Multiple species effects and spatial autocorrelation in detecting species associations

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Abstract
The traditional approach to the analysis of species association within a community, based upon co‐occurrence in sampling units such as quadrats, has been to test all pairs of species, using a 2 × 2 contingency table for each pair. It has long been recognised that all these tests are not independent of each other, but there is an additional problem in that the association between any particular pair may depend on the combination of the other species that are present or on the environmental factors that determine that combination. We use a 2kcontingency table to examine this problem and find that pairwise associations are not independent of the other species.The second problem that we consider is the effect of spatial autocorrelation in the data which makes the statistical tests too liberal. In the absence of a derived solution for a deflation factor to correct the test statistic calculated from a 2ktable, we describe a Monte Carlo approach that provides an approximate solution to this problem. In our data the amount of deflation that is necessary for a 2ktable is small compared to the amount required for the 2 × 2 tables used to test pairwise association.