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.
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Acknowledgments
The authors would like to thank two reviewers, A. Laurec and M. Pierotti, for their constructive comments on an earlier version of this paper. The data used for illustration were kindly provided by the authors of Fonteneau et al. [14]. This research has been supported by the Spanish Ministry of Education and Science under projects: ‘Ingenio Mathematica (i-MATH)’ (Ref. No. CSD2006-00032), and ‘CODA-RSS’ (Ref. MTM2009-13272), from the Spanish Ministry of Economy and Competitiveness under the project ‘METRICS’ (Ref. MTM2012-33236); and from the Agència de Gestió d’Ajuts Universitaris i de Recerca of the Generalitat de Catalunya under the project Ref. 2009SGR424.
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Pawlowsky-Glahn, V., Monreal-Pawlowsky, T., Egozcue, J.J. (2016). Representation of Species Composition. In: Martín-Fernández, J., Thió-Henestrosa, S. (eds) Compositional Data Analysis. CoDaWork 2015. Springer Proceedings in Mathematics & Statistics, vol 187. Springer, Cham. https://doi.org/10.1007/978-3-319-44811-4_11
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