| Title: |
Continuous limits of large plant-pollinator random networks and some applications |
| Authors: |
Billiard, Sylvain; Leman, Hélène; Rey, Thomas; Tran, Viet-Chi |
| Contributors: |
Évolution, Écologie et Paléontologie (Evo-Eco-Paleo) - UMR 8198 (Evo-Eco-Paléo (EEP)); Université de Lille-Centre National de la Recherche Scientifique (CNRS); Unité de Mathématiques Pures et Appliquées (UMPA-ENSL); École normale supérieure de Lyon (ENS de Lyon); Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS); Centre Inria de Lyon; Institut National de Recherche en Informatique et en Automatique (Inria); Laboratoire Paul Painlevé - UMR 8524 (LPP); Reliable numerical approximations of dissipative systems (RAPSODI); Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centre Inria de l'Université de Lille; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria); Laboratoire Analyse et de Mathématiques Appliquées (LAMA); Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel; Chaire Modélisation Mathématique et Biodiversité (MMB)'' of Veolia-Ecole Polytechnique-Museum National d'Histoire Naturelle-Fondation X; ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011); ANR-10-LABX-0058,Bézout,Models and algorithms: from the discrete to the continuous(2010); ANR-17-CE40-0027,MoHyCon,Modèles multi-échelles et simulation numérique hybride de semi-conducteurs(2017); ANR-18-CE02-0010,EcoNet,Modèles statistiques avancés pour les réseaux écologiques(2018); ANR-16-CE32-0007,CADENCE,Propagation de processus épidémiques sur des réseaux dynamiques de mouvements d'animaux avec application aux bovins en France(2016) |
| Source: |
EISSN: 2102-5754 ; MathematicS In Action ; https://cnrs.hal.science/hal-03525607 ; MathematicS In Action, In press |
| Publisher Information: |
CCSD; Société de Mathématiques Appliquées et Industrielles (SMAI) |
| Publication Year: |
2022 |
| Collection: |
LillOA (HAL Lille Open Archive, Université de Lille) |
| Subject Terms: |
stationary solution; integro-differential equation; graphon; kinetic limit; limit theorem; interacting particles; birth and death process; ecological mutualistic community; AMS: 92D40; 92D25; 05C90; 60J80; 60F17; 47G20; [MATH.MATH-PR]Mathematics [math]/Probability [math.PR]; [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]; [SDV.EE.IEO]Life Sciences [q-bio]/Ecology; environment/Symbiosis |
| Description: |
International audience ; 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. |
| Document Type: |
article in journal/newspaper |
| Language: |
English |
| Availability: |
https://cnrs.hal.science/hal-03525607; https://cnrs.hal.science/hal-03525607v2/document; https://cnrs.hal.science/hal-03525607v2/file/plantes-pollinisateurs-v23062022.pdf |
| Rights: |
info:eu-repo/semantics/OpenAccess |
| Accession Number: |
edsbas.DA07E31C |
| Database: |
BASE |