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Assessing environmental suitability for species based on Tukey's depth*

Assessing environmental suitability for species based on Tukey's depth*. Maria João Martins 1 with : J.O.Cerdeira 1,2 , T. Monteiro- Henriques 1 , P.C . Silva 1 , D. Alagador 3 , A. Franco 4 , M. Campagnolo 1 , P. Arsénio 1 , F. Aguiar 1 , M. Cabeza 5

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Assessing environmental suitability for species based on Tukey's depth*

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  1. Assessing environmental suitability for species based on Tukey's depth* Maria João Martins1with: J.O.Cerdeira1,2, T. Monteiro-Henriques1, P.C. Silva1, D. Alagador3, A. Franco4, M. Campagnolo1, P. Arsénio1, F. Aguiar1, M. Cabeza5 1CEF, Instituto Superior de Agronomia, UniversidadeTécnica de Lisboa, Portugal 2Dept of Math., Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Portugal 3RuiNabeiroBiodiversityChair, Universidade de Évora, Portugal 4School of Environment Sciences, University of East Anglia, UK 5Dept of Biosciences, University of Helsinki, Finland * under the projectS-PerforMA : A Species Performance Modeling Algorithm (PTDC/AAC-AMB/113394/2009)

  2. (1957) Formally quantifies the niche concept in terms of geometric space v2 two independent environmental variables d a, b, c, d define the limiting values permitting a species to survive and reproduce c v1 a b possible environmental state permitting the species to exist indefinitely 2 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

  3. (1957) Formally quantifies the niche concept in terms of geometric space v2 independence fails d rectangle → polygon c v1 a b possible environmental state permitting the species to exist indefinitely 3 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

  4. (1957) Introduce v3, v4, ..., vn until all the ecological factors relative to the species have been considered n-dimensional hypervolume: every point corresponds to a state of the environment which would permit the species to exist indefinitely Fundamental niche of the species 4 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

  5. (1957) 5 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

  6. Theoretical Question: How to differentiate the niche according to the probability of persistence of the species (or environmental suitability)? Data: occurrences of the species and environmental variables in occurrence points Practical Question: How to estimate the niche, distinguishing between areas of different suitability? Independence For each variable individually consider percentiles BIOCLIM (Nix 1986; Busby 1991) (with percentiles) 6 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

  7. Independence BIOCLIM (with percentiles) as implemented in package dismo x is a quantile of order 1/10 (or 9/10) of (x1,...,x10) (x,y) or y is a quantile of order 1/10 (or 9/10) of (y1,...,y10) 7 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

  8. Independence BIOCLIM (with percentiles) as implemented in package dismo 0 0.2 0.6 0.4 0.8 median 1 8 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

  9. How to dealwithdependence(of the ecological variables on their effect over species)? Propose: to use a generalization of quantile in multi-dimensional space Tukey depth (Tukey 1975) If P is a set of k points of ℝn, the Tukey depth of q with respect to P, is dq(P)=m/k, where m is the minimum number of points needed to remove from P so that q is not in the convex-hull of the remaining points of P. The Tukey depth is implemented in package depth 9 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

  10. Tukey depth If P is a set of k points of ℝn, the Tukey depth of q with respect to P, is dq(P)=m/k, where m is the minimum number of points needed to remove from P so that q is not in the convex-hull of the remaining points of P. n=2, k=10 P={∙} q dq(P)=1/10 Tukey depth discriminates the convex hull into nested regions of increasing depth for the interior 10 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

  11. BIOCLIMvsTukey depth If P is a set of k points of ℝn, the depth of q with respect to P is m/k, where m is the minimum number of points needed to remove from P so that q is not in the hyper rectangle is not in the convex hull of the remaining points of P. 11 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

  12. BIOCLIMvsTukey depth Computational complexity k points of ℝn, the depth of q with respect to P needs a search in 2 directions if n=2 k directions if n=2 3 directions if n=3 k(k-1) directions if n=3 n directions kCn-1 directions 12 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

  13. Application: main Quercus species of the Iberian Peninsula Data:Occurrences from the ProyectoAnthos (Anthos 2011) and from the Herbarium “João de Carvalho e Vasconcellos” (Lisbon, LISI) Four environmental variables from Worldclim website (Hijmanset al. 2006) – isothermality, the minimum temperature of coldest month, annual precipitation and the precipitation of driest quarter. Methods: For each site within the Iberian Peninsula (ca. 1 km x 1 km resolution) - the binary environmental suitability (suitable vs. unsuitable) was obtained through the BIOCLIM and the Convex Hull. - the environmental suitability was obtained by the Tukey depth Results: Geographical maps of the environmental suitability 13 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

  14. Application: main Quercus species of the Iberian Peninsula binary environmental suitability BIOCLIM Convex Hull 14 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

  15. Application: main Quercus species of the Iberian Peninsula binary environmental suitability BIOCLIM Convex Hull 15 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

  16. Application: main Quercus species of the Iberian Peninsula binary environmental suitability BIOCLIM Convex Hull 16 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

  17. Application: main Quercus species of the Iberian Peninsula environmental suitability by Tukey depth 17 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

  18. Application: main Quercus species of the Iberian Peninsula environmental suitability by Tukey depth 18 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

  19. Using Tukey depth to assess the separability of a partition In a recent paper we propose to assess the separability of clusters based on a general notion of interiority. The separability index (oDSI) lies between zero and one. Taking the Tukey depth as the interiority criterion: oDSI = 1 when every point is outside the convex hulls of all other clusters of the partition oDSI = 0 when every point is in the convex hull of some other cluster of the partition for two sets with the same cardinality and the same statistical distribution, oDSI ≈ 0.5 19 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

  20. Using Tukey depth to assess the separability of a partition oDSI=0.93 oDSI=0.07 20 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

  21. Main advantages of Tukey depth methodology easy geometric interpretation straightforward relationship with Hutchinson's niche theory results invariant to the scale of ecological variable (do not depend on the units of measurement of the variables) robustness to outliers (for deeper points) THANK YOU FOR YOUR ATTENTION 21 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

  22. References • Busby, J.R. (1991). BIOCLIM - A Bioclimate Analysis and Prediction System. In: Nature Conservation: Cost Effective Biological Surveys and Data Analysis, eds. C.R. Margules & M.P. Austin, 64–68. CSIRO. • CerdeiraJ.O., Martins M.J. and Silva P.C. (2012). A combinatorial approach to assess the separability of clusters, Journal of Classification, 29: 7-22. • Hutchinson, G.E. (1957). Concluding remarks. • Cold Spring Harbor Symposia on Quantitative Biology22: 415–427. • Nix, H.A. (1986). A biogeographic analysis of Australian elapid snakes. In: Atlas • of elapid snakes of Australia, ed. R. Longmore, 4–15. Canberra: Australian Government • Publishing Service. • Tukey, J. (1975). Mathematics and the picturing of data. Proc. 1975 Inter. Cong. Math., Vancouver, 523-531. 22 Assessing environmental suitability for species based on Tukey's depth. IAVS 2013, Tartu, Estonia

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