Free Access
Issue
Math. Model. Nat. Phenom.
Volume 5, Number 6, 2010
Ecology (Part 2)
Page(s) 38 - 69
DOI https://doi.org/10.1051/mmnp/20105603
Published online 08 April 2010
  1. J.A. AlonsoL. Sanz. Aproximating the Distribution of Population Size in Stochastic Multiregional Matrix Models withFast Migration. Phil. Trans. R. Soc. A, 367 (2009), 4801-4827. [CrossRef] [Google Scholar]
  2. K. B. Athreya, P. E. Ney. Branching processes. Springer-Verlag, Berlin, 1972. [Google Scholar]
  3. P. Auger. Dynamics and Thermodynamics in Hierarchically Organized Systems, Applications in Physics, Biology and Economics. Pergamon Press, Oxford, 1989. [Google Scholar]
  4. P. AugerR. Roussarie. Complex ecological models with simple dynamics: from individuals to populations. Acta Biotheoretica, 42 (1994), 111-136. [CrossRef] [Google Scholar]
  5. P. AugerJ.C. Poggiale. Aggregation and Emergence in Systems of Ordinary Differential Equations. Mathematical Computer Modelling, 27 (1998), 1-22. [Google Scholar]
  6. P. Auger, M Rachid, C. Tanmay, S. Gauthier, T. MauriceC. Joydev. Effects of a disease affecting a predator on the dynamics of a predator-prey system. Journal of theoretical biology, 258 (2009), 344-351. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  7. P. Auger, C. Lett. Integrative Biology: Linking Levels of Organization. Comptes Rendus de l’Académie des Sciences Biologies, 326 (2003):517-522. [CrossRef] [Google Scholar]
  8. P. Auger, R. Bravo de la Parra, J.C. Poggiale, E. SánchezL. Sanz. Aggregation methods in dynamical systems variables and applications in population and community dynamics. Physics of Life Reviews, 5 (2008), 79-105. [CrossRef] [Google Scholar]
  9. N. BerglundB. Gentz. Geometric singular perturbation theory for stochastic differential equations. J. Diff. Equat., 191 (2003), 1-54. [CrossRef] [Google Scholar]
  10. J.D. Biggins, H. CohnO. Nerman. Multi-type branching in varying environment. Stoc. Proc. Appl., 83 (1999), 357-400. [CrossRef] [Google Scholar]
  11. A. Blasco, L. Sanz, P. Auger, R. Bravo de la Parra. Linear Discrete Population Models with Two Time Scales in Fast Changing Environments I: Autonomous Case. Acta Biotheoretica, 49 (2001), 261-276. [CrossRef] [PubMed] [Google Scholar]
  12. A. Blasco, L. Sanz, P. AugerR. Bravo de la Parra. Linear Discrete Population Models with Two Time Scales in Fast Changing Environments II: Non Autonomous Case. Acta Biotheoretica, 1 (2002), 15-38. [CrossRef] [Google Scholar]
  13. A. Blasco, L. Sanz, R. Bravo de la Parra. Approximate reduction of multiregional birth-death models with fast migration. Mathematical and Computer Modelling, 36 (2002), 47-65. [CrossRef] [MathSciNet] [Google Scholar]
  14. G. L BlockL. J. S. Allen. Population extinction and quasi-stationary behavior in stochastic density-dependent structured models. Bull. Math. Bio., 62 (2000), 199-228. [CrossRef] [Google Scholar]
  15. R. Bravo, P. AugerE. Sánchez. Aggregation methods in discrete Models, J. Biol. Sys., 3 (1995), 603-612. [CrossRef] [Google Scholar]
  16. R. Bravo de la Parra, E. Sánchez, O. ArinoP. Auger. A Discrete Model with Density Dependent Fast Migration. Mathematical Biosciences, 157 (1999), 91-110. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  17. H. Caswell, M. FujiwaraS. Brault. Declining survival probability threatens the North Atlantic right whale. Proc. Natl. Acad. Sci. USA, 96 (1999), 3308-3313. [CrossRef] [Google Scholar]
  18. H. Caswell. Matrix population models (2nded.). Sinauer Associates, Sunderland, Massachusetts, 2001. [Google Scholar]
  19. S. Charles, R. Bravo de la Parra, J.P. Mallet, H. PersatP. Auger. Population dynamics modelling in an hierarchical arborescent river network: an attempt with Salmo trutta. Acta Biotheoretica, 46 (1998), 223-234. [CrossRef] [Google Scholar]
  20. S. Charles, R. Bravo de la Parra , J.P. Mallet, H. Persat, P. Auger. A density dependent model describing Salmo trutta population dynamics in an arborescent river network: effects of dams and channelling. C. R. Acad. Sci. Paris, Sciences de la vie, 321 (1998), 979-990. [Google Scholar]
  21. S. Charles, R. Bravo de la Parra, J.P. Mallet, H. PersatP. Auger. Annual spawning migrations in modeling brown trout population dynamics inside an arborescent river network. Ecological Modelling, 133 (2000), 15-31. [CrossRef] [Google Scholar]
