Skewness enables stabilising effect of hierarchy in complex competition networks

Abstract

1Ecological networks tend to contain many weak and only few strong interactions. Furthermore, interaction strengths are often arranged or patterned in ways that enhance stability. However, little attention has been given to the relation between the "many weak and few strong links" distribution and the stabilising effect of patterning. Here, we focus on the stabilising effect of hierarchy in bryozoan competition networks, and demonstrate that it critically depends on a skewed distribution of interaction strengths. To this end, we first show that, in line with many other ecological networks, the empirically derived interaction strengths in competition networks were characterised by a high level of skewness, with many weak and few strong links. Then, we analysed the relationship between the interaction strength distributions, hierarchy and stability by comparing theoretical competition matrices with different distributions of interaction strengths. We found that the full stabilising effect of hierarchy only appeared when we used skewed interaction 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 study ecological stability, and therefore might overlook stabilising mechanisms. We conclude that since skewed interaction strengths are a common feature of ecological networks, they can be expected to play an important role in the relation between structure and stability in living systems.