Abstract
The consensus that complexity begets stability in ecosystems was challenged in the seventies, a result recently extended to ecologically-inspired networks. The approaches assume the existence of a feasible equilibrium, i.e. with positive abundances. However, this key assumption has not been tested. We provide analytical results complemented by simulations which show that equilibrium feasibility vanishes in species rich systems. This result leaves us in the uncomfortable situation in which the existence of a feasible equilibrium assumed in local stability criteria is far from granted. We extend our analyses by changing interaction structure and intensity, and find that feasibility and stability is warranted irrespective of species richness with weak interactions. Interestingly, we find that the dynamical behaviour of ecologically inspired architectures is very different and richer than that of unstructured systems. Our results suggest that a general understanding of ecosystem dynamics requires focusing on the interplay between interaction strength and network architecture.
Highlights
A central question in ecology is to understand the factors and conditions that ensure ecological systems to persist, a requisite for the sustained provisioning of vital ecosystem services
Finding conditions leading to stable equilibria, i.e. equilibria robust to small perturbations, is a key feature in understanding how persistent are ecological systems
The number of species involved in the ecosystem as well as the number of relations between them has historically been pointed out to be the prominent ingredients determining stability. The latter is always computed for a particular equilibrium, which needs and is usually assumed to contain only positive abundances
Summary
A central question in ecology is to understand the factors and conditions that ensure ecological systems to persist, a requisite for the sustained provisioning of vital ecosystem services. Levins [6, 7], Ashby and Gardner [8], and May [9] showed numerically that large random systems may be expected to be stable up to a certain connectance threshold, contradicting the earlier ideas that complex natural systems are more likely to be stable In his impactful work, May [10, 11] showed mathematically using random matrix theory [12, 13] that large and random ecosystems are inherently unstable. His approach was based on a mathematical study of community matrices, which represented unstructured random networks of interacting species He used a local-stability analysis assuming these systems were at equilibrium. May [11] concluded that there was no comfortable theorem assuring that increased complexity will lead to stable systems, and that the task was to “elucidate the devious strategies which make for the stability in enduring natural systems”
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