Multivariate Techniques in Ecology

Abstract

Multivariate analysis (MA) 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 largely universally applicable. In the life sciences, MA 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 (PCFA). The data are four standard measurements on the conch of the Cenomanian (Upper Cretaceous) ammonite species Metoicoceras praecox from the Midwestern 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 standardised distance measures across the conch and ribbing frequencies for six species of the Cenomanian (Upper Cretaceous) ammonite genus Metoicoceras and a dwarf derivative of Metoicoceras geslinianum, Nannometoicoceras acceleratum, all from the Midwestern 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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Further Reading

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.

Dryden IL and Mardia KV (1998) Statistical Shape Analysis. Wiley Series in Probability and Statistics. New York, NY: Wiley.

Krzanowski WJ (1995) Recent Advances in Descriptive Multivariate Analysis. Oxford: Oxford University Press.

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Reyment, Richard A(Jul 2014) Multivariate Techniques in Ecology. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0003266.pub3]