Skip to main content
SpringerLink
Log in

Representation of Species Composition

  • Conference paper
  • First Online:
Compositional Data Analysis (CoDaWork 2015)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 187))

Included in the following conference series:

  • 1204 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Aitchison, J.: The statistical analysis of compositional data (with discussion). JRSS Ser. B (Stat. Meth.) 44(2), 139–177 (1982)

    Google Scholar 

  2. Aitchison, J.: Principal component analysis of compositional data. Biometrika 70(1), 57–65 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  3. Aitchison, J.: The Statistical Analysis of Compositional Data (Reprinted in 2003 by The Blackburn Press), p. 416. Chapman & Hall Ltd., London (UK) (1986)

    Google Scholar 

  4. Aitchison, J., Greenacre, M.: Biplots for compositional data. JRSS Ser. C (Appl. Stat.) 51(4), 375–392 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Aitchison, J., Shen, S.M.: Logistic-normal distributions. Some properties and uses. Biometrika 67(2), 261–272 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  6. Barceló-Vidal, C., Martín-Fernández, J.A., Pawlowsky-Glahn, V.: Mathematical foundations of compositional data analysis. In: Ross, G. (ed.) Proceedings of IAMG 2001 p. 20. Cancun (Mex) (2001)

    Google Scholar 

  7. Cannings, C., Edwards, A.W.F.: Natural selection and the de Finetti diagram. Ann. Hum. Genet. 31, 421–428 (1968)

    Article  Google Scholar 

  8. Chayes, F.: On correlation between variables of constant sum. J. Geophys. Res. 65(12), 4185–4193 (1960)

    Article  Google Scholar 

  9. Edwards, A.W.F.: Foundations of Mathematical Genetics, 2nd edn, p. 121. Cambridge University Press (2000). ISBN-13: 978-0521775441

    Google Scholar 

  10. Egozcue, J.J., Lovell, D., Pawlowsky-Glahn, V.: Testing compositional association. In: Hron, K., Filzmoser, P., Templ, M. (eds.) Proceedings of CoDaWork 2013, Vorau (AT) (2013). ISBN: 978-3-200-03103-6. 28–36

    Google Scholar 

  11. Egozcue, J.J., Pawlowsky-Glahn, V.: CoDa-dendrogram: a new exploratory tool. In: Mateu-Figueras, G., Barceló-Vidal, C. (eds.) Proceedings of CoDaWork 2005, Girona (E) (2005). ISBN: 84-8458-222-1

    Google Scholar 

  12. Egozcue, J.J., Pawlowsky-Glahn, V. Simplicial geometry for compositional data. In: Compositional Data Analysis in the Geosciences: From Theory to Practice, Special Publications 264, pp. 145–159. Geological Society of London (2006)

    Google Scholar 

  13. Egozcue, J.J., Pawlowsky-Glahn, V., Mateu-Figueras, G., Barceló-Vidal, C.: Isometric logratio transformations for compositional data analysis. Math. Geol. 35(3), 279–300 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Fonteneau, A., Chassot, E., Ortega-Garcia, S., Delgado de Molina, A., Bez, N.: On the use of the de Finetti ternary diagrams to show the species composition of free and FAD associated tuna schools in the Atlantic and Indian Oceans. Trop. Tunas 65(2), 546–555 (2010)

    Google Scholar 

  15. Gabriel, K.R.: The biplot—graphic display of matrices with application to principal component analysis. Biometrika 58(3), 453–467 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  16. Graffelman, J., Camarena, J.: Graphical tests for Hardy-Weinberg equilibrium based on the ternary plot. Hum. Her. 65, 77–84 (2008). doi:10.1159/000108939

    Article  Google Scholar 

  17. Howarth, R.J.: Sources for a history of the ternary diagram. British J. Hist. Sci. 29(3), 337–356 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  18. Lovell, D., Pawlowsky-Glahn, V., Egozcue, J.J.: Have you got things in proportion? A practical strategy for exploring association in high-dimensional compositions. In: Hron, K., Filzmoser, P., Templ, M. (eds.) Proceedings of CoDaWork 2013, Vorau (AT) (2013). ISBN: 978-3-200-03103-6, 100–110

    Google Scholar 

  19. Lovell, D., Pawlowsky-Glahn, V., Egozcue, J.J., Marguerat, S., Bähler, J.: Proportionality: a valid alternative to correlation for relative data. PLoS Comput. Biol. 11(3), e1004075 (2015). doi:10.1371/journal.pcbi.1004075

