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

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## Abstract

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.

## Keywords

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

- RHU
Proportional or random habitat use

- PAT
Portion of animal trajectory

- PAHR
Portion of animal home range

- CODA
Compositional data analysis

## Notes

### Acknowledgments

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

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