Complex systems in ecology: A guided tour with large Lotka-Volterra models and random matrices

Akjouj Imane, Barbier Matthieu, Clenet Maxime, Hachem Walid, Maïda Mylène, Massol François, Najim Jamal, Tran Viet Chi. 2024. Complex systems in ecology: A guided tour with large Lotka-Volterra models and random matrices. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 480 (2285), 35 p.

https://doi.org/10.1098/rspa.2023.0284

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Url - jeu de données - Entrepôt autre : https://doi.org/10.6084/m9.figshare.c.7099701.v1

Résumé : Ecosystems represent archetypal complex dynamical systems, often modelled by coupled differential equations of the form dxi dt = xiφi(x1 , . . . , xN), where N represents the number of species and xi, the abundance of species i. Among these families of coupled differential equations, Lotka–Volterra (LV) equations, corresponding to φi(x1 , . . . , xN) = r i − xi + (Γ x)i, play a privileged role, as the LV model represents an acceptable trade-off between complexity and tractability. Here, r i is the intrinsic growth of species i and Γ stands for the interaction matrix: Γij represents the effect of species j over species i. For large N, estimating matrix Γ is often an overwhelming task and an alternative is to draw Γ at random, parameterizing its statistical distribution by a limited number of model features. Dealing with large random matrices, we naturally rely on random matrix theory (RMT). The aim of this review article is to present an overview of the work at the junction of theoretical ecology and large RMT. It is intended to an interdisciplinary audience spanning theoretical ecology, complex systems, statistical physics and mathematical biology.

Mots-clés Agrovoc : modèle mathématique, écosystème, modèle de simulation, écologie, dynamique des populations, interactions biologiques

Mots-clés libres : Random matrices, Dynamical Systems, Faisability, Stability, Structured networks, Population dynamics

Classification Agris : U10 - Informatique, mathématiques et statistiques

Champ stratégique Cirad : CTS 7 (2019-) - Hors champs stratégiques

Agences de financement européennes : European Commission

Agences de financement hors UE : Centre National de la Recherche Scientifique, Agence Nationale de la Recherche

Projets sur financement : (FRA) KARATE, (FRA) Centre Européen pour les Mathématiques, la Physique et leurs Interactions, (FRA) Models and algorithms: from the discrete to the continuous, (FRA) Modèles statistiques avancés pour les réseaux écologiques, (EU) ERC-AdG SINGER-101054787

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