Many weak and few strong links: the importance of link strength distributions for stabilising patterns in competition networks

Ecological networks tend to contain many weak and only a few strong links. Furthermore, link strengths are often patterned within a network in ways that enhance system stability considerably, increasing the ability of the system to return to equilibrium after a perturbation. However, little attention has been given to the relation between the skewed “many weak and few strong links” distribution and the stabilising effect of patterning. Here, we focus on the stabilising effect of a hierarchical patterning in bryozoan competition networks and demonstrate that this stabilising effect critically depends on a skewed distribution of link strengths. We first show that, in line with many other ecological networks, the empirically derived link strengths in these competition networks were characterised by a high level of skewness, with many weak and few strong links. Then, we analysed the relationship between the link strength distributions, hierarchy and stability by comparing theoretical competition matrices with different distributions of link strengths. We found that the full stabilising effect of hierarchy only appeared when we used skewed link strengths produced by a gamma distribution, but not in matrices built with uniform or half-normal distributions. This has important methodological implications, since theoretical studies often assume normal or uniform distributions to investigate ecological stability, and therefore might overlook stabilising mechanisms. These implications are relevant for theory on the relation between structure and stability of ecological networks in general, since skewed link strengths are also a common feature of food webs and mutualistic systems.