Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-25T07:39:26.931Z Has data issue: false hasContentIssue false
  • English
  • Français

Statistical models for spatially explicit biological data

Published online by Cambridge University Press:  19 October 2012

DAVID J. ROGERS  and
LUIGI SEDDA
DAVID J. ROGERS*
Affiliation:
University of Oxford, Department of Zoology, South Parks Rd., Oxford OX1 3PS, UK
LUIGI SEDDA
Affiliation:
University of Oxford, Department of Zoology, South Parks Rd., Oxford OX1 3PS, UK
*
*Corresponding author: David J RogersUniversity of Oxford, Department of Zoology South Parks Rd., Oxford OX1 3PS Tel.: 01865 271240 Fax: 01865 310447 Email: david.rogers@zoo.ox.ac.uk
Get access Rights & Permissions [Opens in a new window]

Summary

Existing algorithms for predicting species' distributions sit on a continuum between purely statistical and purely biological approaches. Most of the existing algorithms are aspatial because they do not consider the spatial context, the occurrence of the species or conditions conducive to the species' existence, in neighbouring areas. The geostatistical techniques of kriging and cokriging are presented in an attempt to encourage biologists more frequently to consider them. Unlike deterministic spatial techniques they provide estimates of prediction errors. The assumptions and applications of common geostatistical techniques are presented with worked examples drawn from a dataset of the bluetongue outbreak in northwest Europe in 2006. Emphasis is placed on the importance and interpretation of weights in geostatistical calculations. Covarying environmental data may be used to improve predictions of species’ distributions, but only if their sampling frequency is greater than that of the species’ or disease data. Cokriging techniques are unable to determine the biological significance or importance of such environmental data, because they are not designed to do so.

Keywords

Species' distribution modelskrigingcokrigingvariogramsbluetongue
Type
Research Article
Information
Parasitology , Volume 139 , Issue 14: Dynamics of parasite distributions: modern analytical approaches , December 2012 , pp. 1852 - 1869
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Allouche, O., Tsoar, A. and Kadmon, R. (2006). Assessing the accuracy of species distribution models: prevalence, kappa and the true skill statistic (TSS). Journal of Applied Ecology 43, 1223–1232. doi: 10.1111/j.1365-2664.2006.01214.x.CrossRefGoogle Scholar
Atkinson, P. M., Webster, R. and Curran, P. J. (1994). Cokriging with Airborne MSS Imagery. Remote Sensing of Environment 50, 335–345. doi: 10.1016/0034-4257(94)90083-3.CrossRefGoogle Scholar
Austin, M. (2007). Species distribution models and ecological theory: A critical assessment and some possible new approaches. Ecological Modelling 200, 1–19. doi: 10.1016/j.ecolmodel.2006.07.005.CrossRefGoogle Scholar
Austin, M. P. and Van Niel, K. P. (2011). Improving species distribution models for climate change studies: variable selection and scale. Journal of Biogeography 38, 1–8. doi: 10.1111/j.1365-2699.2010.02416.x.CrossRefGoogle Scholar
Bachmaier, M. and Backes, M. (2011). Variogram or semivariogram? Variance or semivariance? Allan variance or introducing a new term? Mathematical Geology 43, 735–740. doi: 10.1007/s11004-011-9348-3.Google Scholar
Bellier, E., Monestiez, P., Durbec, J. P. and Candau, J. N. (2007). Identifying spatial relationships at multiple scales: principal coordinates of neighbour matrices (PCNM) and geostatistical approaches. Ecography 30, 385–399. doi: 10.1111/j.2007.0906-7590.04911.x.CrossRefGoogle Scholar
Ben-Ahmed, K., Bouratbine, A. and El-Aroui, M. A. (2010). Generalized linear spatial models in epidemiology: A case study of zoonotic cutaneous leishmaniasis in Tunisia. Journal of Applied Statistics 37, 159–170. doi: 10.1080/02664760802684169.CrossRefGoogle Scholar
