Beyond connectedness: why pairwise metrics cannot capture community stability

The connectedness of species in a trophic web has long been a key structural characteristic for both theoreticians and empiricists in their understanding of community stability. In the past decades, there has been a shift from focussing on determining the number of interactions to taking into account their relative strengths. The question is: How do the strengths of the interactions determine the stability of a community? Recently, a metric has been proposed which compares the stability of observed communities in terms of the strength of three- and two-link feedback loops (cycles of interaction strengths). However, it has also been suggested that we do not need to go beyond the pairwise structure of interactions to capture stability. Here, we directly compare the performance of the feedback and pairwise metrics. Using observed food-web structures, we show that the pairwise metric does not work as a comparator of stability and is many orders of magnitude away from the actual stability values. We argue that metrics based on pairwise-strength information cannot capture the complex organization of strong and weak links in a community, which is essential for system stability.