Free Access
Math. Model. Nat. Phenom.
Volume 11, Number 4, 2016
Ecology, Epidemiology and Evolution
Page(s) 120 - 134
Published online 19 July 2016
  1. P. Auger, R. Bravo de la Parra, J.-C. Poggiale, E. Sánchez, T. Nguyen-Huu. Aggregation of variables and applications to population dynamics. In: P. Magal, S. Ruan (Eds.). Structured Population Models in Biology and Epidemiology. Lecture Notes in Mathematics 1936, Mathematical Biosciences Subseries, Springer Verlag, Berlin, 2008, 209–263. [Google Scholar]
  2. P. Auger, R. Bravo de la Parra, J.-C. Poggiale, E. Sánchez, L. Sanz. Aggregation methods in dynamical systems and applications in population and community dynamics. Phys. Life. Rev., 5(2) (2008), 79–105. [Google Scholar]
  3. R. Bravo de la Parra, M. Marvá, E. Sánchez and L. Sanz. Reduction of Discrete Dynamical Systems with Applications to Dynamics Population Models, Math. Model. Nat. Phenom., 8(6) (2013), 107–129. [Google Scholar]
  4. M.G. Bulmer. Periodical insects. Am. Nat., 111(982) (1977), 1099–1117. [CrossRef] [Google Scholar]
  5. R.S. Cantrell, S. Lenhart, Y. Lou, S. Ruan (Eds.). Special issue on movement and dispersal in ecology, epidemiology and environmental science. Discret Contin Dyn S B, 20(6) (2015). [Google Scholar]
  6. J.M. Cushing. An Introduction to Structured Population Dynamics, CBMS-NSF Regional Conference Ser. in Appl. Math Vol. 71. SIAM, Philadelphia, 1998. [Google Scholar]
  7. J.M. Cushing. Nonlinear semelparous Leslie models. Math. Biosci. Eng., 3(1) (2006), 17–36. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  8. J.M. Cushing. Three stage semelparous Leslie models. J. Math. Biol., 59 (2009), 75–104. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  9. J.M. Cushing. A dynamic dichotomy for a system of hierarchical difference equations. J. Difference Equ. Appl., 18(1) (2012), 1–26. [CrossRef] [MathSciNet] [Google Scholar]
  10. J.M. Cushing, S.M. Henson. Stable bifurcations in semelparous Leslie models. J. Biol. Dyn., 6(Suppl. 2) (2012), 80–102. [CrossRef] [Google Scholar]
  11. J.M. Cushing, J. Li. On Ebenman's model for the dynamics of a population with competing juveniles and adults. Bull. Math. Biol., 51(6) (1989), 687–713. [CrossRef] [Google Scholar]
  12. N.V. Davydova, O. Diekmann, S.A. van Gils. Year class coexistence or competitive exclusion for strict biennials? J. Math. Biol., 46 (2003), 95–131. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  13. Y. Iwasa, V. Andreasen, S. Levin. Aggregation in model ecosystems I: Perfect Aggregation. Ecol. Model., 37(3–4) (1987), 287–302. [CrossRef] [Google Scholar]
  14. R. Kon. Competitive exclusion between year-classes in a semelparous biennial population. In Mathematical Modeling of Biological Systems, A. Deutsch, R. Bravo de la Parra, R. de Boer, O. Diekmann, P. Jagers, E. Kisdi, M. Kretzschmar, P. Lansky, H. Metz, eds., Vol. II, Birkhäuser, Boston, MA, 2008, 79–90. [Google Scholar]
  15. R. Kon, Y. Iwasa. Single-class orbits in nonlinear Leslie matrix models for semelparous populations. J. Math. Biol., 55 (2007), 781–802. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  16. R. Kon, Y. Saito, Y. Takeuchi. Permanence of single-species stage-structured models. J. Math. Biol., 48 (2004), 515–528. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  17. Y. Iwasa, S. Levin, V. Andreasen. Aggregation in model ecosystems. II. Approximate Aggregation. J. Math. Appl. Med. Biol., 6(1) (1989), 1–23. [CrossRef] [MathSciNet] [Google Scholar]
  18. M.A. Lewis, P.K. Maini, S.V. Petrovskii (Eds.). Dispersal, Individual Movement and Spatial Ecology: A Mathematical Perspective. Springer-Verlag, Berlin, Heidelberg, 2013. [Google Scholar]
  19. H. Lischke, T.J. Löffler, P.E. Thornton, N.E. Zimmermann. Up-scaling of biological properties and models to the landscape level. In: F. Kienast, S. Ghosh, O. Wildi (Eds.). A Changing World: Challenges for Landscape Research. Landscape Series 8, Springer Verlag, Berlin, 2007, 273–296. [CrossRef] [Google Scholar]
  20. N.K. Luckyanov, Yu.M. Svirezhev, O.V. Voronkova. Aggregation of variables in simulation models of water ecosystems. Ecol. Model., 18(3–4) (1983), 235–240. [CrossRef] [Google Scholar]
  21. M.A. McCarthy, C.J. Thompson, H.P. Possingham. Theory for Designing Nature Reserves for Single Species. Am. Nat., 165(2) (2005), 250–257. [CrossRef] [PubMed] [Google Scholar]
  22. M. Marvá, E. Sánchez, R. Bravo de la Parra, L. Sanz. Reduction of slow-fast discrete models coupling migration and demography. J. Theor. Biol., 258(3) (2009), 371–379. [CrossRef] [PubMed] [Google Scholar]
  23. L. Sanz, R. Bravo de la Parra, E. Sánchez. Two time scales non-linear discrete models approximate reduction. J. Differ. Equ. Appl., 14(6) (2008), 607–627. [CrossRef] [MathSciNet] [Google Scholar]
  24. D. Tilman, P. Kareiva. Spatial Ecology. Princeton University Press, Princeton, 1997. [Google Scholar]
  25. G.M. Viswanathan, M.G.E. da Luz, E.P. Raposo, H.E. Stanley. The Physics of Foraging: An Introduction to Random Searches and Biological Encounters. Cambridge University Press, Cambridge, 2011. [Google Scholar]
  26. H.H. Wei, F. Lutscher. From Individual Movement Rules to Population Level Patterns: The Case of Central-Place Foragers. In M.A. Lewis, P.K. Maini, S.V. Petrovskii (Eds.). Dispersal, Individual Movement and Spatial Ecology: A Mathematical Perspective. Springer-Verlag, Berlin, Heidelberg, 2013, 159–175. [Google Scholar]

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