Berke, O. (2004). Exploratory disease mapping: kriging the spatial risk function from regional count data. International Journal of Health Geographics 3:18, 1–11. doi: 10.1016/j.prevetmed.2005.07.003.Google Scholar
Breiman, L. (1984). Classification and Regression Trees. Wadsworth International Group, Belmont, Calif.Google Scholar
Breiman, L. (2001). Random forests. Machine Learning 45, 5–32. doi: 10.1023/A:1010933404324.CrossRefGoogle Scholar
Carrat, F. and Valleron, A. J. (1992). Epidemiologic mapping using the “kriging” method: application to an influenza-like illness in France. American Journal of Epidemiology 135, 1293–1300.CrossRefGoogle Scholar
Chiogna, M. and Gaetan, C. (2010). An interchangeable approach for modelling spatio-temporal count data. Environmetrics 21, 844–862. doi: 10.1002/Env.1078.CrossRefGoogle Scholar
Christakos, G. (2000). Modern Spatiotemporal Geostatistics. 1st Edn.Oxford University Press, Oxford.Google Scholar
Christensen, R. (2001). Advanced Linear Modeling : Multivariate, Time Series, and Spatial Data; Nonparametric Regression and Response Surface Maximization, 2nd edn. Springer, New York.CrossRefGoogle Scholar
Congalton, R. G. (1991). A review assessing the accuracy of classification of remotely sensed data. Remote Sensing and Environment 37, 35–46. doi: 10.1016/0034-4257(91)90048-B.CrossRefGoogle Scholar
Crase, B., Liedloff, A. C. and Wintle, B. A. (2012). A new method for dealing with residual spatial autocorrelation in species distribution models. Ecography 35, 1–10. doi: 10.1111/j.1600-0587.2011.07138.xCrossRefGoogle Scholar
De Iaco, S., Maggio, S., Palma, M. and Posa, D. (2012). Towards an automatic procedure for modeling multivariate space-time data. Computers & Geosciences 41, 1–11. doi: 10.1016/j.cageo.2011.08.008.CrossRefGoogle Scholar
de Koeijer, A. A., Boender, G. J., Nodelijk, G., Staubach, C., Meroc, E. and Elbers, A. R. W. (2011). Quantitative analysis of transmission parameters for bluetongue virus serotype 8 in Western Europe in 2006. Veterinary Research 42. doi 10.1186/1297-9716-42-53.CrossRefGoogle ScholarPubMed
Deutsch, C. V. and Journel, A. G. (1998). GSLIB Geostatistical Software Library and User's Guide, 2nd edn. Oxford University Press, New York.Google Scholar
Diggle, P. J. (2003). Statistical Analysis of Spatial Point Patterns, 2nd edn. Arnold, London.Google Scholar
Diggle, P. J., Tawn, J. A. and Moyeed, R. A. (1998). Model-based geostatistics. Journal of the Royal Statistical Society Series C-Applied Statistics 47, 299–326. doi: 10.1111/1467-9876.00113.CrossRefGoogle Scholar
Dormann, C. F., McPherson, J. M., Araujo, M. B., Bivand, R., Bolliger, J., Carl, G., Davies, R. G., Hirzel, A., Jetz, W., Kissling, W. D., Kuhn, I., Ohlemuller, R., Peres-Neto, P. R., Reineking, B., Schroder, B., Schurr, F. M. and Wilson, R. (2007). Methods to account for spatial autocorrelation in the analysis of species distributional data: a review. Ecography 30, 609–628. doi: 10.1111/j.2007.0906-7590.05171.x.CrossRefGoogle Scholar
Dunn, M. R. (1983). A simple sufficient condition for a variogram model to yield positive variances under restrictions. Journal of the International Association for Mathematical Geology 15, 553–564. doi: 10.1007/BF01031177.CrossRefGoogle Scholar
Ecker, M. D. and Gelfand, A. E. (1997). Bayesian variogram modelling for an isotropic spatial process. Journal of Agricultural, Biological, and Environmental Statistics 2, 347–369.CrossRefGoogle Scholar
Elith, J., Graham, C. H., Anderson, R. P., Dudik, M., Ferrier, S., Guisan, A., Hijmans, R. J., Huettmann, F., Leathwick, J. R., Lehmann, A., Li, J., Lohmann, L. G., Loiselle, B. A., Manion, G., Moritz, C., Nakamura, M., Nakazawa, Y., Overton, J. M., Townsend Peterson, A., Phillips, S. J., Richardson, K., Scachetti-Pereira, R., Schapire, R. E., Soberon, J., Williams, S., Wisz, M. S. and Zimmermann, E. (2006). Novel methods improve predictions of species' distributions from occurrence data. Ecography 29, 129–151. doi: 10.1111/j.2006.0906-7590.04596.xCrossRefGoogle Scholar
