A statistical-reaction-diffusion approach for analyzing expansion processes

Journal of Theoretical Biology

Volumn 274, Issue 1, 2011, Pages 43-51

  Roques, Lionel ^a   Soubeyrand, Samuel ^a   Rousselet, Jérôme ^b  

^a INRA   (France)

^b Inst Natl de la Rech Agronom   (France)

Author keywords

Bayesian inference; Mechanistic statistical model; Pine processionary moth; Reaction diffusion; Species range

Indexed keywords

BAYESIAN ANALYSIS; INVASIVE SPECIES; NUMERICAL MODEL; POPULATION DYNAMICS; RANGE EXPANSION; SPATIAL VARIATION; STATISTICAL ANALYSIS;

ARTICLE; BAYES THEOREM; DIFFUSION; ENVIRONMENTAL FACTOR; FRANCE; GEOGRAPHICAL VARIATION (SPECIES); LIFE CYCLE; MOTH; PINE; POPULATION GROWTH; PRIORITY JOURNAL; STATISTICAL ANALYSIS; STATISTICAL MODEL;

ANIMAL MIGRATION; ANIMALS; BAYES THEOREM; DIFFUSION; FRANCE; INTRODUCED SPECIES; LIFE CYCLE STAGES; LIKELIHOOD FUNCTIONS; MODELS, BIOLOGICAL; MODELS, STATISTICAL; MOTHS; PINUS; TIME FACTORS;

FRANCE;

THAUMETOPOEA PITYOCAMPA;

EID: 78951482249     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2011.01.006     Document Type: Article

References (39)

