Food-web stability emerges from allometric link-degree distributions

In natural ecosystems, species are linked to each other by feeding interactions (hereafter links) that determine energy fluxes and compose complex food webs. The coexistence of species and the biodiversity of natural ecosystems depend on the stability of these food webs. Recent theoretical approaches have identified that predator-prey body-mass ratios are critically important for food-web stability. Yet, they are lacking mechanistic explanations.

In our study we used a bioenergetic consumer-resource model to fill this void and to show how predator-prey body-mass ratios in tri-trophic food chains promote food-web stability. We show in simulations that only certain combinations of body-mass ratios between the three species allow their stable co-existence and define this range as the 'stability domain'. It is restricted by bottom-up energy availability towards low and enrichment-driven dynamics towards high body-mass ratios. Consistent with our model predictions, more than 90% of the three-species food chains across five natural food webs exhibit body-mass ratios within this 'stability domain'. Random re-wiring analyses of the food webs demonstrate that allometric link-degree distributions in natural food webs are critically important for this consistency. They hold that the numbers of predators per species decreases whereas the number of prey per species increases with species’ body masses. Food-web stability emerges from these simple allometric link-degree distributions that are caused by physical constraints on predator-prey interactions. Our results demonstrate how simple, species-level correlations between body-masses and linking drive community-level processes such as food-web stability.