Methods to account for spatial autocorrelation in the analysis of species distributional data: a review

Authors

  • Carsten F. Dormann,

  • Jana M. McPherson,

  • Miguel B. Araújo,

  • Roger Bivand,

  • Janine Bolliger,

  • Gudrun Carl,

  • Richard G. Davies,

  • Alexandre Hirzel,

  • Walter Jetz,

  • W. Daniel Kissling,

  • Ingolf Kühn,

  • Ralf Ohlemüller,

  • Pedro R. Peres-Neto,

  • Björn Reineking,

  • Boris Schröder,

  • Frank M. Schurr,

  • Robert Wilson


C. F. Dormann (carsten.dormann@ufz.de), Dept of Computational Landscape Ecology, UFZ Helmholtz Centre for Environmental Research, Permoserstr. 15, DE-04318 Leipzig, Germany. – J. M. McPherson, Dept of Biology, Dalhousie Univ., 1355 Oxford Street HAlifax NS, B3H 4J1 Canada. – M. B. Araújo, Dept de Biodiversidad y Biología Evolutiva, Museo Nacional de Ciencias Naturales, CSIC, C/ Gutiérrez Abascal, 2, ES-28006 Madrid, Spain, and Centre for Macroecology, Inst. of Biology, Universitetsparken 15, DK-2100 Copenhagen Ø, Denmark. – R. Bivand, Economic Geography Section, Dept of Economics, Norwegian School of Economics and Business Administration, Helleveien 30, NO-5045 Bergen, Norway. – J. Bolliger, Swiss Federal Research Inst. WSL, Zürcherstrasse 111, CH-8903 Birmensdorf, Switzerland. – G. Carl and I. Kühn, Dept of Community Ecology (BZF), UFZ Helmholtz Centre for Environmental Research, Theodor-Lieser-Strasse 4, DE-06120 Halle, Germany, and Virtual Inst. Macroecology, Theodor-Lieser-Strasse 4, DE-06120 Halle, Germany. – R. G. Davies, Biodiversity and Macroecology Group, Dept of Animal and Plant Sciences, Univ. of Sheffield, Sheffield S10 2TN, U.K. – A. Hirzel, Ecology and Evolution Dept, Univ. de Lausanne, Biophore Building, CH-1015 Lausanne, Switzerland. – W. Jetz, Ecology Behavior and Evolution Section, Div. of Biological Sciences, Univ. of California, San Diego, 9500 Gilman Drive, MC 0116, La Jolla, CA 92093-0116, USA. – W. D. Kissling, Community and Macroecology Group, Inst. of Zoology, Dept of Ecology, Johannes Gutenberg Univ. of Mainz, DE-55099 Mainz, Germany, and Virtual Inst. Macroecology, Theodor-Lieser-Strasse 4, DE-06120 Halle, Germany. – R. Ohlemüller, Dept of Biology, Univ. of York, PO Box 373, York YO10 5YW, U.K. – P. R. Peres-Neto, Dept of Biology, Univ. of Regina, SK, S4S 0A2 Canada, present address: Dept of Biological Sciences, Univ. of Quebec at Montreal, CP 8888, Succ. Centre Ville, Montreal, QC, H3C 3P8, Canada. – B. Reineking, Forest Ecology, ETH Zurich CHN G 75.3, Universitätstr. 16, CH-8092 Zürich, Switzerland. – B. Schröder, Inst. for Geoecology, Univ. of Potsdam, Karl-Liebknecht-Strasse 24-25, DE-14476 Potsdam, Germany. – F. M. Schurr, Plant Ecology and Nature Conservation, Inst. of Biochemistry and Biology, Univ. of Potsdam, Maulbeerallee 2, DE-14469 Potsdam, Germany. – R. Wilson, Área de Biodiversidad y Conservación, Escuela Superior de Ciencias Experimentales y Tecnología, Univ. Rey Juan Carlos, Tulipán s/n, Móstoles, ES-28933 Madrid, Spain.

Abstract

Species distributional or trait data based on range map (extent-of-occurrence) or atlas survey data often display spatial autocorrelation, i.e. locations close to each other exhibit more similar values than those further apart. If this pattern remains present in the residuals of a statistical model based on such data, one of the key assumptions of standard statistical analyses, that residuals are independent and identically distributed (i.i.d), is violated. The violation of the assumption of i.i.d. residuals may bias parameter estimates and can increase type I error rates (falsely rejecting the null hypothesis of no effect). While this is increasingly recognised by researchers analysing species distribution data, there is, to our knowledge, no comprehensive overview of the many available spatial statistical methods to take spatial autocorrelation into account in tests of statistical significance. Here, we describe six different statistical approaches to infer correlates of species’ distributions, for both presence/absence (binary response) and species abundance data (poisson or normally distributed response), while accounting for spatial autocorrelation in model residuals: autocovariate regression; spatial eigenvector mapping; generalised least squares; (conditional and simultaneous) autoregressive models and generalised estimating equations. A comprehensive comparison of the relative merits of these methods is beyond the scope of this paper. To demonstrate each method's implementation, however, we undertook preliminary tests based on simulated data. These preliminary tests verified that most of the spatial modeling techniques we examined showed good type I error control and precise parameter estimates, at least when confronted with simplistic simulated data containing spatial autocorrelation in the errors. However, we found that for presence/absence data the results and conclusions were very variable between the different methods. This is likely due to the low information content of binary maps. Also, in contrast with previous studies, we found that autocovariate methods consistently underestimated the effects of environmental controls of species distributions. Given their widespread use, in particular for the modelling of species presence/absence data (e.g. climate envelope models), we argue that this warrants further study and caution in their use. To aid other ecologists in making use of the methods described, code to implement them in freely available software is provided in an electronic appendix.

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