Chapter

Compositional Data Analysis

Volume 187 of the series Springer Proceedings in Mathematics & Statistics pp 167-180

Date:

Representation of Species Composition

  • V. Pawlowsky-GlahnAffiliated withDepartment of Computer Science, Applied Mathematics, and Statistics, University of Girona Email author 
  • , T. Monreal-PawlowskyAffiliated withIZVG
  • , J. J. EgozcueAffiliated withDepartment of Civil and Environmental Engineering, Technical University of Catalonia

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Abstract

The Aitchison geometry of the simplex, the sample space of compositional data, allows statistical modelling and analysis of compositions without the problems derived from spurious correlation. Here, it is used to show that it offers an alternative to the de Finetti ternary diagram for representing variability of species composition avoiding the problems typical of a standard analysis of proportions, namely spurious correlation and limitation to three or at most four components. The method is illustrated with data representing the species composition of Free and FAD tuna school sets sampled in the Indian and Atlantic Oceans during the 2002–2008 period by purse seiners.

Keywords

Simplex Ternary diagram Aitchison geometry Tuna Fisheries