Multivariate Techniques in Ecology

Richard A Reyment, Paleozoologiska Avdelningen, Naturhistoriska Riksmuseet, Stockholm, Sweden

Published online: September 2007

DOI: 10.1002/9780470015902.a0003266.pub2

Multivariate statistical analysis is concerned with the simultaneous examination of two or more variables (in the case of full space) or parts (in the case of simplex space) by means of procedures based on the application of standard methods of linear algebra and differential geometry. The methods are universally applicable. In the life sciences, multivariate analysis is of wide use in animal and plant taxonomy, quantitative genetics, environmetrics, ecology and aspects of evolutionary biology.

Keywords: biometrics; morphometrics; latent variables; ordination; reification; compositional data

Figure 1. Example of ordination by principal component factor analysis. The data are four standard measurements on the conch of the Cenomanian (Upper Cretaceous) ammonite species Metoicoceras praecox from the Mid-Western United States. The plot discloses polymorphism in this species, presumably a manifestation of dimorphism in the shell (termed macroconchs and microconchs).
Figure 2. An example of ordination of compositional canonical variate (CV) means upon which a minimum spanning linkage is superimposed. The data consist of seven standardized distance measures across the conch and ribbing frequencies for six species of the Cenomanian (Upper Cretaceous) ammonite genus Metoicoceras and a dwarf derivative of M. geslinianum, Nannometoicoceras acceleratum, all from the Mid-Western United States. The evolutionary relationships indicated by the multivariate morphometrical analysis of parameters determining shell-shape and ornament echo to a high degree the conclusions arrived at by traditional subjective methods of taxonomy supported by biostratigraphy.
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 References
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 Further Reading
    other Buccianti A, Mateu-Figueras G and Pawlowsky-Glahn V (2007) Compositional Data analysis in the Geosciences. Geological Society Special Publication 204. London: The Geological Society.
    other Dryden IL and Mardia KV (1998) Statistical Shape Analysis. Wiley Series in Probability and Statistics. New York: Wiley.
    book Krzanowski WJ (1995) Recent Advances in Descriptive Multivariate Analysis. Oxford: Oxford University Press.

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Article Title: Multivariate Techniques in Ecology
 
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Reyment, Richard A(Sep 2007) Multivariate Techniques in Ecology. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0003266.pub2]