Impact of a block structure on the Lotka-Volterra model
The Lotka-Volterra (LV) model is a simple, robust, and versatile model used to describe large interacting systems such as food webs or microbiomes. The model consists of n coupled differential equations linking the abundances of n different species. We consider a large random interaction matrix with...
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2024-09-01
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| Online Access: | https://peercommunityjournal.org/articles/10.24072/pcjournal.460/ |
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| author | Clenet, Maxime Massol, François Najim, Jamal |
| author_facet | Clenet, Maxime Massol, François Najim, Jamal |
| author_sort | Clenet, Maxime |
| collection | DOAJ |
| description | The Lotka-Volterra (LV) model is a simple, robust, and versatile model used to describe large interacting systems such as food webs or microbiomes. The model consists of n coupled differential equations linking the abundances of n different species. We consider a large random interaction matrix with independent entries and a block variance profile. The ith diagonal block represents the intra-community interaction in community i, while the off-diagonal blocks represent the inter-community interactions. The variance remains constant within each block, but may vary across blocks. We investigate the important case of two communities of interacting species, study how interactions affect their respective equilibrium. We also describe equilibrium with feasibility (i.e., whether there exists an equilibrium with all species at non-zero abundances) and the existence of an attrition phenomenon (some species may vanish) within each community. Information about the general case of b communities (b > 2) is provided in the appendix |
| format | Article |
| id | doaj-art-ff6901986bfa419a9c711515d75d56d3 |
| institution | Kabale University |
| issn | 2804-3871 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | Peer Community In |
| record_format | Article |
| series | Peer Community Journal |
| spelling | doaj-art-ff6901986bfa419a9c711515d75d56d32025-02-07T10:17:17ZengPeer Community InPeer Community Journal2804-38712024-09-01410.24072/pcjournal.46010.24072/pcjournal.460Impact of a block structure on the Lotka-Volterra model Clenet, Maxime0Massol, François1https://orcid.org/0000-0002-4098-955XNajim, Jamal2https://orcid.org/0000-0002-2097-3649CNRS, Université Gustave Eiffel, France; Université de Sherbrooke, CanadaCNRS, Université de Lille, INSERM, CHU, Institut Pasteur Lille, FranceCNRS, Université Gustave Eiffel, FranceThe Lotka-Volterra (LV) model is a simple, robust, and versatile model used to describe large interacting systems such as food webs or microbiomes. The model consists of n coupled differential equations linking the abundances of n different species. We consider a large random interaction matrix with independent entries and a block variance profile. The ith diagonal block represents the intra-community interaction in community i, while the off-diagonal blocks represent the inter-community interactions. The variance remains constant within each block, but may vary across blocks. We investigate the important case of two communities of interacting species, study how interactions affect their respective equilibrium. We also describe equilibrium with feasibility (i.e., whether there exists an equilibrium with all species at non-zero abundances) and the existence of an attrition phenomenon (some species may vanish) within each community. Information about the general case of b communities (b > 2) is provided in the appendixhttps://peercommunityjournal.org/articles/10.24072/pcjournal.460/Lotka-Volterra model, Block structure, Linear Complementarity Problems, Large Random Matrices, Stability of food webs. |
| spellingShingle | Clenet, Maxime Massol, François Najim, Jamal Impact of a block structure on the Lotka-Volterra model Peer Community Journal Lotka-Volterra model, Block structure, Linear Complementarity Problems, Large Random Matrices, Stability of food webs. |
| title | Impact of a block structure on the Lotka-Volterra model
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| title_full | Impact of a block structure on the Lotka-Volterra model
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| title_fullStr | Impact of a block structure on the Lotka-Volterra model
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| title_full_unstemmed | Impact of a block structure on the Lotka-Volterra model
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| title_short | Impact of a block structure on the Lotka-Volterra model
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| title_sort | impact of a block structure on the lotka volterra model |
| topic | Lotka-Volterra model, Block structure, Linear Complementarity Problems, Large Random Matrices, Stability of food webs. |
| url | https://peercommunityjournal.org/articles/10.24072/pcjournal.460/ |
| work_keys_str_mv | AT clenetmaxime impactofablockstructureonthelotkavolterramodel AT massolfrancois impactofablockstructureonthelotkavolterramodel AT najimjamal impactofablockstructureonthelotkavolterramodel |