# Modeling Habitat Suitability for Complex Species Distributions by Environmental-Distance Geometric Mean

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## Abstract

This paper presents a new habitat suitability modeling method whose main properties are as follows: (1) It is based on the density of observation points in the environmental space, which enables it to fit complex distributions (e.g. nongaussian, bimodal, asymmetrical, etc.). (2) This density is modeled by computing the geometric mean to all observation points, which we show to be a good trade-off between goodness of fit and prediction power. (3) It does not need any absence information, which is generally difficult to collect and of dubious reliability. (4) The environmental space is represented either by an expert-selection of standardized variables or the axes of a factor analysis [in this paper we used the Ecological Niche Factor Analysis (ENFA)].We first explain the details of the geometric mean algorithm and then we apply it to the bearded vulture (*Gypaetus barbatus*) habitat in the Swiss Alps. The results are compared to those obtained by the “median algorithm” and tested by jack-knife cross-validation. We also discuss other related algorithms (BIOCLIM, HABITAT, and DOMAIN). All these analyses were implemented into and performed with the ecology-oriented GIS software BIOMAPPER 2.0.The results show the geometric mean to perform better than the median algorithm, as it produces a tighter fit to the bimodal distribution of the bearded vulture in the environmental space. However, the “median algorithm” being quicker, it could be preferred when modeling more usual distribution.

## Keywords

Bearded vulture*Gypaetus barbatus*Ecological niche factor analysis Ecological envelopes Environmental space Habitat suitability model Jack-knife cross-validation Median algorithm

## Notes

### Acknowledgements

We thank the Réseau Gypaète Suisse occidentale (Bertrand Posse), the Service de la chasse, de la pêche et de la faune du canton du Valais (Yvon Crettenand), the Swiss Ornithological Institute (Hans Schmid), and the Foundation Pro Bartgeier (Anne-Marie and Chasper Buchli) which gave us free access to the bearded vulture databases. Special thanks go to Christian Glenz and P. A Oggier. We are also grateful to Nicolas Perrin, Antoine Guisan, and William Hargrove for their interesting insights during the conception of these algorithms, and to Anthony Lehmann, Virginia H. Dale, and two anonymous reviewers for their keen comments about our manuscript.

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