  22. A. Chaumot, S. Charles, P. Flammarion, P. Auger. Do Migratory or Demographic Disruptions Rule the Population Impact of Pollution in Spatial Networks?. Theoretical Population Biology, 64 (2003), 473-480. [CrossRef] [PubMed] [Google Scholar]
  23. J. E. Cohen. Ergodicity of Age Structure in Populations with Markovian Vital Rates, II, General States. Advances in Appl. Probability, 9 (1977), 18-37. [CrossRef] [MathSciNet] [Google Scholar]
  24. J. E. Cohen. Ergodics Theorems of Demography. Bulletin of the American Mathematical Society N.S., 1 (1979), 275-295. [CrossRef] [Google Scholar]
  25. J. E. Cohen. Multiregional age structured populations with changing vital rates: weak and strong stochastic ergodic theorems. In Land, K.C., A. Rogers editors. Multiregional mathematical demography. Academic Press, New York, 477-503, 1982. [Google Scholar]
  26. J.E. Cohen, S.W. ChristensenC.P. Goodyear. A stochastic age-structured model of Striped Bass (Morone saxatilis) in the Potomac River. Can. J. Fish. Aquat. Sci., 40 (1983), 2170-2183. [CrossRef] [Google Scholar]
  27. H. FurstenbergH. Kesten. Products of Random Matrices. Ann. Math. Statist. 31 (1960), 457-469. [CrossRef] [MathSciNet] [Google Scholar]
  28. T.C. Gard. Aggregation in stochastic ecosystem models. Ecol. Modelling, 44 (1988), 153-164. [CrossRef] [Google Scholar]
  29. P. Haccou, P. Jagers, V. Vatutin. Branching processes: Variation, growth, and extinction of populations, Cambridge University Press, 2005. [Google Scholar]
  30. T. Harris. The theory of branching processes, Springer-Verlag, Berlín, 1963. [Google Scholar]
  31. C.C. Heyde, J. E. Cohen. Confidence Intervals for Demographic Projections Based on Products of Random Matrices. Theoretical Population Biology 27 (1985), 120-153. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  32. K. E. Holsinger. Demography and extinction in small populations, in: Genetics, demography and the viability of fragmented populations, eds. A. Young, G. Clarke, Cambridge University Press, 2000. [Google Scholar]
  33. R. Horn, C. Johnson. Matrix Analysis. Cambridge Univ. Press, 1985. [Google Scholar]
  34. Y. Iwasa, V. AndreasenS. Levin. Aggregation in model ecosystems I: Perfect Aggregation. Ecological Modeling, 37 (1987), 287-302. [CrossRef] [Google Scholar]
  35. A. Joffe, F. Spitzer. On multitype branching processes with ρ ≤ 1. Journal of Mathematical Analysis and Its Applications, 19 (1967), 409-430. [CrossRef] [Google Scholar]
  36. M. Khaladi, V. GrosboisJ. D. Lebreton. An explicit approach to evolutionarily stable dispersal strategies with a cost of dispersal. Nonlinear Anal.: Real World Appl., 1 (2000), 137–144. [CrossRef] [MathSciNet] [Google Scholar]
  37. M. Kimmel, D.E. Axelrod. Branching Processes in Biology, Springer, New York, 2002. [Google Scholar]
  38. F. Klebaner, Population Size Dependent Processes. In: Branching Processes: Variation, Growth and Extinction of Populations, P. Haccou, P. Jagers and V.A. Vatutin, 133-135, Cambridge University Press, 2005. [Google Scholar]
  39. S. Legendre, J. Clobert, A. P. MollerG. Sorci. Demographic stochasticity and social mating system in the process of extinction of small populations: the case of passerines introduced to New Zealand. The American Naturalist, 153 (1999), 449-463. [CrossRef] [PubMed] [Google Scholar]
  40. C. Lett, P. AugerR. Bravo de la Parra. Migration Frequency and the Persistence of Host-Parasitoid Interactions. Journal of Theoretical Biology, 221 (2003), 639-654. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  41. C. Lett, P. AugerF. Fleury. Effects of asymmetric dispersal and environmental gradients on the stability of host-parasitoid systems. Oikos, 109 (2005), 603-613. [CrossRef] [Google Scholar]
  42. K.L. Liaw. Multistate dynamics: the convergence of an age-by-region population system. Environment and Planning A, 12 (1980), 589-613. [CrossRef] [Google Scholar]
  43. L. Liaw. Spatial Popuylation Dynamics. In Migration and Settlement: A multiregional comparative study; A. Rogers, Willekens eds, 419-455. Dordrecht, D. Reidel, 1986. [Google Scholar]
