Coupling strength between omnivory loops and their one-species-delete subloops drives real food web stability

A central and fundamental issue in ecology is to understand the relationship between complexity and stability. Increased empirical evidences demonstrated no clear relationships between complexity metrics and stability, and recent food web loop analyses suggested that maximum loop weight as well as the summation ratio between 3- and 2-link feedback loop weights could be better estimators of system stability. However, the importance of longer loops than 3-link on the stability remains unclear. Here, we use 127 marine food webs and the matrix product and trace method to investigate the relationship between loops with maximum of 7 links and food web stability. We found that feedback metrics | a_2n+1/ a_2n| , i.e., the ratio of the sums of (2n + 1)-link and 2n-link loop weights, are strongly related with stability. These sum weight ratios can be regarded as the coupling strength between omnivory loops and their one-species-delete subloops, including the smallest three species and high-level omnivory ones. Further theoretical simulations of bioenergetic consumer-resource models with allometric constraints strengthen this finding. These results suggest that both longer loops and omnivory are important drivers of the food web stability.