Species persistence decreases with habitat fragmentation: An analysis in periodic stochastic environments

Journal of Mathematical Biology

Volumn 55, Issue 2, 2007, Pages 189-205

  Roques, Lionel ^a   Stoica, Radu S ^b  

^a INRA   (France)

^b UNIVERSITÉ LILLE 1   (France)

Author keywords

Fragmentation; Gibbs measures; Reaction diffusion; Species conservation; Stochastic landscape models

Indexed keywords

ALGORITHM; ARTICLE; BIOLOGICAL MODEL; COMPUTER SIMULATION; ECOSYSTEM; NONLINEAR SYSTEM; POPULATION DYNAMICS; SPECIES EXTINCTION; STATISTICS;

ALGORITHMS; COMPUTER SIMULATION; ECOSYSTEM; EXTINCTION, BIOLOGICAL; MODELS, BIOLOGICAL; NONLINEAR DYNAMICS; POPULATION DYNAMICS; STOCHASTIC PROCESSES;

EID: 34547331298     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-007-0076-8     Document Type: Article

References (37)

1. Adams, R.A.: Sobolev Spaces. Academic, New York (1975)
2. Amann, H.: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev. 18, 620-709 (1976)
3. Baillie, J.E.M., Hilton-Taylor, C, Stuart, S.N. (eds): 2004IUCN Red List of Threatened Species. A Global Species Assessment. IUCN, Gland, Switzerland and Cambridge (2004)
4. Berestycki, H., Hamel, F.: Front propagation in periodic excitable media. Comm. Pure Appl. Math. 55, 949-1032 (2002)
5. Berestycki, H., Hamel, F., Roques, L.: Analysis of the periodically fragmented environment model : I - Species persistence. J. Math. Biol. 51(1), 75-113 (2005)
6. Berestycki, H., Hamel, F., Roques, L.: Analysis of the periodically fragmented environment model : II - Biological invasions and pulsating travelling fronts. J. Math. Pures Appl. 84(8), 1101-1146 (2005)
7. Berestycki, H., Hamel, F., Rossi, L.: Liouville type results for semilinear elliptic equations in unbounded domains. Ann. Mat. Pura Appl. (to appear) (2007)
8. Cantrell, R.S., Cosner, C.: Diffusive logistic equations with indefinite weights: population models in disrupted environments. Proc. Roy. Soc. Edinburgh 112, 293-318 (1989)
9. Cantrell, R.S., Cosner, C.: Diffusive logistic equations with indefinite weights: population models in disrupted environments II. SIAM J. Math. Anal. 22(4), 1043-1064 (1991)
10. Cantrell, R.S., Cosner, C.: The effects of spatial heterogeneity in population dynamics. J. Math. Biol. 29, 315-338 (1991)
11. Cantrell, R.S., Cosner, C.: Spatial ecology via reaction-diffusion equations. Series In: Mathematical and Computational Biology. Wiley, Chichester, Sussex (2003)
12. Chekroun, M.D., Roques, L.J.: Models of population dynamics under the influence of external perturbations: mathematical results. C. R. Acad. Sci. Paris, Ser. I 343, 307-310 (2006)
13. Ciarlet, P.G.: Numerical Analysis of the Finite Element Method. Seminaire de Mathematiques Supérieures 59, Les Presses de l'Universite de Montreal. Montreal (1976)
14. Engländer, J., Kyprianou, A.E.: Local extinction versus local exponential growth for spatial branching processes. Ann. Probab. 32, 78-99 (2004)
15. Fisher, R. A.: The advance of advantageous genes. Ann. Eugenics 7, 335-369 (1937)
16. Gardner, R.H., Milne, B.T., Turner, M.G., O'Neill, R.V.: Neutral models for the analysis of broad-scale landscape pattern. Landscape Ecol. 1(1), 19-28 (1987)
17. Gross, L.J., Rose, K. A., Rykiel, E.J., Van Winkle, W., Werner, E.E.: Individual-based modeling. In: DeAngelis, D.L., Gross, L.J. (eds.) Summary of a workshop. Individual-based Models and Approaches in Ecology: Populations, Communities, and Ecosystems, pp. 511-552. Routledge, Chapman and Hall, New York (1992)
18. Hastings, W.K.: Monte Carlo sampling methods using Markov Chains and their applications. Biometrika 57, 97-109 (1970)
19. Hess, P.: Periodic-parabolic boundary value problems and positivity. Pitman Research Notes in Mathematics Series, vol. 247. Longman Scientific & Technical, Harlow (1991)
20. Hutson, V., Mischaikow, K., Polacik, P.: The Evolution of dispersal rates in a heterogeneous time-periodic environment. J. Math. Biol. 43, 501-533 (2001)
21. Kareiva, P.M., Shigesada, N.: Analyzing insect movement as a correlated random walk. Oecologia 56, 234-238 (1983)
22. Keitt, T.H.: Spectral representation of neutral landscapes. Landscape Ecol. 15, 479-494 (2000)
23. 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 Université d'État à Moscou (Bjul. Moskowskogo Gos. Univ.), Série internationale A 1:1-26 (1937)
24. Marsh, L.M., Jones, R.E.: The form and consequences of random walk movement models. J. Theor. Biol. 133, 113-131 (1988)
25. Metropolis, N., Rosenbluth, A.W., Rosenbluth, N.M., Teller, A.H., Teller, E.: Equation of state calculations for fast computing machines. J. Chem. Phys. 21, 1087-1092 (1953)
26. Murray, J.D.: Mathematical Biology. Second corrected edition. Springer, Heidelberg (1993)
27. Okubo, A., Levin, S.A.: Diffusion and Ecological Problems - Modern Perspectives, 2nd edn. Springer, Heidelberg (2002)
28. Palmer, M.W.: The coexistence of species in fractal landscapes. Am. Nat. 139, 375-397 (1992)
29. Robert, C.P., Casella, G.: Monte Carlo statistical methods. Springer, Heidelberg (1999)
30. Roques, L., Hamel, F.: On optimal habitat configurations for species persistence. INRA research report RR2006_25 (2006)
31. Saunders, D.A., Hobbs, R.J., Margules, C.R.: Biological consequences of ecosystem fragmentation: a review. Conserv. Biol. 51, 18-32 (1991)
32. Shigesada, N., Kawasaki, K.: Biological invasions: theory and practice. Oxford Series in Ecology and Evolution. Oxford University Press, Oxford (1997)
33. Shigesada, N., Kawasaki, K., Teramoto, E.: Traveling periodic waves in heterogeneous environments. Theor. Popul. Biol. 30, 143-160 (1986)
34. Sprent, P.: Applied Nonparametric Statistical Methods, 2nd edn. Chapman and Hall, London (1993)
35. Stoyan, D., Kendall, W.S., Mecke, J.: Stochastic Geometry and its Applications, 2nd edn. Wiley Series in Probability and Statistics. Wiley, Chichester (1995)
36. Turchin, P.: Quantitative Analysis of Movement: Measuring and Modeling Population Redistribution in Animals and Plants. Sinauer Associates, Sunderland (1998)
37. With, K.A., King, A.W.: Extinction thresholds for species in fractal landscapes. Conserv. Biol. 13, 314-326 (1999)