title: Trophic coherence determines food-web stability.
abstract: Why are large, complex ecosystems stable? Both theory and simulations of current models predict the onset of instability with growing size and complexity, so for decades it has been conjectured that ecosystems must have some unidentified structural property exempting them from this outcome. We show that trophic coherence--a hitherto ignored feature of food webs that current structural models fail to reproduce--is a better statistical predictor of linear stability than size or complexity. Furthermore, we prove that a maximally coherent network with constant interaction strengths will always be linearly stable. We also propose a simple model that, by correctly capturing the trophic coherence of food webs, accurately reproduces their stability and other basic structural features. Most remarkably, our model shows that stability can increase with size and complexity. This suggests a key to May's paradox, and a range of opportunities and concerns for biodiversity conservation.
authors.affiliation: Warwick Mathematics Institute, and Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom; S.Johnson.2@warwick.ac.uk.
authors.forename: Samuel
authors.initials: S
authors.lastname: Johnson
authors.affiliation: Departamento de Electromagnetismo y Física de la Materia, and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain; and.
authors.forename: Virginia
authors.initials: V
authors.lastname: Domínguez-García
authors.affiliation: Departamento de Electrónica y Tecnología de Computadores and Centro de Investigación en Tecnologías de la Información y de las Comunicaciones, Universidad de Granada, 18071 Granada, Spain.
authors.forename: Luca
authors.initials: L
authors.lastname: Donetti
authors.affiliation: Departamento de Electromagnetismo y Física de la Materia, and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain; and.
authors.forename: Miguel A
authors.initials: MA
authors.lastname: Muñoz
mesh_terms: D000818:Animals; D003247:Conservation of Natural Resources / Q000379:methods; D017753:Ecosystem; D020387:Food Chain; D005518:Food Preferences / Q000502:physiology*; D008954:Models, Biological; D013045:Species Specificity
keywords: May's paradox; complex networks; diversity–stability debate; dynamical stability; food webs