Environmental and Ecological Statistics

, Volume 21, Issue 2, pp 161–187 | Cite as

A permutation-based combination of sign tests for assessing habitat selection

  • Lorenzo Fattorini
  • Caterina Pisani
  • Francesco Riga
  • Marco Zaccaroni


The analysis of habitat selection in radio-tagged animals is approached by comparing the portions of use against the portions of availability observed for each habitat type. Since data are linearly dependent with singular variance-covariance matrices, standard multivariate statistical tests cannot be applied. To bypass the problem, compositional data analysis is customarily performed via log-ratio transform of sample observations. The procedure is criticized in this paper, emphasizing the several drawbacks which may arise from the use of compositional analysis. An alternative nonparametric solution is proposed in the framework of multiple testing. The habitat use is assessed separately for each habitat type by means of the sign test performed on the original observations. The resulting p values are combined in an overall test statistic whose significance is determined permuting sample observations. The theoretical findings of the paper are checked by simulation studies. Applications to case studies previously considered in literature are discussed.


Compositional data analysis Johnson’s second order selection Johnson’s third order selection Monte Carlo studies Multiple testing  Random habitat use 



Proportional or random habitat use


Portion of animal trajectory


Portion of animal home range


Compositional data analysis



The authors thank Luca Pratelli for his helpful suggestions in the theoretical aspects of the work.


  1. Aebischer NJ, Robertson PA, Kenward RE (1993) Compositional analysis of habitat use from animal radio-tracking data. Ecology 74:1315–1325CrossRefGoogle Scholar
  2. Aitchison J (1986) The statistical analysis of compositional data. Chapman and Hall, LondonCrossRefGoogle Scholar
  3. Aitchison J (1994) Principles of compositional data analysis. In: Anderson TW, Fang KT, Olkin J (eds) Multivariate analysis and its applications. Institute of Mathematical Statistics, Hayward, pp 73–81CrossRefGoogle Scholar
  4. Calenge C (2006) The package “adehabitat” for the R software: A tool for the analysis of space and habitat use by animal. Ecol Model 197:516–519CrossRefGoogle Scholar
  5. Fang KT, Kotz S, Ng KW (1990) Symmetric multivariate distributions. Chapman and Hall, LondonCrossRefGoogle Scholar
  6. Johnson DH (1980) The comparison of usage and availability measurements for evaluating resource preference. Ecology 61:65–71CrossRefGoogle Scholar
  7. Johnson NL, Kotz S, Balakrishnan N (1995) Continuous univariate distributions, vol 2. Wiley, New YorkGoogle Scholar
  8. Johnson DS, Thomas DL, Ver Hoef TJ, Christ A (2008) A general framework for the analysis of animal resource selection from telemetry data. Biometrics 64:968–976PubMedCrossRefGoogle Scholar
  9. Kneib T, Knauer F, Küchenhoff H (2011) A general approach to the analysis of habitat selection. Environ Ecol Stat 18:1–25CrossRefGoogle Scholar
  10. Kooper N, Manseau M (2009) Generalized estimating equations and generalized linear mixed-effects models for modelling resource selection. J Appl Ecol 46:590–599CrossRefGoogle Scholar
  11. Manly BFJ, McDonald LL, Thomas DL, McDonald TL, Erickson WP (2002) Resource selection by animals. Kluwer, DordrechtGoogle Scholar
  12. Pesarin F (1992) A resampling procedure for nonparametric combination of several dependent tests. J Italian Stat Soc 1:87–101CrossRefGoogle Scholar
  13. Pesarin F (2001) Multivariate permutation tests: with applications in biostatistics. Wiley, New YorkGoogle Scholar
  14. Randles RH, Wolfe DA (1979) Introduction to the theory of nonparametric statistics. Wiley, New YorkGoogle Scholar
  15. Strickland MD, McDonald LL (2006) Introduction to the special section on resource selection. J Wildl Manag 70:321–323CrossRefGoogle Scholar
  16. Westfall PH, Young SS (1993) Resampling-based multiple testing. Wiley, New YorkGoogle Scholar
  17. Worton BJ (1989) Kernel methods for estimating the utilization distribution in home-range studies. Ecology 70:164–168CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Lorenzo Fattorini
    • 1
  • Caterina Pisani
    • 1
  • Francesco Riga
    • 2
  • Marco Zaccaroni
    • 3
  1. 1.Department of Economics and StatisticsUniversity of SienaSienaItaly
  2. 2.Italian Institute for Environmental Protection and Research (ISPRA)Ozzano EmiliaItaly
  3. 3.Department of BiologyUniversity of FlorenceFlorenceItaly

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