Marginally stable equilibria in critical ecosystems
In this work we study the stability of the equilibria reached by ecosystems formed by a large number of species. The model we focus on are Lotka–Volterra equations with symmetric random interactions. Our theoretical analysis, confirmed by our numerical studies, shows that for strong and heterogeneou...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2018-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/aada58 |
| _version_ | 1797750610173362176 |
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| author | Giulio Biroli Guy Bunin Chiara Cammarota |
| author_facet | Giulio Biroli Guy Bunin Chiara Cammarota |
| author_sort | Giulio Biroli |
| collection | DOAJ |
| description | In this work we study the stability of the equilibria reached by ecosystems formed by a large number of species. The model we focus on are Lotka–Volterra equations with symmetric random interactions. Our theoretical analysis, confirmed by our numerical studies, shows that for strong and heterogeneous interactions the system displays multiple equilibria which are all marginally stable. This property allows us to obtain general identities between diversity and single species responses, which generalize and saturate May’s stability bound. By connecting the model to systems studied in condensed matter physics, we show that the multiple equilibria regime is analogous to a critical spin-glass phase. This relation suggests new experimental ways to probe marginal stability. |
| first_indexed | 2024-03-12T16:35:19Z |
| format | Article |
| id | doaj.art-3ae570385a0c4262bec092bc21c07e78 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:35:19Z |
| publishDate | 2018-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-3ae570385a0c4262bec092bc21c07e782023-08-08T14:53:25ZengIOP PublishingNew Journal of Physics1367-26302018-01-0120808305110.1088/1367-2630/aada58Marginally stable equilibria in critical ecosystemsGiulio Biroli0Guy Bunin1Chiara Cammarota2Institut de physique théorique, Université Paris Saclay , CEA, CNRS, F-91191 Gif-sur-Yvette, France; Laboratoire de Physique Statistique, École Normale Supérieure, CNRS, PSL Research University , Sorbonne Universités, F-75005 Paris, FranceDepartment of Physics, Technion-Israel Institute of Technology, Haifa 32000, IsraelDepartment of Mathematics, King’s College London, Strand, London WC2R 2LS, United KingdomIn this work we study the stability of the equilibria reached by ecosystems formed by a large number of species. The model we focus on are Lotka–Volterra equations with symmetric random interactions. Our theoretical analysis, confirmed by our numerical studies, shows that for strong and heterogeneous interactions the system displays multiple equilibria which are all marginally stable. This property allows us to obtain general identities between diversity and single species responses, which generalize and saturate May’s stability bound. By connecting the model to systems studied in condensed matter physics, we show that the multiple equilibria regime is analogous to a critical spin-glass phase. This relation suggests new experimental ways to probe marginal stability.https://doi.org/10.1088/1367-2630/aada58ecologystabilityself organized criticality |
| spellingShingle | Giulio Biroli Guy Bunin Chiara Cammarota Marginally stable equilibria in critical ecosystems New Journal of Physics ecology stability self organized criticality |
| title | Marginally stable equilibria in critical ecosystems |
| title_full | Marginally stable equilibria in critical ecosystems |
| title_fullStr | Marginally stable equilibria in critical ecosystems |
| title_full_unstemmed | Marginally stable equilibria in critical ecosystems |
| title_short | Marginally stable equilibria in critical ecosystems |
| title_sort | marginally stable equilibria in critical ecosystems |
| topic | ecology stability self organized criticality |
| url | https://doi.org/10.1088/1367-2630/aada58 |
| work_keys_str_mv | AT giuliobiroli marginallystableequilibriaincriticalecosystems AT guybunin marginallystableequilibriaincriticalecosystems AT chiaracammarota marginallystableequilibriaincriticalecosystems |