A null model for randomization tests of nestedness in species assemblages

Analysis of the degree of order in species assemblages in terms of nested s ubsets has received increased interest during the last decade. However, rec ently a series of papers have questioned the validity of methods employed f or testing whether observed patterns deviate from random expectations. The current view seems to be that the randomization procedure should control fo r both number of species per site and species frequencies. The randomizatio n procedures used also choose to keep the total number of observations cons tant in each resample. In this paper I question some of these assumptions w hen analyzing species-by-site matrices for detecting whether the biota is s ignificantly nested or not. My basic assumption is that the observed specie s frequency is only an estimate of the probability of occurrence for the pa rticular species. For a test of degree of nestedness all sites should be re garded as being equal. To what extent size, isolation or habitat quality ma y influence species distribution is a secondary question if nestedness can be statistically proven. This implies that generation of random matrices sh ould only consider the frequency of the species las an estimate of their pr obability of occurring in any patch). Such matrices are computationally sim ple and besides providing a test of nestedness also open the possibility of testing whether the range in species richness is smaller or larger than ex pected under random expectations. The choice of null model for the test sho uld always be viewed in relation to the question asked. If nestedness is co ncerned the methods proposed here should be used. However, if other questio ns are at hand the restrictions of previous approaches may be valid. This i s for instance the case if pairwise species co-occurrences are analyzed. In this case, the richness of each site should obviously be incorporated in t he randomization to control for the higher probability of co-occurrence at species-rich sites.