The Statistical Validation of Null Models Used in Spatial Association Analyses

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Traditional statistical techniques for detecting between-species spatial association patterns are invalidated when within-species spatial distributions exhibit patchy, clumped, or other kinds of spatial autocorrelation. To overcome this problem three alternative null models are considered. They are the 'patch model', the 'random shifts' model, and the 'random patterns' model. However, none of these three models has been satisfactorily validated, in the sense of confirming that they are able to generate acceptable type I error rates with randomly generated data which is itself spatially autocorrelated. The primary aim of this article is to provide such a validation in the context of a statistical test for pairwise species association. Three different pattern-generating algorithms were used to create pseudo-observed' spatially autocorrelated species distribution maps. When applied to these distribution maps, the random patterns null model generated acceptable type I error rates across a wide range of levels of spatial autocorrelation. The random shifts null model was excessively liberal at the highest levels of spatial autocorrelation, and the patch model showed a trend for conservatism. However generalisations could not be made, as there was evidence that the validation results were sensitive to differences in the type of spatial autocorrelation modelled by the three different pattern-generating algorithms. Application of each null model to field data highlighted two general statistical issues. The first is well known, and is the requirement of ensuring that the assumptions underlying the null model are met by the data. Violation of assumptions can lead to shifts in the type I error rate, and hence invalidation of the test. The second is more subtle, and is the question of whether the null model being used is the most appropriate one for investigating the question of interest. This latter issue is illustrated through comparison of the patch model with the other null models, as the patch model is based on different underlying ecological assumptions.