    Article  Google Scholar 

  20. Martín-Fernández, J.A., Barceló-Vidal, C., Pawlowsky-Glahn, V.: Dealing with zeros and missing values in compositional data sets using nonparametric imputation. Math. Geol. 35(3), 253–278 (2003)

    Article  MATH  Google Scholar 

  21. Martín-Fernández, J.A., Palarea, J., Olea, R.: Dealing with zeros. See Pawlowsky-Glahn and Buccianti 2011, 43–58 (2011)

    Google Scholar 

  22. Mateu-Figueras, G., Pawlowsky-Glahn, V., Egozcue, J.J.: The normal distribution in some constrained sample spaces. SORT 37(1), 29–56 (2013)

    MathSciNet  MATH  Google Scholar 

  23. Mateu-Figueras, G., Pawlowsky-Glahn, V., Egozcue, J.J.: The principle of working on coordinates. See Pawlowsky-Glahn and Buccianti 2011, 31–42 (2011)

    Google Scholar 

  24. Palarea-Albaladejo, J., Martín-Fernández, J.A.: A modified EM alr-algorithm for replacing rounded zeros in compositional data sets. Comp. Geosc. 34(8), 2233–2251 (2008)

    Article  Google Scholar 

  25. Palarea-Albaladejo, J., Martín-Fernández, J.A., Gómez-García, J.A.: Parametric approach for dealing with compositional rounded zeros. Math. Geol. 39(7), 625–645 (2007)

    Article  MATH  Google Scholar 

  26. Pawlowsky-Glahn, V., Buccianti, A.: Visualization and modeling of subpopulations of compositional data: statistical methods illustrated by means of geochemical data from fumarolic fluids. Int. J. Earth Sci. (Geol. Rundschau) 91(2), 357–368 (2002)

    Article  Google Scholar 

  27. Pawlowsky-Glahn, V., Buccianti, A. (eds.): Compositional Data Analysis: Theory and Applications, p. 378. Wiley & Sons (2011)

    Google Scholar 

  28. Pawlowsky-Glahn, V., Egozcue, J.J.: Exploring compositional data with the CoDa-Dendrogram. Austr. J. Stat. 40(1 & 2), 103–113 (2011)

    Google Scholar 

  29. Pawlowsky-Glahn, V., Egozcue, J.J.: Geometric approach to statistical analysis on the simplex. SERRA 15(5), 384–398 (2001)

    MATH  Google Scholar 

  30. Pawlowsky-Glahn, V., Egozcue, J.J., Tolosana-Delgado, R.: Modeling and Analysis of Compositional Data. Wiley & Sons, Chichester UK (2015). 272 pp

    Google Scholar 

  31. Pearson, K.: Mathematical contributions to the theory of evolution. On a form of spurious correlation which may arise when indices are used in the measurement of organs. Proc. R. Soc. Lond. LX, 489–502 (1897)

    Google Scholar 

  32. Thió-Henestrosa, S., Daunis-i-Estadella, J., Barceló-Vidal, C.: Exploratory compositional data analysis using CoDaPack 3D. See Pawlowsky-Glahn and Buccianti 2011, 329–340 (2011)

    Google Scholar 

  33. Thió-Henestrosa, S., Egozcue, J.J., Pawlowsky-Glahn, V., Kovács, L.Ó., Kovács, G.: Balance-dendrogram. A new routine of CoDaPack. Comp. Geosc. 34(12), 1682–1696 (2008)

    Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Department of Computer Science, Applied Mathematics, and Statistics, University of Girona, Girona, Spain

    V. Pawlowsky-Glahn

  2. IZVG, Keighley, UK

    T. Monreal-Pawlowsky

  3. Department of Civil and Environmental Engineering, Technical University of Catalonia, Barcelona, Spain

    J. J. Egozcue

Authors
  1. V. Pawlowsky-Glahn
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Monreal-Pawlowsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. J. Egozcue
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Pawlowsky-Glahn .

Editor information

Editors and Affiliations

  1. Department of Computer Science and Applied Mathematics, University of Girona, Girona, Spain

    Josep Antoni Martín-Fernández

  2. Department of Computer Science and Applied Mathematics, University of Girona, Girona, Spain

    Santiago Thió-Henestrosa

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

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

Download citation

Publish with us

Policies and ethics

Search

Navigation