Null model analyses are not adequate to summarize strong associations: Rebuttal to Ulrich et al. (2022)

Abstract

We recently developed a novel metric of association in pairwise co-occurrence data (Mainali et al., 2022) to address fundamental flaws in traditional indices, as elaborately discussed and conclusively shown in our published paper. Our new metric, the maximum likelihood estimator (MLE) alpha-hat of a statistical parameter alpha, quantifies the degree of association between species occupancy at ecological sites, and it is insensitive to the species prevalences and number of sites. In contrast, we showed that classic indices of co-occurrence (Jaccard, Simpson, Sørensen–Dice) can be highly sensitive to fixed margins of contingency tables, estimating wildly variable degrees of association and even reversing the direction of association for tables with different margins but the same degree-of-association alpha.