The statistical validation of null models used in spatial association analyses

Traditional statistical techniques for detecting between-species spatial as sociation patterns are invalidated when within-species spatial distribution s exhibit patchy, clumped. or other kinds of spatial autocorrelation. To ov ercome this problem three alternative null models are considered They are t he 'patch model', the 'random shifts' model, and the 'random patterns' mode l. However, none of these three models has been satisfactorily validated, i n the sense of confirming that they are able to generate acceptable type I error rates with randomly generated data which is itself spatially autocorr elated. The primary aim of this article is to provide such a validation in the context of a statistical test for pairwise species association. Three d ifferent 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 typ e I error rates across a wide range of levels of spatial autocorrelation. T he random shifts null model was excessively liberal at the highest levels o f spatial autocorrelation, and the patch model showed a trend for conservat ism. 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 algorit hms. Application of each null model to field data highlighted two general statis tical issues. The first is well known, and is the requirement of ensuring t hat the assumptions underlying the null model are met by the data. Violatio n of assumptions can lead to shifts in the type I error rate, and hence inv alidation of the test. The second is more subtle, and is the question of wh ether the null model being used is the most appropriate one for investigati ng the question of interest. This latter issue is illustrated through compa rison of the patch model with the other null models, as the patch model is based on different underlying ecological assumptions.