A multi-species co-occurrence index to avoid type II errors in null model testing

Community structure is determined by the interplay among different processes, including biotic interactions, abiotic filtering and dispersal. Their effects can be detected by comparing observed patterns of co-occurrence between different species (e.g. C-score and the natural metric) to patterns generated by null models based on permutations of species-by-site matrices under constraints on row or column sums. These comparisons enable us to detect significant signals of species association or dissociation, from which the type of biotic interactions between species (e.g. facilitative or antagonistic) can be inferred. Commonly used patterns are based on the levels of co-occurrence between randomly paired species. The level of co-occurrence for three or more species is rarely considered, ignoring the potential existence of functional guilds or motifs composed of multiple species within the community. Null model tests that do not consider multi-species co-occurrence could therefore generate false negatives (Type II error) in detecting non-random forces at play that would only be apparent for such guilds. Here, we propose a multi-species co-occurrence index (hereafter, joint occupancy) that measures the number of sites jointly occupied by multiple species simultaneously, of which the pairwise metric of co-occurrence is a special case. Using this joint occupancy index along with standard permutation algorithms for null model testing, we illustrate nine archetypes of multi-species co-occurrence and explore how frequent they are in the seminal database of 289 species-by-site community matrices published by Atmar and Patterson in 1995. We show that null model testing using pairwise co-occurrence metrics could indeed lead to severe Type II errors in one specific archetype, accounting for 2.4% of the tested community matrices.