title: Network impact on persistence in a finite population dynamic diffusion model: application to an emergent seed exchange network.
abstract: Dynamic extinction colonisation models (also called contact processes) are widely studied in epidemiology and in metapopulation theory. Contacts are usually assumed to be possible only through a network of connected patches. This network accounts for a spatial landscape or a social organization of interactions. Thanks to social network literature, heterogeneous networks of contacts can be considered. A major issue is to assess the influence of the network in the dynamic model. Most work with this common purpose uses deterministic models or an approximation of a stochastic Extinction-Colonisation model (sEC) which are relevant only for large networks. When working with a limited size network, the induced stochasticity is essential and has to be taken into account in the conclusions. Here, a rigorous framework is proposed for limited size networks and the limitations of the deterministic approximation are exhibited. This framework allows exact computations when the number of patches is small. Otherwise, simulations are used and enhanced by adapted simulation techniques when necessary. A sensitivity analysis was conducted to compare four main topologies of networks in contrasting settings to determine the role of the network. A challenging case was studied in this context: seed exchange of crop species in the Réseau Semences Paysannes (RSP), an emergent French farmers׳ organisation. A stochastic Extinction-Colonisation model was used to characterize the consequences of substantial changes in terms of RSP׳s social organization on the ability of the system to maintain crop varieties.
authors.affiliation: AgroParisTech / UMR INRA MIA, F-75005 Paris, France; INRA, UMR 518, F-75005 Paris, France. Electronic address: pierre.barbillon@agroparistech.fr.
authors.forename: Pierre
authors.initials: P
authors.lastname: Barbillon
authors.affiliation: AgroParisTech / UMR INRA MIA, F-75005 Paris, France; INRA, UMR 518, F-75005 Paris, France; INRA, UMR 0320 / UMR 8120 Génétique Végétale, F-91190 Gif-sur-Yvette, France.
authors.forename: Mathieu
authors.initials: M
authors.lastname: Thomas
authors.affiliation: INRA, UMR 0320 / UMR 8120 Génétique Végétale, F-91190 Gif-sur-Yvette, France.
authors.forename: Isabelle
authors.initials: I
authors.lastname: Goldringer
authors.affiliation: INRA, UMR 1313 Génétique Animale et Biologie Intégrative, F-78352 Jouy-en-Josas, France.
authors.forename: Frédéric
authors.initials: F
authors.lastname: Hospital
authors.affiliation: AgroParisTech / UMR INRA MIA, F-75005 Paris, France; INRA, UMR 518, F-75005 Paris, France.
authors.forename: Stéphane
authors.initials: S
authors.lastname: Robin
mesh_terms: D005075:Biological Evolution; D004058:Diffusion; D005602:France; D008954:Models, Biological; D011157:Population Dynamics; D011336:Probability; D012639:Seeds / Q000502:physiology*; D014908:Triticum / Q000502:physiology
keywords: Farmer-to-farmer seed diffusion; Finite-population model; Metapopulation; Sensitivity analysis; Social network