Complex systems in Ecology: A guided tour ...
Document type :
Compte-rendu et recension critique d'ouvrage
Title :
Complex systems in Ecology: A guided tour with large Lotka-Volterra models and random matrices
Author(s) :
Akjouj, Imane [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Barbier, Matthieu [Auteur]
Montpellier Cirad
Clenet, Maxime [Auteur]
Laboratoire d'Informatique Gaspard-Monge [LIGM]
Hachem, Walid [Auteur]
Laboratoire d'Informatique Gaspard-Monge [LIGM]
Maïda, Mylène [Auteur]
International Research Lab [IRL CRM-CNRS]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Massol, Francois [Auteur]
Centre d’Infection et d’Immunité de Lille - INSERM U 1019 - UMR 9017 - UMR 8204 [CIIL]
Najim, Jamal [Auteur]
Laboratoire d'Informatique Gaspard-Monge [LIGM]
Tran, Chi [Auteur]
International Research Lab [IRL CRM-CNRS]
Laboratoire Analyse et de Mathématiques Appliquées [LAMA]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Barbier, Matthieu [Auteur]
Montpellier Cirad
Clenet, Maxime [Auteur]
Laboratoire d'Informatique Gaspard-Monge [LIGM]
Hachem, Walid [Auteur]
Laboratoire d'Informatique Gaspard-Monge [LIGM]
Maïda, Mylène [Auteur]
International Research Lab [IRL CRM-CNRS]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Massol, Francois [Auteur]

Centre d’Infection et d’Immunité de Lille - INSERM U 1019 - UMR 9017 - UMR 8204 [CIIL]
Najim, Jamal [Auteur]
Laboratoire d'Informatique Gaspard-Monge [LIGM]
Tran, Chi [Auteur]

International Research Lab [IRL CRM-CNRS]
Laboratoire Analyse et de Mathématiques Appliquées [LAMA]
Journal title :
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Publisher :
Royal Society, The
Publication date :
2024
ISSN :
1364-5021
English keyword(s) :
random matrices
dynamical systems
faisability
population dynamics
Stability
Structured networks
dynamical systems
faisability
population dynamics
Stability
Structured networks
HAL domain(s) :
Mathématiques [math]/Probabilités [math.PR]
Sciences du Vivant [q-bio]/Ecologie, Environnement
Sciences du Vivant [q-bio]/Ecologie, Environnement/Ecosystèmes
Sciences du Vivant [q-bio]/Ecologie, Environnement/Interactions entre organismes
Sciences du Vivant [q-bio]/Ecologie, Environnement
Sciences du Vivant [q-bio]/Ecologie, Environnement/Ecosystèmes
Sciences du Vivant [q-bio]/Ecologie, Environnement/Interactions entre organismes
English abstract : [en]
Ecosystems represent archetypal complex dynamical systems, often modelled by coupled differential equations of the form$$\frac{d x_i}{d t} = x_i \varphi_i(x_1,\cdots, x_N)\ ,$$where $N$ represents the number of species ...
Show more >Ecosystems represent archetypal complex dynamical systems, often modelled by coupled differential equations of the form$$\frac{d x_i}{d t} = x_i \varphi_i(x_1,\cdots, x_N)\ ,$$where $N$ represents the number of species and $x_i$, the abundance of species $i$. Among these families of coupled diffential equations, Lotka-Volterra (LV) equations $$\frac{d x_i}{d t} = x_i ( r_i - x_i +(\Gamma \mathbf{x})_i)\ ,$$play a privileged role, as the LV model represents an acceptable trade-off between complexity and tractability. Here, $r_i$ represents the intrinsic growth of species $i$ and $\Gamma$ stands for the interaction matrix: $\Gamma_{ij}$ represents the effect of species $j$ over species $i$. For large $N$, estimating matrix $\Gamma$ is often an overwhelming task and an alternative is to draw $\Gamma$ at random, parametrizing 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 random matrix theory. It is intended to an interdisciplinary audience spanning theoretical ecology, complex systems, statistical physics and mathematical biology.Show less >
Show more >Ecosystems represent archetypal complex dynamical systems, often modelled by coupled differential equations of the form$$\frac{d x_i}{d t} = x_i \varphi_i(x_1,\cdots, x_N)\ ,$$where $N$ represents the number of species and $x_i$, the abundance of species $i$. Among these families of coupled diffential equations, Lotka-Volterra (LV) equations $$\frac{d x_i}{d t} = x_i ( r_i - x_i +(\Gamma \mathbf{x})_i)\ ,$$play a privileged role, as the LV model represents an acceptable trade-off between complexity and tractability. Here, $r_i$ represents the intrinsic growth of species $i$ and $\Gamma$ stands for the interaction matrix: $\Gamma_{ij}$ represents the effect of species $j$ over species $i$. For large $N$, estimating matrix $\Gamma$ is often an overwhelming task and an alternative is to draw $\Gamma$ at random, parametrizing 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 random matrix theory. It is intended to an interdisciplinary audience spanning theoretical ecology, complex systems, statistical physics and mathematical biology.Show less >
Language :
Anglais
ANR Project :
Source :
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