Species distributional data such as species range maps (extent-of-occurrence), breeding bird surveys and biodiversity atlases are a common source for analyses of species-environment relationships. These, in turn, form the basis for conservation and management plans for endangered species, for calculating distributions under future climate and land-use scenarios and other forms of environmental risk assessment.

The analysis of spatial data is complicated by a phenomenon known as spatial autocorrelation. Spatial autocorrelation (SAC) occurs when the values of variables sampled at nearby locations are not independent from each other (Tobler 1970). The causes of spatial autocorrelation are manifold, but three factors are particularly common (Legendre and Fortin 1989, Legendre 1993, Legendre and Legendre 1998): 1) biological processes such as speciation, extinction, dispersal or species interactions are distance-related; 2) non-linear relationships between environment and species are modelled erroneously as linear; 3) the statistical model fails to account for an important environmental determinant that in itself is spatially structured and thus causes spatial structuring in the response (Besag 1974). The second and third points are not always referred to as spatial autocorrelation, but rather spatial dependency (Legendre et al. 2002). Since they also lead to autocorrelated residuals, these are equally problematic. A fourth source of spatial autocorrelation relates to spatial resolution, because coarser grains lead to a spatial smoothing of data. In all of these cases, SAC may confound the analysis of species distribution data.

Spatial autocorrelation may be seen as both an opportunity and a challenge for spatial analysis. It is an opportunity when it provides useful information for inference of process from pattern (Palma et al. 1999) by, for example, increasing our understanding of contagious biotic processes such as population growth, geographic dispersal, differential mortality, social organization or competition dynamics (Griffith and Peres-Neto 2006). In most cases, however, the presence of spatial autocorrelation is seen as posing a serious shortcoming for hypothesis testing and prediction ( Lennon 2000, Dormann 2007b), because it violates the assumption of independently and identically distributed (i.i.d.) errors of most standard statistical procedures (Anselin 2002) and hence inflates type I errors, occasionally even inverting the slope of relationships from non-spatial analysis (Kühn 2007).

A variety of methods have consequently been developed to correct for the effects of spatial autocorrelation (partially reviewed in Keitt et al. 2002, Miller et al. 2007, see below), but only a few have made it into the ecological literature. The aims of this paper are to 1) present and explain methods that account for spatial autocorrelation in analyses of spatial data; the approaches considered are: autocovariate regression, spatial eigenvector mapping (SEVM), generalised least squares (GLS), conditional autoregressive models (CAR), simultaneous autoregressive models (SAR), generalised linear mixed models (GLMM) and generalised estimation equations (GEE); 2) describe which of these methods can be used for which error distribution, and discuss potential problems with implementation; 3) illustrate how to implement these methods using simulated data sets and by providing computing code (Anon. 2005).