Titre :

Feasibility of sparse large Lotka-Volterra ecosystems

Auteur(s) :

Akjouj, Imane [Auteur]
Université de Lille
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Najim, Jamal [Auteur]
Laboratoire d'Informatique Gaspard-Monge [LIGM]

Titre de la revue :

Journal of Mathematical Biology

Pagination :

1-28

Éditeur :

Springer

Date de publication :

2022

ISSN :

0303-6812

Mot(s)-clé(s) en anglais :

Theoretical ecology
Foodwebs
Feasibility and stability
Lotka-Volterra systems
Large random matrices
Gaussian concentration. MSC Classification 2010: Primary 15B52
60G70
Secondary 60B20
92D40

Discipline(s) HAL :

Mathématiques [math]/Probabilités [math.PR]
Sciences de l'environnement/Biodiversité et Ecologie

Résumé en anglais : [en]

Consider a large ecosystem (foodweb) with n species, where the abundances follow a Lotka-Volterra system of coupled differential equations. We assume that each species interacts with d other species and that their interaction ...
Lire la suite >Consider a large ecosystem (foodweb) with n species, where the abundances follow a Lotka-Volterra system of coupled differential equations. We assume that each species interacts with d other species and that their interaction coefficients are independent random variables. This parameter d reflects the connectance of the foodweb and the sparsity of its interactions especially if d is much smaller that n. We address the question of feasibility of the foodweb, that is the existence of an equilibrium solution of the Lotka-Volterra system with no vanishing species. We establish that for a given range of d with an extra condition on the sparsity structure, there exists an explicit threshold depending on n and d and reflecting the strength of the interactions, which guarantees the existence of a positive equilibrium as the number of species n gets large. From a mathematical point of view, the study of feasibility is equivalent to the existence of a positive solution (component-wise) to the equilibrium linear equation. The analysis of such positive solutions essentially relies on large random matrix theory for sparse matrices and Gaussian concentration of measure. The stability of the equilibrium is established. The results in this article extend to a sparse setting the results obtained by Bizeul and Najim in Proc. AMS 2021.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL