The feasibility of equilibria in large ecosystems: A primary but neglected concept in the complexity-stability debate

Dougoud, Michaël; Vinckenbosch, Laura; Rohr, Rudolf P.; Bersier, Louis-Félix; Mazza, Christian

doi:10.1371/journal.pcbi.1005988

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The feasibility of equilibria in large ecosystems: A primary but neglected concept in the complexity-stability debate

Dougoud, Michaël Department of Mathematics, University of Fribourg, Switzerland
Vinckenbosch, Laura Department of Mathematics, University of Fribourg, Switzerland - University of Applied Sciences, Western Switzerland - HES-SO, Yverdon-les-Bains, Switzerland
Rohr, Rudolf P. Department of Biology, Unit of Ecology and Evolution, University of Fribourg, Switzerland
Bersier, Louis-Félix Department of Biology, Unit of Ecology and Evolution, University of Fribourg, Switzerland
Mazza, Christian Department of Mathematics, University of Fribourg, Switzerland

08.02.2018

Published in:

PLOS Computational Biology. - 2018, vol. 14, no. 2, p. e1005988

English 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.

Faculty

Faculté des sciences et de médecine

Department

Département de Biologie, Département de Mathématiques

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