Topological constraints on the dynamics of wasp-waist ecosystems

Small pelagic fish species like anchovy or sardines are of high ecological and economical importance. As marine food webs are fished down, these small pelagics tend to be more exploited and overfished. It is not yet very well known what the possible effects of their collapse can be, therefore there is an urgent need to outline a theoretical framework for understanding their dynamics. These fish occupy very special position in food webs, ensuring energy transfer between species lower and higher levels, while forming narrow “wasp-waists” poor in number of species (but very abundant). Our purpose was to quantify the interaction structure of model food webs of equal complexity but different levels of “wasp-waistedness”. We analysed the topological properties of the webs by characterising every direct and indirect interactions between individual species, as well as by assessing the relative positional importance of each species in each web. We found that (1) the shorter the interaction pathways considered, the weaker the predictive power of node degree for positional importance, (2) the importance of species varies more in wasp-waist food webs, (3) if longer indirect chain effects are considered, indirect effects can well be stronger than direct ones, (4) interactions between coexisting wasp-waist species are stronger than the average, and (5) the “self-regulatory” looping effects are also stronger for wasp-waist species. Based on the topological properties of the networks, our results describe constraints acting on the dynamical behaviour of wasp-waist ecosystems. We give explanations, from this viewpoint, for regime shifts in which one WW species replaces another, and for the unpredictable dynamics of these fish stocks. From a marine conservation viewpoint, we illustrate that as the abundance of wasp-waist species decreases, the architecture of energy flows becomes highly vulnerable and unreliable. We provide an approach for quantifying these structural changes.