  44. M. Marvá, E. Sánchez, R. Bravo de la ParraL. Sanz. Reduction of slow–fast discrete models coupling migration and demography. Journal of Theoretical Biology, 258 (2009), 371-379. [CrossRef] [PubMed] [Google Scholar]
  45. C.J. Mode. Multitype Branching Processes. Theory and Applications. American Elsevier Publishing Co., Inc., New York, 1971. [Google Scholar]
  46. M. A. Rincón, J.A. AlonsoL. Sanz. Supercritical multiregional stochastic models with fast migration. Acta Biotheoretica, 57 (2009), 479-500. [CrossRef] [PubMed] [Google Scholar]
  47. A. Rogers. Shrinking large-scale population projection models by aggregation and decomposition. Environment and Planning A, 8 (1976), 515-541. [CrossRef] [Google Scholar]
  48. A. Rogers. Multiregional Demography, Chichester, New York, 1995. [Google Scholar]
  49. J. M. Saboia. Arima models for birth forecasting. Journal of the American Statistical Association, 72 (1977), 264-270. [CrossRef] [Google Scholar]
  50. E. Sánchez, R. Bravo de la Parra, P. Auger. Linear discrete models with different time scales. Acta Bio., 43 (1995), 465-479. [Google Scholar]
  51. L. SanzR. Bravo de la Parra. Variables Aggregation in Time Varying Discrete Systems. Acta Biotheoretica, 46 (1998), 273-297. [CrossRef] [Google Scholar]
  52. L. SanzR. Bravo de la Parra. Variables aggregation in a time discrete linear model. Math. Biosc. 157 (1999), 111-146. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  53. L. SanzR. Bravo de la Parra. Time scales in stochastic multiregional models. Nonlinear Analysis: Real World Applications, 1 (2000), 89-122. [CrossRef] [MathSciNet] [Google Scholar]
  54. L. SanzR. Bravo de la Parra. Time scales in a non autonomous linear discrete model. Mathematical Models and Methods in Applied Sciences, 11 (2001), 1-33. [CrossRef] [MathSciNet] [Google Scholar]
  55. L. Sanz, R. Bravo de la Parra. Approximate Reduction Techniques in Population Models with Two Time Scales: Study of the Approximation, Acta Biotheoretica, 50 (2002), 297-322. [CrossRef] [PubMed] [Google Scholar]
  56. L. Sanz, A. Blasco and R. Bravo de la Parra, Approximate reduction of Galton-Watson processes with two time scales, Mathematical Models and Methods in Applied Sciences 13:491-525, 2003. [CrossRef] [MathSciNet] [Google Scholar]
  57. L. SanzR. Bravo de la Parra. Approximate reduction of multiregional models with environmental stochasticity. Mathematical Biosciences, 206 (2007), 134-154. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  58. L. Sanz, R. Bravo de la Parra, E. Sánchez. Approximate Reduction of Non-Linear Discrete Models with Two Time Scales. Journal of Difference Equations and Applications, 14 (2008), 607-627. [CrossRef] [MathSciNet] [Google Scholar]
  59. G.W. Stewart, J.I. Guang Sun. Matrix Perturbation Theory, Academic Press, Boston, 1990. [Google Scholar]
  60. Z. M. Sykes. Some stochastic versions of the matrix model for population dynamics. J. Amer. Statist. Assoc., 64 (1969), 111-130. [CrossRef] [MathSciNet] [Google Scholar]
  61. T. Nguyen-Huu, C. Lett, P. Auger P. J.C. Poggiale. Spatial synchrony in host-parasitoid models using aggregation of variables. Mathematical Biosciences, 203 (2006), 204-221. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  62. T. Nguyen-Huu, P. Auger, C. Lett, M. Marvá. Emergence of global behaviour in a host-parasitoid model with density-dependent dispersal in a chain of patches. Ecological Complexity, 5 (2008), 9-21. [CrossRef] [Google Scholar]
  63. S. Tuljapurkar, S. Orzack. Population dynamics in variable environments. I. Long-run growth rates and extinction. Theor. Popul. Biol., 18 (1980) 314–342. [CrossRef] [Google Scholar]
  64. S. Tuljapurkar. Demography in stochastic environments. I. Exact distributions of age structure. J. Math. Biol., 19 (1984), 335-350. [MathSciNet] [PubMed] [Google Scholar]
  65. S. Tuljapurkar. Population Dynamics in Variable Environments, Springer-Verlag, Berlin, 1990. [Google Scholar]
  66. S. Tuljapurkar, H. Caswell (eds). Structured-Population Models in Marine, Terrestrial, and Freshwater Systems, Chapman and Hall, New York, 1997. [Google Scholar]
  67. G. Wang, W. D. EdgeJ. O. Wolff. Demographic uncertainty in ecological risk assessments. Ecological Modelling, 136 (2001), 95-102. [CrossRef] [Google Scholar]

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