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| 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. | |
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