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.