Section: Mathematical & Computational Biology
Topic: Ecology, Applied mathematics

Impact of a block structure on the Lotka-Volterra model

Clenet, Maxime1, 2 ; Massol, François3 ; Najim, Jamal1 
1 CNRS, Université Gustave Eiffel, France
2 Université de Sherbrooke, Canada
3 CNRS, Université de Lille, INSERM, CHU, Institut Pasteur Lille, France

Corresponding author(s): Clenet, Maxime (maxime.clenet@usherbrooke.ca)

10.24072/pcjournal.460 - Peer Community Journal, Volume 4 (2024), article no. e86.

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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

Published online:
DOI: 10.24072/pcjournal.460
Type: Research article
Keywords: Lotka-Volterra model, Block structure, Linear Complementarity Problems, Large Random Matrices, Stability of food webs.

Clenet, Maxime 1, 2; Massol, François 3; Najim, Jamal 1

1 CNRS, Université Gustave Eiffel, France
2 Université de Sherbrooke, Canada
3 CNRS, Université de Lille, INSERM, CHU, Institut Pasteur Lille, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Clenet, Maxime; Massol, François; Najim, Jamal. Impact of a block structure on the Lotka-Volterra model. Peer Community Journal, Volume 4 (2024), article  no. e86. doi : 10.24072/pcjournal.460. https://peercommunityjournal.org/articles/10.24072/pcjournal.460/

PCI peer reviews and recommendation, and links to data, scripts, code and supplementary information: 10.24072/pci.mcb.100235

Conflict of interest of the recommender and peer reviewers:
The recommender in charge of the evaluation of the article and the reviewers declared that they have no conflict of interest (as defined in the code of conduct of PCI) with the authors or with the content of the article.

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