Title :

Continuous limits of large plant-pollinator random networks and some applications

Author(s) :

Billiard, Sylvain [Auteur]
Évolution, Écologie et Paléontologie (Evo-Eco-Paleo) - UMR 8198 [Evo-Eco-Paléo (EEP)]
Leman, Hélène [Auteur]
Unité de Mathématiques Pures et Appliquées [UMPA-ENSL]
Inria Lyon
Rey, Thomas [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]
Tran, Chi [Auteur]
Laboratoire Analyse et de Mathématiques Appliquées [LAMA]

Journal title :

MathematicS In Action

Publisher :

Société de Mathématiques Appliquées et Industrielles (SMAI)

Publication date :

2022

English keyword(s) :

stationary solution
integro-differential equation
graphon
kinetic limit
limit theorem
interacting particles
birth and death process
ecological mutualistic community

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Sciences du Vivant [q-bio]/Ecologie, Environnement/Interactions entre organismes

English abstract : [en]

We study a stochastic individual-based model of interacting plant and pollinator species through a bipartite graph: each species is a node of the graph, an edge representing interactions between a pair of species. The ...
Show more >We study a stochastic individual-based model of interacting plant and pollinator species through a bipartite graph: each species is a node of the graph, an edge representing interactions between a pair of species. The dynamics of the system depends on the between- and within-species interactions: pollination by insects increases plant reproduction rate but has a cost which can increase plant death rate, depending on pollinators density. Pollinators reproduction is increased by the resources harvested on plants. Each species is characterized by a trait corresponding to its degree of generalism. This trait determines the structure of the interactions graph and the quantity of resources exchanged between species. Our model includes in particular nested or modular networks. Deterministic approximations of the stochastic measure-valued process by systems of ordinary differential equations or integro-differential equations are established and studied, when the population is large or when the graph is dense and can be replaced with a graphon. The long-time behaviors of these limits are studied and central limit theorems are established to quantify the difference between the discrete stochastic individual-based model and the deterministic approximations. Finally, studying the continuous limits of the interaction network and the resulting PDEs, we show that nested plant-pollinator communities are expected to collapse towards a coexistence between a single pair of species of plants and pollinators.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions
Models and algorithms: from the discrete to the continuous
Modèles multi-échelles et simulation numérique hybride de semi-conducteurs
Modèles statistiques avancés pour les réseaux écologiques
Propagation de processus épidémiques sur des réseaux dynamiques de mouvements d'animaux avec application aux bovins en France

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL