Progresses in <i>R</i>– and <i>Q</i>–Mode Analysis: Correspondence Analysis and its Application to the Study of Geological Processes

Mouat, D. A.; Campiglio, Carlo; Darling, Richard S.

doi:10.1139/e74-012

Cited by 52 publications

(12 citation statements)

References 1 publication

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“…Attempts have been made, e.g. by Miesch et al (1966), David et al (1974) and Teil and Cheminée (1975), to explore compositional variability through the use of SVDs based on the raw or standardized compositional data. These approaches do not recognize specifically the compositional nature of the data and do not have the property of subcompositional coherence.…”

Section: Discussionmentioning

confidence: 99%

Biplots of Compositional Data

Aitchison

Greenacre

2002

Journal of the Royal Statistical Society Series C: Applied Statistics

535

386

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1 SummaryThe singular value decomposition and its interpretation as a linear biplot has proved to be a powerful tool for analysing many forms of multivariate data. Here we adapt biplot methodology to the speci¯c case of compositional data consisting of positive vectors each of which is constrained to have unit sum. These relative variation biplots have properties relating to special features of compositional data: the study of ratios, subcompositions and models of compositional relationships. The methodology is demonstrated on a data set consisting of six-part colour compositions in 22 abstract paintings, showing how the singular value decomposition can achieve an accurate biplot of the colour ratios and how possible models interrelating the colours can be diagnosed.2

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Section: Discussionmentioning

confidence: 99%

Biplots of Compositional Data

Aitchison

Greenacre

2002

Journal of the Royal Statistical Society Series C: Applied Statistics

535

386

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“…Martin & Lepart, 1989; Poulin et al ., 1993; Spitzer et al ., 1993), CA and its modified forms have been utilized extensively for analyses in various sectors of quantitative science (e.g. David et al ., 1974; Melguen, 1974; Greenacre & Vrba, 1984; Montaña & Greig‐Smith, 1990; Bojórquez‐Tapia et al ., 1995). Correspondence analysis uses graphical display to obtain a summary description of a large dataset comprising a large number of variables.…”

Section: Methodsmentioning

confidence: 99%

Ecological characterization of bat species distributions in Michoacán, México, using a geographic information system

Wang

Owen

Sánchez-Hernández

et al. 2003

Global Ecology and Biogeography

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Aim To investigate the relationship between chiropteran species distributions and four fundamental environmental factors — temperature, precipitation, soil and vegetation — and to construct a species richness prediction map based on the environmental factors. Location The state of Michoacán, México. Methods Bat specimens collected during a 2‐year project were combined with museum specimens to form a dataset of over 3200 entries pertaining to 71 species of bats. Coordinates of the collection localities were recorded with GPS receivers or determined from maps. ArcView GIS was used to characterize the distribution of the species relative to the four environmental factors by projecting coordinates of the collection sites onto digitized maps of those factors. Correspondence analysis (CA) was used to evaluate the relationship between species distributions and the environmental factors. Results The CA results indicated that the order of importance of these factors is (from highest to lowest): temperature, vegetation, precipitation and soil. A predicted distribution map was constructed for each species of bat, based on the result of the CA analysis, using correspondences of each species to climate, vegetation and precipitation. Soil types were excluded from the prediction model because soil type does not appear to carry high predictive value for bat species in Michoacán. Distribution maps of the 71 bat species were then overlaid to generate a map of bat species richness for the state of Michoacán. Main conclusions Neither family membership nor feeding guild affiliation appear to play important roles in chiropteran species distributions in Michoacán. The bat species richness prediction map will be a useful tool for conservation works in the region.

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“…Correspondence analysis is a multivariate method that can be regarded as a variation of principal component analysis in which the properties of both R-mode and Q-mode techniques are combined. By a special method of scaling, a simultaneous representation of samples and variables on the same factoffal axes can be obtained [David et al, 1974;Ted, 1975]. The possibility of interpreting the sample points and the variable points in the same plane has obvious advantages and provides the following information:…”

Section: Multivariate Analysismentioning

confidence: 99%

Impact of productivity events on the benthic foraminiferal fauna in the Arabian Sea over the last 150,000 years

Otto¹,

Hermelin²,

Shimmield³

1995

Paleoceanography

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We have studied the sediment geochemistry and benthic foraminiferal fauna in a piston core from the northwest Arabian Sea (covering the last 150,000 years), and compared the results with the stable isotopic record from both benthic (Uvigerina peregrina) and planktonic (Globigerinoides sacculifer) foraminifera. The δ18O record of the planktonic foraminiferal species shows excursions towards heavier δ18O values when compared to the benthic record and the SPECMAP stack, particularly in stage 3, between approximately 30 and 45–50 kyr. We call this the “stage 3 event.” Species diversity and relative abundance data on benthic foraminifera reveal that some species, e.g. Cibicidoides wuellerstorfi, Oridorsalis umbonatus, Pullenia bulloides, Pyrgo spp., and the uvigerinids increased in relative abundance during glacial stages 2 and 4 and during the stage 3 event, whereas other (e.g., Astrononion novozealandicum, Cibicidoides bradyi, Eggerella bradyi, Gyroidina altiformis, Hoeglundina elegans, Pullenia subcarinata, and Sigmoilina edwardsii) decreased. Using correspondence analysis we determined that approximately 50% of the total sample variation may be accounted for by three first factors which all are interpreted as primarily related to surface water productivity and the quality of the organic matter that reaches the seafloor. The relative abundance of some species appears to vary on a precessional cycle, perhaps responding to monsoon‐driven upwelling and associated increased food supply, whilst the abundances of other species are related to the 100 kyr ice volume cycle, and may be responding to changes in intermediate and deep water chemistry. Geochemical paleoproductivity tracers, such as the Ba content of the sediment, have a very similar distribution to specific foraminiferal factors in both time and frequency domains. Certain planktonic foraminifera, (e.g., Globigerina bulloides), also display obvious maxima in the stage 3 event. The stage 3 event occurs at a time of reduced rate of amplitude change in both solar radiation and monsoon pressure index. We conclude, that there was a period 15 to 20 kyr duration during stage 3 with cooler‐than‐normal surface waters, enhanced productivity and rapid settling of biogenic matter.

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Progresses in R– and Q–Mode Analysis: Correspondence Analysis and its Application to the Study of Geological Processes

Cited by 52 publications

References 1 publication

Biplots of Compositional Data

Biplots of Compositional Data

Ecological characterization of bat species distributions in Michoacán, México, using a geographic information system

Impact of productivity events on the benthic foraminiferal fauna in the Arabian Sea over the last 150,000 years

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