Species co-occurrence analysis: pairwise versus matrix-level approaches

Veech (2013, Global Ecology and Biogeography, 22, 252-260) introduced a formula to calculate the probability of two species co-occurring in various sites under the assumption of statistical independence between the two distributional patterns. He presented his model as a new procedure, a pairwise approach', different from analyses of whole presence-absence matrices to examine patterns of co-occurrence. Here I show that: (1) Veech's method is identical to Fisher's exact test, a standard procedure for measuring the statistical association between two discrete variables; (2) in a broad sense, the pairwise approach is very similar to early analyses of spatial association, such as the one advanced by Forbes in 1907; (3) implicit in Veech's formula is a sampling scheme that is indistinguishable from well-known matrix-level null models that randomize the distribution of species among equiprobable sites; (4) pairwise co-occurrence patterns can be analysed using any matrix-level null model, so pairwise comparisons are not limited to using Veech's formula. The methodological distinction that Veech proposed between pairwise and matrix-level approaches does not in fact exist, although the conceptual distinction between the two approaches is still a debated topic.