Consequences of spatial autocorrelation for niche-based models

1. Spatial autocorrelation is an important source of bias in most spatial analyses. We explored the bias introduced by spatial autocorrelation on the explanatory and predictive power of species' distribution models, and make recommendations for dealing with the problem. 2. Analyses were based on the distribution of two species of freshwater turtle and two virtual species with simulated spatial structures within two equally sized areas located on the Iberian Peninsula. Sequential permutations of environmental variables were used to generate predictor variables that retained the spatial structure of the original variables. Univariate models of species' distributions using generalized linear models (GLM), generalized additive models (GAM) and classification tree analysis (CTA) were fitted for each variable permutation. Variation of accuracy measures with spatial autocorrelation of the original predictor variables, as measured by Moran's I, was analysed and compared between models. The effects of systematic subsampling of the data set and the inclusion of a contagion term to deal with spatial autocorrelation in models were assessed with projections made with GLM, as it was with this method that estimates of significance based on randomizations were obtained. 3. Spatial autocorrelation was shown to represent a serious problem for niche-based species' distribution models. Significance values were found to be inflated up to 90-fold. 4. In general, GAM and CTA performed better than GLM, although all three methods were vulnerable to the effects of spatial autocorrelation. 5. The procedures utilized to reduce the effects of spatial autocorrelation had varying degrees of success. Subsampling was partially effective in avoiding the inflation effect, whereas the inclusion of a contagion term fully eliminated or even overcompensated for this effect. Direct estimation of probability using variable simulations was effective, yet seemed to show some residual spatial autocorrelation effects. 6. Synthesis and applications. Given the expected inflation in the estimates of significance when analysing spatially autocorrelated variables, these need to be adjusted. The reliability and value of niche-based distribution models for management and other applied ecology purposes can be improved if certain techniques and procedures, such as the null model approach recommended in this study, are implemented during the model-building process.