteristic for Campeche. Disturbance caused by coconut plantations, cattle grazing and tourism favours the invasion of ruderal species from waste places behind the dunes, which attain local dominance in the dunes described here. Consequently some separate community types had to be distinguished. The distribution of community types is analyzed in the context of the transitions between calcareous and siliceous substrates in the study area.     

Measurement of the predictive value of species lists for species cover in phytosociological samples

The method known as Analysis of Concentration (AOC) is proposed as a tool to measure the predictivity of binary data for cover data. The application of AOC to structured tables of oak forests of Central Italy has proved that binary data are more predictive for cover than cover for binary data. The ordinations produced by AOC with binary and cover data are very similar and interpretable with similar results.     

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.     

Book reviews

The numbers of perch Perca fluviatilis in the Cikola backwater system of the river Danube were estimated by mark-recapture techniques using multiple fishings. Fish were caught by fyke nets and electrical fishing. The latter method was unselective for sex and the catch data could be used to correct the sex bias in the fyke net catches. A population estimate in April of 6059 ind ha^–1 (95% C.L. 5135–7386) for perch > 5 cm was obtained for a 0.6 ha area of backwater and 1665 ind ha^–1 (95% C.L. 1204–2692) in May for a 0.4 ha area of a small bay.     

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。     

The robustness of Correspondence,Detrended Correspondence,and TWINSPAN Analysis

Abstract. Simulated vegetation data of known structure and varying complexity were analyzed with Correspondence Analysis (CA), Detrended Correspondence Analysis (DCA), and a polythetic divisive method of classification as incorporated in the computer program TWINSPAN. The CA and DCA axes were statistically compared with the original gradients. In the case of TWINSPAN, the results were visually evaluated. The analyses showed that both CA and DCA will recover the first vegetation gradient in an acceptable manner only if the variation in the vegetation due to second or higher order gradients is small. Second gradients were never recovered in a meaningful manner. The sample points along these axes were so far displaced from their original positions along the gradients that the axes could not be used to represent the gradients. In particular, when the two gradients have the same length, CA and DCA gave very poor results for both the first and the second axes. This is thought to be one of the main reasons why TWINSPAN does not perform well, especially after the first division.     

Patterns in the species composition of fish assemblages among Wisconsin streams

Synopsis To better understand patterns of fish assemblage composition in Wisconsin streams in relation to major environmental gradients, I carried out multivariate direct gradient analysis (canonical correspondence analysis) of two large independent datasets on fish species abundance in Wisconsin streams. Analysis of the two datasets yielded similar results, suggesting that observed patterns and relationships were real. Stream sites were distributed along fish species-environment gradients, but segregation into distinct stream temperature and geographic groups was also evident. The strongest gradient in both datasets was related to summer water temperature patterns, and encompassed a transition from small, coldwater streams dominated by salmonids, cottids, certain cyprinids, and few other species, to both small and large, warmwater streams dominated by a high diversity of different cyprinids, catostomids, ictalurids, centrarchids, and percids. A second gradient in both datasets was complex but largely geographic. Within it, sites from each of the four ecoregions that occupy Wisconsin formed fairly discrete groups. The strongest differences were between sites in the two southern Wisconsin ecoregions, the Driftless Area and the Southeastern Wisconsin Till Plains, that were dominated by certain cyprinids, ictalurids, and centrarchids, and sites in the two northern Wisconsin ecoregions, the North Central Hardwood Forests and the Northern Lakes and Forests, that were dominated by a different set of cyprinids and ictalurids, plus some petromyzontids, salmonids, catostomids, and percids. Sites from the Driftless Area that were mostly higher-gradient (steep stream slope) and had many riffle-dwelling species could also be distinguished from sites in the Southeastern Wisconsin Till Plains that were mostly lower-gradient and had many pool-dwelling species. The patterns of fish assemblage composition among sites and the associated fish species-environment relationships that were revealed by the analyses provided a framework for developing an ecologically meaningful hierarchical classification of Wisconsin stream sites based on stream thermal regime, ecoregion, stream size, and stream gradient.     

广西热带石灰岩季节雨林分类与排序

本文利用二歧指示种分析法TWINSPAN将广西热带石灰岩季节雨林的30个样地划分两大类共6个群落：洼地季节雨林(1)火焰花+萍婆群落; (2)海南风吹楠+人面果群落,石山季节雨林(1)东京桐+广西顶果豆群落; (2)假肥牛树+安南牡荆群落;(3)肥牛树群落; (4)肥牛树+蚬木群落。文章还利用无偏对应分析法DCA对群落进行了排序,指出由洼地至山坡水分条件由湿到干是影响群落变化的主导因素。环境的封闭程度对群落变化也有一定影响。     

Book reviews

A new medium is described for the growth of the freshwater diatom Melosira italica subsp. subarctica which allows prolonged exponential growth in batch culture. The medium was optimized for cell yield and observations are reported on varying the pH, shaking rate and trace-metal concentrations in the medium. The medium contained no vitamins. Preliminary results suggest that the silica usage was 0·163 mg Si mm^-3 filament volume, the molar ratio of Si:P uptake varied between 46:1 during exponential growth and 30:1 during silica limitation; the molar N:P ratio of the cells averaged 5·6:1.