×

Network impact on persistence in a finite population dynamic diffusion model: application to an emergent seed exchange network. (English) Zbl 1314.92095

Summary: 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.

MSC:

92C80 Plant biology
92D25 Population dynamics (general)

Software:

igraph
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Abay, F.; de Boef, W.; Bjørnstad, A., Network analysis of barley seed flows in Tigray, Ethiopiasupporting the design of strategies that contribute to on-farm management of plant genetic resources, Plant Genet. Resour., 9, 495-505 (2011)
[2] Adler, F.; Nuernberger, B., Persistence in patchy irregular landscapes, Theor. Popul. Biol., 45, 41-75 (1994) · Zbl 0792.92024
[3] Albert, R.; Barabási, A. L., Statistical mechanics of complex networks, Rev. Mod. Phys., 74, 47-97 (2002) · Zbl 1205.82086
[4] Amrein, M.; Künsch, H. R., A variant of importance splitting for rare event estimationfixed number of successes, ACM Trans. Model. Comput. Simul., 21 (2011), 13:1-13:20 · Zbl 1490.62210
[5] Aw-Hassan, A.; Mazid, A.; Salahieh, H., The role of informal farmer-to-farmer seed distribution in diffusion of new barley varieties in Syria, Exp. Agric., 44, 413-431 (2008)
[6] Barabási, A. L.; Albert, R., Emergence of scaling in random networks, Science, 286, 509-512 (1999) · Zbl 1226.05223
[7] Bocci, R.; Chable, V., Peasant seeds in Europestakes and prospects, Cah. Agric., 17, 216-221 (2008)
[8] Calvet-Mir, L.; Calvet-Mir, M.; Molina, J. L.; Reyes-García, V., Seed exchange as an agrobiodiversity conservation mechanism. a case study in Vail Fosca, Catalan Pyrenees, Iberian Peninsula, Ecol. Soc., 17, 29 (2012)
[9] Cator, E.; Van Mieghem, P., Susceptible-infected-susceptible epidemics on the complete graph and the star graphexact analysis, Phys. Rev. E, 87, 012811 (2013)
[10] Chakrabarti, D.; Wang, Y.; Wang, C.; Leskovec, J.; Faloutsos, C., Epidemic thresholds in real networks, ACM Trans. Inf. Syst. Secur., 10 (2008), 1:1-1:26
[11] Csardi, G.; Nepusz, T., The igraph software package for complex network research, Int. J. Complex Syst., 1695 (2006)
[12] Darroch, J.; Seneta, E., On quasi-stationary distributions in absorbing discrete-time finite markov chains, J. Appl. Probab., 4 (1967) · Zbl 0168.16303
[13] Darroch, J. N.; Seneta, E., On quasi-stationary distributions in absorbing discrete-time finite Markov chains, J. Appl. Probab., 2, 88-100 (1965) · Zbl 0134.34704
[14] Day, J. R.; Possingham, H. P., A stochastic metapopulation model with variability in patch size and position, Theor. Popul. Biol., 48, 333-360 (1995) · Zbl 0840.92025
[16] Demeulenaere, E.; Bonneuil, C., Des Semences en partageconstruction sociale et identitaire d׳un collectif “paysan” autour de pratiques semencières alternatives, Tech. Culture, 57, 202-221 (2011)
[17] Demeulenaere, E.; Bonneuil, C.; Balfourier, F.; Basson, A.; Berthellot, J.; Chesneau, V.; Ferté, H.; Galic, N.; Kastler, G.; Koening, J.; Mercier, F.; Payement, J.; Pommart, A.; Ronot, B.; Rousselle, Y.; Supiot, N.; Zaharia, H.; Goldringer, I., Étude des complémentarités entre gestion dynamique à la ferme et gestion statique en collectionCas de la variété de blé Rouge de Bordeaux, Les Actes du BRG, 7, 117-138 (2008)
[18] van Doorn, E.; Pollett, P., Quasi-stationary distributions for reducible absorbing Markov chains in discrete time, Markov Process. Relat. Fields, 15, 191-204 (2009) · Zbl 1184.60026
[19] Eloy, L.; Emperaire, L., La circulation de l׳agrobiodiversité sur les fronts pionniers d׳Amazonie (région de Cruzeiro do Sul, état de l׳Acre, Brésil), L׳Espace géographique, 40, 62-74 (2011)
[20] Erdös, P.; Rényi, A., On random graphs, I, Publ. Math. Debr., 6, 290-297 (1959) · Zbl 0092.15705
[21] Franc, A., Metapopulation dynamics as a contact process on a graph, Ecol. Complex., 1, 49-63 (2004)
