A null model for randomization tests of nestedness in species assemblages

Analysis of the degree of order in species assemblages in terms of nested subsets has received increased interest during the last decade. However, recently a series of papers have questioned the validity of methods employed for testing whether observed patterns deviate from random expectations. The current view seems to be that the randomization procedure should control for both number of species per site and species frequencies. The randomization procedures used also choose to keep the total number of observations constant in each resample. In this paper I question some of these assumptions when analyzing species-by-site matrices for detecting whether the biota is significantly nested or not. My basic assumption is that the observed species frequency is only an estimate of the probability of occurrence for the particular species. For a test of degree of nestedness all sites should be regarded as being equal. To what extent size, isolation or habitat quality may influence species distribution is a secondary question if nestedness can be statistically proven. This implies that generation of random matrices should only consider the frequency of the species (as an estimate of their probability of occurring in any patch). Such matrices are computationally simple and besides providing a test of nestedness also open the possibility of testing whether the range in species richness is smaller or larger than expected under random expectations. The choice of null model for the test should always be viewed in relation to the question asked. If nestedness is concerned the methods proposed here should be used. However, if other questions are at hand the restrictions of previous approaches may be valid. This is for instance the case if pairwise species co-occurrences are analyzed. In this case, the richness of each site should obviously be incorporated in the randomization to control for the higher probability of co-occurrence at species-rich sites.