Elith, J., Kearney, M. and Phillips, S. (2010). The art of modelling range-shifting species. Methods in Ecology and Evolution 1, 330–342. doi: 10.1111/j.2041-210X.2010.00036.x.CrossRefGoogle Scholar
Elith, J., Leathwick, J. R. and Hastie, T. (2008). A working guide to boosted regression trees. Journal of Animal Ecology 77, 802–813. doi: 10.1111/j.1365-2656.2008.01390.x.CrossRefGoogle ScholarPubMed
Fortin, M.-J. and Dale, M. R. T. (2005). Spatial Analysis : A Guide for Ecologists, Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Franklin, J. and Miller, J. A. (2009). Mapping Species Distributions : Spatial Inference and Prediction, Cambridge University Press, Cambridge.Google Scholar
Furrer, R., Nychka, D. and Sain, S. (2012). fields: Tools for spatial data. R package version 6.01, URL http://CRAN.R-project.org/package=fields.Google Scholar
Gaetan, C. and Guyon, X. (2010). Spatial Statistics and Modeling. Springer, New York, London.CrossRefGoogle Scholar
Gerbier, G., Baldet, T., Tran, A., Hendrickx, G., Guis, H., Mintiens, K., Elbers, A. R. W. and Staubach, C. (2008). Modelling local dispersal of bluetongue virus serotype 8 using random walk. Preventive Veterinary Medicine 87, 119–130. doi: 10.1016/j.prevetmed.2008.06.012.CrossRefGoogle ScholarPubMed
Goovaerts, P. (1997). Geostatistics for Natural Resources Evaluation. Oxford University Press, New York.CrossRefGoogle Scholar
Goovaerts, P. and Kerry, R. (2010). Using ancillary data to improve prediction of soil and crop attributes in precision agriculture. In Geostatistical Applications for Precision Agriculture (ed. Oliver, M. A.), pp. 167–194. Springer Science + Business Media B.V., Dordrecht.CrossRefGoogle Scholar
Graham, M. H. (2003). Confronting multicollinearity in ecological multiple regression. Ecology 84, 2809–2815.CrossRefGoogle Scholar
Guisan, A., Edwards, T. C. and Hastie, T. (2002). Generalized linear and generalized additive models in studies of species distributions: setting the scene. Ecological Modelling 157, 89–100. doi: 10.1016/S0304-3800(02)00204-1.CrossRefGoogle Scholar
Guisan, A. and Thuiller, W. (2005). Predicting species distribution: offering more than simple habitat models. Ecology Letters 8, 993–1009. doi: 10.1111/j.1461-0248.2005.00792.x.CrossRefGoogle ScholarPubMed
Hampton, K. H., Serre, M. L., Gesink, D. C., Pilcher, C. D. and Miller, W. C. (2011). Adjusting for sampling variability in sparse data: geostatistical approaches to disease mapping. International Journal of Health Geographics 10:54. doi 10.1186/1476-072x-10-54.Google Scholar
Hastie, T. and Tibshirani, R. (1986). Generalized additive models. Statistical Science 1, 297–318.Google Scholar
Hendrickx, G., Gilbert, M., Staubach, C., Elbers, A., Mintiens, K., Gerbier, G. and Ducheyne, E. (2008). A wind density model to quantify the airborne spread of Culicoides species during North-Western Europe bluetongue epidemic, 2006. Preventive Veterinary Medicine 87, 162–181. doi: 10.1016/j.prevetmed.2008.06.009.CrossRefGoogle ScholarPubMed
Hoeting, J. A., Davis, R. A., Merton, A. A. and Thompson, S. E. (2006). Model selection for geostatistical models. Ecological Applications 16, 87–98. doi: 10.1890/04-0576.CrossRefGoogle ScholarPubMed
Isaaks, E. H. and Srivastava, R. M. (1989). An Introduction to Applied Geostatistics. Oxford University Press, Oxford.Google Scholar
Journel, A. G. and Huijbregts, C. J. (1978). Mining Geostatistics. Academic Press, London.Google Scholar
Journel, A. G. and Rossi, M. E. (1989). When do we need a trend model in kriging? Mathematical Geology 21, 715–739. doi: 10.1007/BF00893318.CrossRefGoogle Scholar