[22] Gilarranz, L. J.; Bascompte, J., Spatial network structure and metapopulation persistence, J. Theor. Biol., 297, 11-16 (2012)
[23] Hanski, I.; Ovaskainen, O., The metapopulation capacity of a fragmented landscape, Nature, 404, 755-758 (2000)
[24] Hill, A. L.; Rand, D. G.; Nowak, M. A.; Christakis, N. A., Emotions as infectious diseases in a large social networkthe SISa model, Proc. R. Soc. B, 277, 3827-3835 (2010)
[25] Kawa, N. C.; McCarty, C.; Clement, C. R., Manioc varietal diversity, social networks, and distribution constraints in rural Amazonia, Curr. Anthropol., 54, 764-770 (2013)
[26] Levins, R., Some demographic and genetic consequences of environmental heterogeneity for biological control, Bull. ESA, 237-240 (1969)
[27] Li, C.; van de Bovenkamp, R.; Van Mieghem, P., Susceptible-infected-susceptible modela comparison of N-intertwined and heterogeneous mean-field approximations, Phys. Rev. E, 86, 026116 (2012)
[28] Méléard, S.; Villemonais, D., Quasi-stationary distributions and population processes, Probab. Surv., 9, 340-410 (2012) · Zbl 1261.92056
[29] Nowicki, K.; Snijders, T. A.B., Estimation and prediction for stochastic blockstructures, J. Am. Stat. Assoc., 96, 1077-1087 (2001) · Zbl 1072.62542
[30] Pastor-Satorras, R.; Vespignani, A., Epidemic dynamics and endemic states in complex networks, Phys. Rev. E, 63, 066117 (2001)
[31] Pautasso, M.; Aistara, G.; Barnaud, A.; Caillon, S.; Clouvel, P.; Coomes, O. T.; Delêtre, M.; Demeulenaere, E.; Santis, P. D.; Döring, T.; Eloy, L.; Emperaire, L.; Garine, E.; Goldringer, I.; Jarvis, D.; Joly, H. I.; Leclerc, C.; Louafi, S.; Martin, P.; Massol, F.; McGuire, S.; McKey, D.; Padoch, C.; Soler, C.; Thomas, M.; Tramontini, S., Seed exchange networks for agrobiodiversity conservation. A review, Agron. Sust. Dev., 33, 151-175 (2013)
[32] Peyrard, N.; Dieckmann, U.; Franc, A., Long-range correlations improve understanding of the influence of network structure on contact dynamics, Theor. Popul. Biol., 73, 383-394 (2008) · Zbl 1210.92043
[33] Read, J. M.; Eames, K. T.D.; Edmunds, W. J., Dynamic social networks and the implications for the spread of infectious disease, J. R. Soc. Interface, 5, 1001-1007 (2008)
[34] Reyes-Garcéa, V.; Molina, J. L.; Calvet-Mir, L.; Aceituno-Mata, L.; Lastra, J. J.; Ontillera, R.; Parada, M.; Pardo-de Santayana, M.; Rigat, M.; Vallès, J., “ Tertius gaudens”Germplasm exchange networks and agroecological knowledge among home gardeners in the Iberian Peninsula, J. Ethnobiol. Ethnomed., 9, 1-11 (2013)
[35] (Rubino, G.; Tuffin, B., Rare Event Simulation using Monte Carlo Methods (2009), John Wiley and Sons: John Wiley and Sons Chichester, West Sussex, UK) · Zbl 1159.65003
[36] Solé, R. V.; Bascompte, J., Self-Organization in Complex Ecosystems (2006), Princeton University Press: Princeton University Press Princeton, New Jersey, USA
[37] Subedi, A.; Chaudhary, P.; Baniya, B. K.; Rana, R. B.; Tiwari, R. K.; Rijal, D. K.; Sthapit, B. R.; Jarvis, D., Who maintains crop genetic diversity and how?implications for on-farm conservation and utilization, Culture Agric., 25, 41-50 (2003)
[38] Thomas, M.; Dawson, J. C.; Goldringer, I.; Bonneuil, C., Seed exchanges, a key to analyze crop diversity dynamics in farmer-led on-farm conservation, Genet. Resour. Crop Evol., 58, 321-338 (2011)
[39] Thomas, M.; Demeulenaere, E.; Dawson, J. C.; Khan, A. R.; Galic, N.; Jouanne-Pin, S.; Remoue, C.; Bonneuil, C.; Goldringer, I., On-farm dynamic management of genetic diversitythe impact of seed diffusions and seed saving practices on a population-variety of bread wheat, Evol. Appl., 5, 779-795 (2012)
[40] Van Mieghem, P., The N-intertwined SIS epidemic network model, Computing, 93, 147-169 (2011) · Zbl 1293.68041
[41] Van Mieghem, P.; Cator, E., Epidemics in networks with nodal self-infection and the epidemic threshold, Phys. Rev. E, 86, 016116 (2012)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.