1. Allee W.C. The Social Life of Animals 1938, Norton, New York.
2. Battisti A., Stastny M., Netherer S., Robinet C., Schopf A., Roques A., Larsson S. Expansion of geographic range in the pine processionary moth caused by increased winter temperatures. Ecological Applications 2005, 15:2084-2096.
3. Berliner L.M. Physical-statistical modeling in geophysics. Journal of Geophysical Research 2003, 108:8776.
4. Cristofol M., Roques L. Biological invasions: deriving the regions at risk from partial measurements. Mathematical Biosciences 2008, 215:158-166.
5. Dennis B. Allee effects: population growth, critical density, and the chance of extinction. Natural Resource Modeling 1989, 3:481-538.
6. Doutre M.S. Occupational contact urticaria and protein contact dermatitis. European Journal of Dermatology 2005, 15:419-424.
7. Fisher R.A. The wave of advance of advantageous genes. Annals of Eugenics 1937, 7:335-369.
8. Gross L.J., Rose K.A., Rykiel E.J., Van Winkle W., Werner E.E. Individual-based Modeling 1992, Chapman and Hall, New York, pp. 511-552.
9. Hamel F., Fayard J., Roques L. Spreading speeds in slowly oscillating environments. Bulletin of Mathematical Biology 2010, 72:1166-1191.
10. Hamel F., Roques L. Fast propagation for KPP equations with slowly decaying initial conditions. Journal of Differential Equations 2010, 249:1726-1745.
11. Hastings W.K. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 1970, 57:97-109.
12. Huchon, H., Demolin, G., 1970. La bioécologie de la processionnaire du pin. Dispersion potentielle - Dispersion actuelle. Revue Forestière Française Numéro spécial "La lutte biologique en forĉt", 220-234.
13. Kareiva P.M. Local movement in herbivorous insects: applying a passive diffusion model to mark-recapture field experiments. Oecologia 1983, 57:322-327.
14. Kareiva P.M., Shigesada N. Analyzing insect movement as a correlated random-walk. Oecologia 1983, 56:234-238.
15. Kawasaki K., Shigesada N. An integrodifference model for biological invasions in a periodically fragmented environment. Japan Journal of Industrial and Applied Mathematics 2007, 24:3-15.
16. Klein E.K., Desassis N., Oddou-Muratorio S. Pollen flow in the wildservice tree, Sorbus torminalis (L.) Crantz. Whole inter-individual variance of male fecundity estimated jointly with dispersal kernel. Molecular Ecology 2008, 17:3323-3336.
17. Kolmogorov A.N., Petrovsky I.G., Piskunov N.S. Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique. Bulletin de l'Université d'État de Moscou, Série Internationale A 1937, 1:1-26.
18. Kot M., Lewis M., van den Driessche P. Dispersal data and the spread of invading organisms. Ecology 1996, 77:2027-2042.
19. Manly B.F.J. Randomization Bootstrap and Monte Carlo Methods in Biology 1997, Chapman and Hall, London. second ed.
20. Marsh L.M., Jones R.E. The form and consequences of random-walk movement models. Journal of Theoretical Biology 1988, 133:113-131.
21. Metropolis N., Rosenbluth A.W., Rosenbluth N.M., Teller A.H., Teller E. Equation of state calculations for fast computing machines. Journal of Chemical Physics 1953, 21:1087-1092.
22. Murray J.D. Mathematical biology. Interdisciplinary Applied Mathematics, third ed. 2002, 17. Springer-Verlag, New York.
23. Okubo A., Levin S.A. Diffusion and ecological problems-modern perspectives 2002, Springer-Verlag, New York. second ed.
24. Pérez-Contreras T., Soler J.J., Soler M. Why do pine processionary caterpillars Thaumetopoea pityocampa (Lepidoptera, Thaumetopoeidae) live in large groups? An experimental study. Annales Zoologici Fennici 2003, 40:505-515.
25. Protter M.H., Weinberger H.F. Maximum Principles in Differential Equations 1967, Prentice-Hall, Englewood Cliffs, NJ.
26. Réaumur R.A.F. Mémoires pour servir à l'histoire des insectes, Tome second 1736, Imprimerie Poyale, Paris.
27. Robinet, C., 2006. Mathematical modelling of invasion processes in ecology: the pine processionary moth as a case study. Ph.D. Thesis, CAMS, EHESS, Paris.
28. Robinet C., Baier P., Josef P., Schopf A., Roques A. Modelling the effects of climate change on the potential feeding activity of thaumetopoea pityocampa (den. & schiff.) (lep., notodontidae in france). Global Ecology and Biogeography 2007, 16:460-471.
29. Robinet, C., Imbert, C.-E., Rousselet, J., Sauvard, D., Garcia, J., Goussard, F., Roques, A., in press Human mediated long distance jumps of an urticating insect. Preprint.
30. Roques L., Auger-Rozenberg M.A., Roques A. Modelling the impact of an invasive insect via reaction-diffusion. Mathematical Biosciences 2008, 216:47-55.
31. Roques L., Cristofol M. On the determination of the nonlinearity from localized measurements in a reaction-diffusion equation. Nonlinearity 2010, 23:675-686.
32. Roques L., Hamel F., Fayard J., Fady B., Klein E.K. Recolonisation by diffusion can generate increasing rates of spread. Theoretical Population Biology 2010, 77:205-212.
33. Shigesada N., Kawasaki K. Biological Invasions: Theory and Practice. Oxford Series in Ecology and Evolution 1997, Oxford University Press, Oxford.
34. Soubeyrand S., Laine A.L., Hanski I., Penttinen A. Spatio-temporal structure of host-pathogen interactions in a metapopulation. The American Naturalist 2009, 174:308-320.
35. Soubeyrand S., Neuvonen S., Penttinen A. Mechanical-statistical modeling in ecology: from outbreak detections to pest dynamics. Bulletin of Mathematical Biology 2009, 71:318-338.
36. Spiegelhalter D.J., Best N.G., Carlin B.P., van der Linde A. Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B 2002, 64:583-639.
37. Turchin P. Quantitative Analysis of Movement: Measuring and Modeling Population Redistribution in Animals and Plants 1998, Sinauer Associates, Sunderland, MA.
38. Veit R.R., Lewis M.A. Dispersal, population growth, and the Allee effect: dynamics of the house finch invasion of eastern North America. American Naturalist 1996, 148:255-274.
39. Wikle C.K. Hierarchical models in environmental science. International Statistical Review 2003, 71:181-199.