Justice, C., Townshend, J., Vermote, E., Sohlberg, R., Descloitres, J., Roy, D., Hall, D., Salomonson, V., Riggs, G., Huete, A., Didan, K., Miura, T., Wan, Z. M., Strahler, A., Schaaf, C., Myneni, R., Running, S., Glassy, J., Nemani, R., El Saleous, N. and Wolfe, R. (2000). Preliminary land surface products from the NASA moderate resolution imaging spectroradiometer (MODIS). IGARSS 2000: IEEE 2000 International Geoscience and Remote Sensing Symposium, Vol I–Vi, Proceedings 1157–1162.Google Scholar
Kelsall, J. and Wakefield, J. (2002). Modeling spatial variation in disease risk: A geostatistical approach. Journal of the American Statistical Association 97, 692–701. doi: 10.1198/016214502388618438.CrossRefGoogle Scholar
Kravchenko, A. N. (2003). Influence of spatial structure on accuracy of interpolation methods. Soil Science Society of America Journal 67, 1564–1571. doi: 10.2136/sssaj2003.1564.CrossRefGoogle Scholar
Krige, D. G. (1951). A statistical approach to some basic mine valuation problems on the Witwatersrand. Journal of the Chemistry, Metallurgical and Mining Society of South Africa 52, 119–139.Google Scholar
Lai, P. C., So, F. M. and Chan, K. W. (2009). Spatial Epidemiological Approaches in Disease Mapping and Analysis, CRC Press, Boca Raton.Google Scholar
Latimer, A. M., Wu, S., Gelfand, A. E. and Silander, J. A. (2006). Building statistical models to analyze species distributions. Ecological Applications 16, 33–50. doi: 10.1890/04-0609.CrossRefGoogle ScholarPubMed
Lennon, J. J. (2000). Red-shift and red herrings in geographical ecology. Ecography 23, 101–113. doi: 10.1111/j.1600-0587.2000.tb00265.x.CrossRefGoogle Scholar
Li, J. and Heap, A. D. (2011). A review of comparative studies of spatial interpolation methods in environmental sciences: Performance and impact factors. Ecological Informatics 6, 228–241. doi: 10.1016/j.ecoinf.2010.12.003.CrossRefGoogle Scholar
Liu, Y. X., Jiang, S. W., Liu, Y. X., Wang, R., Li, X., Yuan, Z. S., Wang, L. X. and Xue, F. Z. (2011). Spatial epidemiology and spatial ecology study of worldwide drug-resistant tuberculosis. International Journal of Health Geographics 10:50. doi: 10.1186/1476-072x-10-50.Google Scholar
Macarthur, R. H. (1972). Geographical Ecology. Harper & Row, New York.Google Scholar
Matheron, G. (1963). Principles of geostatistics. Economic Geology 58, 1246–1266. doi: 10.2113/gsecongeo.58.8.1246CrossRefGoogle Scholar
Matheron, G. (1965). Les variables régionalisées et leur estimation : une application de la théorie des fonctions aléatoires aux sciences de la nature. Masson et Cie, Paris.Google Scholar
Mintiens, K., Meroc, E., Faes, C., Abrahantes, J. C., Hendrickx, G., Staubach, C., Gerbier, G., Elbers, A. R. W., Aerts, M. and De Clercq, K. (2008). Impact of human interventions on the spread of bluetongue virus serotype 8 during the 2006 epidemic in North-Western Europe. Preventive Veterinary Medicine 87, 145–161. doi: 10.1016/j.prevetmed.2008.06.010.CrossRefGoogle ScholarPubMed
Myers, D. E. (1989). To be or not to be…stationary? That is the question. Mathematical Geology 21, 347–362. doi: 10.1007/BF00893695.CrossRefGoogle Scholar
Oliver, M. A. (2010). The variogram and kriging. In Handbook of Applied Spatial Analysis: Software, Tools, Methods and Applications (eds. Fischer, M. M. and Getis, A.), pp. 319–352. Springer, Heidelberg.CrossRefGoogle Scholar
Oliver, M. A., Muir, K. R., Webster, R., Parkes, S. E., Cameron, A. H., Stevens, M. C. G. and Mann, J. R. (1992). A Geostatistical Approach to the Analysis of Pattern in Rare Disease. Journal of Public Health Medicine 14, 280–289.Google Scholar
Pearson, R. G., Dawson, T. P., Berry, P. M. and Harrison, P. A. (2002). SPECIES: A Spatial Evaluation of Climate Impact on the Envelope of Species. Ecological Modelling 154, 289–300. doi: 10.1016/S0304-3800(02)00056-X.CrossRefGoogle Scholar
Pebesma, E. J. (2004). Multivariable geostatistics in S: the gstat package. Computers & Geosciences 30, 683–691. doi: 10.1016/j.cargo.2004.03.012.CrossRefGoogle Scholar
