Multivariate Bioclimatic Indices Modelling: A Coregionalised Approach

  • Xavier BarberEmail author
  • David Conesa
  • Antonio López-Quílez
  • Javier Morales


A methodological approach for modelling the spatial multivariate distribution of multiple bioclimatic indices is presented. The value of the indices is modelled by means of a Bayesian conditional coregionalised linear model. Elicitation of prior distributions and approximation of posterior distributions of the parameters in the proposed model are also discussed. A posterior predictive distribution and a spatial bioclimatic probability distribution for each bioclimatic index are obtained. This allows researchers to obtain the probability of each location belonging to different bioclimates. The presented methodology is applied in a practical setting showing that the spatial bioclimatic probability distributions are more realistic than the ones obtained in the univariate setting, while providing an interesting tool in the context of climate change.


Bioclimatology Coregionalised models Multivariate Bayesian spatial models Spatial prediction Spatial bioclimatic probability distribution 



This work was partially supported by research Grants MTM2016-77501-P and TEC2016-81900-REDT from the Spanish Ministry of Economy and Competiveness. We thank Dr. J.J. López-Espín, Miguel Hernández University-Center for Operations Research, for assistance with parallel computing code.


  1. Abramowitz, M., Stegun, I.: Handbook of mathematical functions: with formulas, graphs, and mathematical tables. National Bureau of Standards (1964)Google Scholar
  2. Angetter, L., Loetters, D., Roedder, D.: Climate niche shift in invasive species: the case of the brown anole. Biological Journal of the Linnean Society 104(4), 943–954 (2011)Google Scholar
  3. Banerjee, S., Carlin, B., Gelfand, A.: Hierarchical Modeling and Analysis for Spatial Data, Second Edition. Chapman and Hall/CRC, Boca Raton (2014)zbMATHGoogle Scholar
  4. Barber, A., Tun, J., Crespo, M.: A new approach on the bioclimatology and potential vegetation of the Yucatan peninsula (Mexico). Phytocoenologia 31(1), 1–31 (2001)Google Scholar
  5. Barber, X., Conesa, D., López-Quílez, A., Mayoral, A., Morales, J., Barber, A.: Bayesian hierarchical models for analysing the spatial distribution of bioclimatic indices. SORT-Statistics and Operations Research Transactions 1(2), 277–296 (2017)MathSciNetzbMATHGoogle Scholar
  6. Burrough, P.: GIS and geostatistics: Essential partners for spatial analysis. Environmental and Ecological Statistics 8(4), 361–377 (2001)MathSciNetGoogle Scholar
  7. Buttafuoco, G., Castrignano, A., Busoni, E., Dimase, A.: Studying the spatial structure evolution of soil water content using multivariate geostatistics. Journal of Hydrology 311(1), 202–218 (2005)Google Scholar
  8. Camps, J., Ramos, M.: Grape harvest and yield responses to inter-annual changes in temperature and precipitation in an area of north-east Spain with a Mediterranean climate. International Journal of Biometeorology 56(5), 853–864 (2012)Google Scholar
  9. Canu, S., Rosati, L., Fiori, M., Motroni, A., Filigheddu, R., Farris, E.: Bioclimate map of sardinia (italy). Journal of Maps 11(5), 711–718 (2015)Google Scholar
  10. Catorci, A., Foglia, M., Tardella, F., Vitanzi, A., Sparvoliand, D., Gatti, R., Galli, P., Paradisi, L.: Map of changes in landscape naturalness in the Fiastra and Salino catchment basins (central Italy). Journal of Maps 8(1), 97–106 (2012)Google Scholar
  11. Chambers, R., Dunstan, R.: Estimating distribution functions from survey data. Biometrika 73(3), 597–604 (1986)MathSciNetzbMATHGoogle Scholar
  12. Chiles, J., Delfiner, P.: Geoestatistics: Modeling Spatial Uncertainty. Wiley, New York (1999)zbMATHGoogle Scholar
  13. Conley, A.K., Fuller, D.O., Haddad, N., Hassan, A.N., Gad, A.M., Beier, J.C.: Modeling the distribution of the west nile and rift valley fever vector culex pipiens in arid and semi-arid regions of the middle east and north africa. Parasites & Vectors 7(1), 289 (2014). Google Scholar
  14. Cressie, N., Zammit-Mangion, A.: Multivariate spatial covariance models: a conditional approach. Biometrika 103(4), 915–935 (2016)MathSciNetGoogle Scholar
  15. del Arco, M., Perez-de Paz, P.L., Acebes, J.R., Gonzalez-Mancebo, J.M., Reyes-Betancort, J.A., Bermejo, J.A., de Armas, S., Gonzalez-Gonzalez, R.: Bioclimatology and climatophilous vegetation of Tenerife (Canary Islands). Annales Botanici Fennici 43(3), 167–192 (2006)Google Scholar
  16. Finley, A., Banerjee, S., Gelfand, A.: spBayes for Large Univariate and Multivariate Point-Referenced Spatio-Temporal Data Models. Journal of Statistical Software 63(13), 1–28 (2015)Google Scholar
