The statistical analysis of geochemical compositions

Aitchison, J.

doi:10.1007/bf01029316

Cited by 155 publications

(82 citation statements)

References 27 publications

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“…Ordination analysis thus was done on fractional compositions that sum to unity, and for which the proportions of the different chemical compounds are not independent within a sample. Accordingly, a centered log ratio transformation (Aitchison 1984; Pawlosky-Glahn and Egozcue 2006) was employed prior to principal components analysis and its canonical equivalent, redundancy analysis, performed using CANOCO 4.5 (ter Braak and Smilauer 2002). In the case where a component was not detected, "0.00000001" was used in place of "0" as the relative peak area for that component in the calculation of centered log ratios (Aitchison and Egozcue 2005).…”

Section: Methodsmentioning

confidence: 99%

Differences in Defensive Volatiles of the Forked Fungus Beetle, Bolitotherus cornutus, Living on Two Species of Fungus

et al. 2009

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Forked fungus beetles, Bolitotherus cornutus, feed, mate, and live on the brackets of several species of shelf fungus that grow on decaying logs. In response to the specific threat stimulus of mammalian breath, B. cornutus beetles produce a volatile defensive secretion. We tested beetles collected from different host fungi to determine whether defensive secretion blends varied with host type. Using solid phase microextraction and gas chromatographymass spectrometry, we detected large amounts of the alkylated benzoquinones, methyl-p-benzoquinone (toluquinone) and ethyl-p-benzoquinone, and smaller quantities of p-benzoquinone, 3-methylphenol (m-cresol), 3-ethylphenol, 2-methylhydroquinone, and 2-ethylhydroquinone in secretions. Volatile composition did not differ between male and female beetles. Secretions did differ between beetles collected from two species of fungus, Ganoderma applanatum and Fomes fomentarius, with the relative amount of pbenzoquinone secreted being the most important factor. Other relationships among the volatile components are discussed.

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Section: Methodsmentioning

confidence: 99%

Differences in Defensive Volatiles of the Forked Fungus Beetle, Bolitotherus cornutus, Living on Two Species of Fungus

et al. 2009

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“…Compositional data transformations, such as log and log-ratio (Aitkison, 1984;Baxter, 1992), were carried out before PCA, and compared with the results of untransformed normalized data analysis; given the agreement of the analytical groups retrieved with the different transformations, only results on standardized chemical data are presented.…”

Section: Laboratory Analysesmentioning

confidence: 99%

Bronze Age ceramics in southwest Spain: An exploratory archaeometric study of technology and function

et al. 2005

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Pottery from the Bronze Age of southwest Spain has traditionally been approached from a "typological" stand seeking the establishment of chronological sequences. This article examines ceramics from two different Bronze Age sites, a settlement (El Trastejón) and a necropolis (La Traviesa), from an archaeometric viewpoint. The methodology involved includes mineralogical characterization by XRD and optical microscopy, chemical analysis by XRF, and morphometric analysis through digital processing of thin sections. The analytical results are contextualized within the general framework of our current archaeological knowledge of both sites and their general background, and then a preliminary interpretation is proposed in terms of the prehistoric technology of pottery manufacture and functionality.

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“…This is known as subcompositional incoherence. Detailed discussions on the properties of compositional data and their consequences can be found in Aitchison (1984Aitchison ( , 1986, Chayes 1971, Rock (1988 and Rollinson (1992), amongst others. However, the essential consequence of these properties is that standard statistical techniques devised for unconstrained random variables, cannot be used to analyse compositional data in crude or raw form (e.g.…”

Section: Essential Properties and Their Consequencesmentioning

confidence: 99%

“…John Aitchison laid the foundations of a new approach to the statistical analysis of compositional data through work undertaken in the early 1980s (Aitchison 1981(Aitchison , 1982(Aitchison , 1983(Aitchison , 1984, culminating in the monograph that brought this work together (Aitchison 1986). He recognized that although new analytical methods had been developed for other forms of constrained data, such as directional data, whose vectors are confined by a unit length constraint, there were none for those data confined by the constant sum.…”

Section: A New Approach: Relative Variations and Log-ratiosmentioning

confidence: 99%

Compositional data and their analysis: an introduction

2006

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Abstract:Compositional data are those which contain only relative information. They are parts of some whole. In most cases they are recorded as closed data, i.e. data summing to a constant, such as 100% -whole-rock geochemical data being classic examples. Compositional data have important and particular properties that preclude the application of standard statistical techniques on such data in raw form. Standard techniques are designed to be used with data that are free to range from -oo to +oo. Compositional data are always positive and range only from 0 to 100, or any other constant, when given in closed form. If one component increases, others must, perforce, decrease, whether or not there is a genetic link between these components. This means that the results of standard statistical analysis of the relationships between raw components or parts in a compositional dataset are clouded by spurious effects. Although such analyses may give apparently interpretable results, they are, at best, approximations and need to be treated with considerable circumspection. The methods outlined in this volume are based on the premise that it is the relative variation of components which is of interest, rather than absolute variation. Log-ratios of components provide the natural means of studying compositional data. In this contribution the basic terms and operations are introduced using simple numerical examples to illustrate their computation and to familiarize the reader with their use.

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The statistical analysis of geochemical compositions

Cited by 155 publications

References 27 publications

Differences in Defensive Volatiles of the Forked Fungus Beetle, Bolitotherus cornutus, Living on Two Species of Fungus

Differences in Defensive Volatiles of the Forked Fungus Beetle, Bolitotherus cornutus, Living on Two Species of Fungus

Bronze Age ceramics in southwest Spain: An exploratory archaeometric study of technology and function

Compositional data and their analysis: an introduction

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