Perez, A. M., Thurmond, M. C. and Carpenter, T. E. (2006). Spatial distribution of foot-and-mouth disease in Pakistan estimated using imperfect data. Preventive Veterinary Medicine 76, 280–289. doi: 0.1016/j.prevetmed.2006.05.013.CrossRefGoogle ScholarPubMed
Porcu, E., Mateu, J., Zini, A. and Pini, R. (2007). Modelling spatio-temporal data: a new variogram and covariance structure proposal. Statistics and Probability Letters 77, 83–89. doi: 10.1016/j.spl.2006.05.013.CrossRefGoogle Scholar
Ribeiro, P. J. J. and Diggle, P. J. (2001). geoR: a package for geostatistical analysis. R News 1, 15–18.Google Scholar
Rogers, D. J. (2000). Satellites, space, time and the African trypanosomiases. In Remote Sensing and Geographic Information Systems in Epidemiology (eds. Hay, S. I., Randolph, S. E. & Rogers, D. J.), pp. 129–171. Academic Press, London.CrossRefGoogle Scholar
Rogers, D. J. (2006). Models for vectors and vector-borne diseases. Advances in Parasitology 62, 1–35. doi: 10.1016/S0065-308X(05)62001-5.CrossRefGoogle ScholarPubMed
Rogers, D. J. and Williams, B. G. (1994). Tsetse distribution in Africa: seeing the wood and the trees. In Large-Scale Ecology and Conservation Biology. British Ecological Society Symposium XXXV (eds. Edwards, P. J., May, R. M. and Webb, N.), pp. 247–271. Blackwell Scientific Publications, Oxford.Google Scholar
Rossi, R. E., Mulla, D. J., Journel, A. G. and Franz, E. H. (1992). Geostatistical tools for modeling and interpreting ecological spatial dependence. Ecological Monographs 62, 277–314. doi: 10.2307/2937096.CrossRefGoogle Scholar
Sedda, L., Brown, H. E., Purse, B. V., Burgin, L., Gloster, J. and Rogers, D. J. (2012). A new algorithm quantifies the roles of wind and midge flight activity in the bluetongue epizootic in northwest Europe. Proceedings of the Royal Society B-Biological Sciences 279, 2354–2362. doi: 10.1098/rspb.2011.2555.CrossRefGoogle ScholarPubMed
Scharlemann, J. P. W., Benz, D., Hay, S. I., Purse, B. V., Tatem, A. J., Wint, G. R. W. and Rogers, D. J. (2008). Global Data for Ecology and Epidemiology: A Novel Algorithm for Temporal Fourier Processing MODIS Data. PLoS ONE 3:1. doi 10·1371/Journal.Pone.0001408.Google Scholar
Schlather, M. (2001). Simulation and analysis of random fields. R News 1, 18–20.Google Scholar
Shapiro, A. and Botha, J. D. (1991). Variogram Fitting with a General-Class of Conditionally Nonnegative Definite Functions. Computational Statistics & Data Analysis 11, 87–96. doi: 10.1016/0167-9473(91)90055-7.CrossRefGoogle Scholar
Souris, M. and Bichaud, L. (2011). Statistical models for bivariate spatial analysis in marked points. Examples in spatial epidemiology. Spatial and Spatio-temporal Epidemiology 2, 227–234. doi: 10.1016/j.sste.2011.06.001.CrossRefGoogle Scholar
Sutherst, R. W. and Maywald, G. F. (1985). A computerised system for matching climates in ecology. Agriculture, Ecosystems and Environment 13, 281–299. doi: 10.1016/0167-8809.CrossRefGoogle Scholar
Tobler, W. R. (1970). A computer movie simulating urban growth in the Detroit region. Economic Geography 46, 232–240.CrossRefGoogle Scholar
Wagner, H. H. and Fortin, M. J. (2005). Spatial analysis of landscapes: Concepts and statistics. Ecology 86, 1975–1987. doi: 10.1890/04-0914.CrossRefGoogle Scholar
Webster, R. and Oliver, M. A. (2007). Geostatistics for Environmental Scientists, 2nd edn. Wiley, Chichester.CrossRefGoogle Scholar
Wilson, A. and Mellor, P. (2009). Bluetongue in Europe: vectors, epidemiology and climate change (vol 103, pg S69, 2008). Parasitology Research 104, 489–489. doi: 10.1007/s00436-008-1314-8.CrossRefGoogle Scholar
Zimmerman, D. L. and Stein, M. (2010). Classical geostatistical methods. In Handbook of Spatial Statistics (eds. Gelfand, A. E., Diggle, P. J., Fuentes, M. and Guttorp, P.). CRC Press, Boca Raton.Google Scholar