  17. Gamerman, D., Lopes, H.: Markov chain Monte Carlo: stochastic simulation for Bayesian inference. CRC Press, Boca Raton (2006)zbMATHGoogle Scholar
  18. Garzón-Machado, V., Otto, R., del Arco Aguilar, M.J.: Bioclimatic and vegetation mapping of a topographically complex oceanic island applying different interpolation techniques. International Journal of Biometeorology 58(5), 887–899 (2014)Google Scholar
  19. Gelfand, A.: Hierarchical modeling for spatial data problems. Spatial statistics 1, 30–39 (2012)Google Scholar
  20. Gelfand, A., Diggle, P., Guttorp, P., Fuentes, Handbook of spatial statistics. CRC press (2010)zbMATHGoogle Scholar
  21. Gelman, A., Jakulin, A., Pittau, M.G., Su, Y.-S.: A weakly informative default prior distribution for logistic and other regression models. The Annals of Applied Statistics 2(4), 1360–1383 (2008)MathSciNetzbMATHGoogle Scholar
  22. Genton, M.G., Kleiber, W.: Cross-covariance functions for multivariate geostatistics. Statistical Science 30(2), 147–163 (2015)MathSciNetzbMATHGoogle Scholar
  23. Goovaerts, P.: Geostatistical approaches for incorporating elevation into the spatial interpolation of rainfall. Journal of Hydrology 228(1-2), 113–129 (2000)Google Scholar
  24. Grzebyk, M., Wackernagel, H.: Multivariate analysis and spatial/temporal scales: real and complex models. In: XVIIth International Biometrics Conference, pp. 19–33. International Biometrics Society, Ontario (1994)Google Scholar
  25. Handcock, M., Wallis, J.: An approach to statistical spatial-temporal modeling of meteorological fields. Journal of the American Statistical Association 89, 368–390 (1994)MathSciNetzbMATHGoogle Scholar
  26. Lin, Y.: Multivariate geostatistical methods to identify and map spatial variations of soil heavy metals. Environmental Geology 42(1), 1–10 (2002)Google Scholar
  27. Lunn, D., Thomas, A., Best, N., Spiegelhalter, D.: WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility. Statistics and Computing 10(4), 325–337 (2000)Google Scholar
  28. Matérn, B.: Spatial Variation, Second Edition. Springer-Verlang, Berlin (1986)zbMATHGoogle Scholar
  29. Monteiro-Henriques, T., Espírito-Santo, M.D.: Climate change and the outdoor regional living plant collections: an example from mainland Portugal. Biodiversity and Conservation 20(2), 335–343 (2011). Google Scholar
  30. Peng, C.: From static biogeographical model to dynamic global vegetation model: a global perspective on modelling vegetation dynamics. Ecological Modelling 135(1), 33–54 (2000)Google Scholar
  31. Rivas-Martínez, S.: Bioclimatic classification system of the Earth. Folia Botanica Matritensis 12, 1–23 (1994)Google Scholar
  32. Rivas-Martínez, S., Rivas-Saenz, S.: Worldwide Bioclimatic Classification System. Phytosociological Research Center, Spain (2017)Google Scholar
  33. Robertson, G.: Geostatistics in ecology: interpolating with known variance. Ecology 68(3), 744–748 (1987)Google Scholar
  34. Rossi, R., Mulla, D., Journel, A., Franz, E.: Geostatistical tools for modeling and interpreting ecological spatial dependence. Ecological Monographs 62(2), 277–314 (1992)Google Scholar
  35. Schmidt, A.M., Gelfand, A.E.: A Bayesian coregionalization approach for multivariate pollutant data. Journal of Geophysical Research: Atmospheres 108(D24) (2003)Google Scholar
  36. Spiegelhalter, D.J., Best, N.G., Carlin, B.P., Van Der Linde, A.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 64(4), 583–639 (2002)MathSciNetzbMATHGoogle Scholar
  37. Stein, M.: Interpolation of spatial statistics data: some theory for kriging. Springer-Verlang, New York (1999)zbMATHGoogle Scholar
  38. Strupczewski, W., Kochanek, K., Weglarczyk, S., Singh, V.: On robustness of large quantile estimates to largest elements of the observation series. Hydrological Processes 21(10), 1328–1344 (2007)zbMATHGoogle Scholar
  39. Verfaillie, E., Van Lancker, V., Van Meirvenne, M.: Multivariate geostatistics for the predictive modelling of the surficial sand distribution in shelf seas. Continental Shelf Research 26(19), 2454–2468 (2006)Google Scholar
  40. Wackernagel, H.: Multivariate Geostatistics: an introduction with applications, 3rd edition. Springer, New York (2003)zbMATHGoogle Scholar
  41. Yan, J., Cowles, M., Wang, S., Armstrong, M.: Parallelizing MCMC for Bayesian spatiotemporal geostatistical models. Statistics and Computing 17(4), 323–335 (2007)MathSciNetGoogle Scholar

Copyright information

© International Biometric Society 2019

Authors and Affiliations

  1. 1.Centro de Investigación OperativaUniversidad Miguel Hernández de ElcheElcheSpain
  2. 2.Dpt. Estadística i Investigació OperativaUniversitat de ValènciaValenciaSpain

Personalised recommendations