title: Feasibility and coexistence of large ecological communities.
abstract: The role of species interactions in controlling the interplay between the stability of ecosystems and their biodiversity is still not well understood. The ability of ecological communities to recover after small perturbations of the species abundances (local asymptotic stability) has been well studied, whereas the likelihood of a community to persist when the conditions change (structural stability) has received much less attention. Our goal is to understand the effects of diversity, interaction strengths and ecological network structure on the volume of parameter space leading to feasible equilibria. We develop a geometrical framework to study the range of conditions necessary for feasible coexistence. We show that feasibility is determined by few quantities describing the interactions, yielding a nontrivial complexity-feasibility relationship. Analysing more than 100 empirical networks, we show that the range of coexistence conditions in mutualistic systems can be analytically predicted. Finally, we characterize the geometric shape of the feasibility domain, thereby identifying the direction of perturbations that are more likely to cause extinctions.
authors.affiliation: Department of Ecology and Evolution, University of Chicago, Chicago, Illinois 60637, USA.
authors.forename: Jacopo
authors.initials: J
authors.lastname: Grilli
authors.affiliation: International School for Advanced Studies (SISSA), via Bonomea 265, I-34136 Trieste, Italy.
authors.forename: Matteo
authors.initials: M
authors.lastname: Adorisio
authors.affiliation: Department of Physics and Astronomy 'Galileo Galilei', Università degli Studi di Padova, INFN and CNISM, Padova 35131, Italy.
authors.forename: Samir
authors.initials: S
authors.lastname: Suweis
authors.affiliation: Department of Ecology and Evolution, University of Chicago, Chicago, Illinois 60637, USA.
authors.forename: György
authors.initials: G
authors.lastname: Barabás
authors.affiliation: Department of Physics, University of Maryland, College Park, Maryland 20742, USA.
authors.forename: Jayanth R
authors.initials: JR
authors.lastname: Banavar
authors.affiliation: Department of Ecology and Evolution, University of Chicago, Chicago, Illinois 60637, USA.|Computation Institute, University of Chicago, Chicago, Illinois 60637, USA.|Northwestern Institute on Complex Systems, Northwestern University, Evanston, Illinois 60208, USA.
authors.forename: Stefano
authors.initials: S
authors.lastname: Allesina
authors.affiliation: Department of Physics and Astronomy 'Galileo Galilei', Università degli Studi di Padova, INFN and CNISM, Padova 35131, Italy.
authors.forename: Amos
authors.initials: A
authors.lastname: Maritan
mesh_terms: D063147:Animal Distribution / Q000502:physiology*; D000818:Animals; D044822:Biodiversity; D058448:Biota / Q000502:physiology*; D060435:Carnivory / Q000502:physiology; D003163:Competitive Behavior / Q000502:physiology; D017753:Ecosystem; D020387:Food Chain; D060434:Herbivory / Q000502:physiology; D008954:Models, Biological; D015233:Models, Statistical; D063148:Plant Dispersal / Q000502:physiology*; D010944:Plants; D011235:Predatory Behavior / Q000502:physiology; D013559:Symbiosis / Q000502:physiology