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All issues Volume 4 / No 6 (2009) Math. Model. Nat. Phenom., 4 6 (2009) 54-90 References
Free Access
Issue
Math. Model. Nat. Phenom.
Volume 4, Number 6, 2009
Ecology (Part 1)
Page(s) 54 - 90
DOI https://doi.org/10.1051/mmnp/20094602
Published online 27 November 2009
  1. P.A. Abrams. Adaptive dynamics: Neither F nor G. Evol. Ecol. Res., 3 (2001), 369–373. [Google Scholar]
  2. P.A. Abrams, H. Matsuda. Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits. Evol. Ecol., 7 (1993), 465–487. [CrossRef] [Google Scholar]
  3. D. Alonso, F. Bartumeus, J. Catalan. Mutual interference between predators can give rise to Turing spatial patterns. Ecology, 83 (2002), 28–34. [CrossRef] [Google Scholar]
  4. H. Anton.and C. Rorres. Elementary linear algebra: applications version. 8th Edition. John Wiley & Sons, New York, 2000. [Google Scholar]
  5. J. Apaloo. Revisting strategic models of evolution: The concept of neighborhood invader strategies. Theor. Pop. Biol.,52 (1997), 71–77. [Google Scholar]
  6. N.F. Britton. Reaction-diffusion equations and their applications to biology. Academic Press, New York, 1986. [Google Scholar]
  7. J.S. Brown, N.B. Pavlovic. Evolution in heterogeneous environments - effects of migtation on habitat specialization. Evol. Ecol. 6 (1992),360–382. [Google Scholar]
  8. J.S. Brown, T.L. Vincent. A theory for the evolutionary game. Theor. Pop. Biol., 31 (1987), 140–166. [CrossRef] [Google Scholar]
  9. J.S. Brown, T.L. Vincent. Organiztion of predator-prey communities as an evolutionary game. Evolution, 46 (1992), 1269–1283. [CrossRef] [PubMed] [Google Scholar]
  10. R.G. Casten, C.J. Holland. Stability properties of solutions of systems of reaction-diffusion equations. SIAM J. Appl. Math. 33 (1977), 353–364. [Google Scholar]
  11. Y. Cohen, J. Pastor, T.L. Vincent. Evolutionary strategies and nutrient cycling in ecosystems. Evol. Ecol. Res., 2 (2000), 719–743. [Google Scholar]
  12. Y. Cohen, T.L. Vincent, J.S. Brown. A G-function approach to fitness minima, fitness maxima, evolutionarily stable strategies and adaptive landscapes. Evol. Ecol. Res., 1 (1999), 923–942. [Google Scholar]
  13. R. Cressman, G.T. Vickers. Spatial and density effects in evolutionary game theory. Math. Biol., 184 (1997), 359–369. [Google Scholar]
  14. U. Dieckmann, R. Law. The dynamical theory of coevolution: A derivation from stochastic ecological processes. J. Math. Biol., 34 (1996), 579–612. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  15. R. Durrett, S. Levin. The importance of being discrete (and spatial). Theor. Pop. Biol., 46 (1994), 363–394. [Google Scholar]
  16. R. Durrett, S. Levin. Allelopathy in spatially distributed populations. J. Theor. Biol., 185 (1997), 165–171. [CrossRef] [PubMed] [Google Scholar]
  17. I. Eshel. Evolutionary and continuous stability. J. Theor. Biol. 108 (1983), 99–111. [Google Scholar]
  18. I. Eshel. On the changing concept of evolutionary population stability as a reflection of a changing point of view in the quantitative theory of evolution. J. Math. Biol. 34 (1996), 485–510. [Google Scholar]
  19. I. Eshel, U. Motro. Kin selection and strong evolutionary stability of mutual help. Theor. Pop. Biol. 19 (1981), 420–433. [Google Scholar]
  20. G. Gause. The struggle for existence. Williams and Wilkins, Baltimore, 1934. [Google Scholar]
  21. S.A.H. Geritz, M. Gyllenberg, F.J.A. Jacobs, K. Parvinen. Invasion dynamics and attractor inheritance. J. Math. Biol., 44 (2002), 548–560. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  22. S.A.H. Geritz, S.A.H. Kisdi, G. Meszéna, J.A.J. Metz. Evolutionary singular strategies and the adaptive growth and branching of the evolutionary tree. Evol. Ecol., 12 (1998), 35–57. [CrossRef] [Google Scholar]
  23. S.A.H. Geritz, J.A.J. Metz. É. Kisdi, G. Meszéna. Dynamics of adaptation and evolutionary branching. Physical Review Letters 78, 2024–2027. [Google Scholar]
  24. A. Gorban. Selection theorem for systems with inheritance. Math. Model. Nat. Phenom., 2 (2007), 1–45. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  25. P. Grindrod. The theory and applications of reaction-diffusion equations: patterns and waves. 2nd Edition. Clarendon press, Oxford, 1996. [Google Scholar]
  26. M. Gyllenberg, J.A. Metz. On fitness in structured metapopulations. J. Math. Biol., 43 (2001), 545–560. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  27. K.P. Hadeler. Diffusion in Fisher's population model. Rocky Mountain J. Math., 11 (1981), 39–45. [Google Scholar]
  28. J. Haldane. The causes of evolution. Princeton University Press, 1932. [Google Scholar]
  29. W.G.S. Hines. Evolutionary stable strategies: A review of basic theory. Theor. Pop. Biol., 31 (1987), 195–272. [CrossRef] [Google Scholar]
  30. V. C.L. Hutson, G.T. Vickers. Travelling waves and dominance of ESS's. J. Math. Biol., 30 (1992), 457–471. [CrossRef] [MathSciNet] [Google Scholar]
  31. N. Kalev-Kronik. Evolutionary games in space. Ph.D. Thesis, University of Minneosta, 2006. [Google Scholar]
  32. W. Kaplan. Advanced calculus. Addison-Wesley, Reading, 1952. [Google Scholar]
  33. C.L. Lehman, D. Tilman. Spatial Ecology : The Role of Space in Population Dynamics and Interspecific Interactions,chapter: Competition in Spatial Habitats.. Princeton University Press, Princeton, 1997. [Google Scholar]
  34. J.L. Lions. Equations differentielles operationelles. Springer-Verlag, New-York, 1961. [Google Scholar]
  35. S. Lipschutz. Linear algebra. McGraw-Hill, New York, 1991. [Google Scholar]
  36. J. Maynard-Smith. Evolution and the theory of games. Cambridge University Press, Cambridge, 1982. [Google Scholar]
  37. J. Maynard-Smith, G. Price. The logic of animal conflict. Nature, 246 (1973), 15–18. [CrossRef] [Google Scholar]
  38. J.A.J. Metz, M. Gyllenberg. How should we define fitness in structured metapopulation models?. Proc. Royal Soc. London B, 268 (2001), 499–508. [Google Scholar]
  39. J. Murray. Mathematical biology, 2nd Edition, Springer-Verlag, Berlin, 1993. [Google Scholar]
  40. C. Neuhauser. Habitat destruction and competitive coexistence in spatially explicit models with local interactions. J. Theor. Biol., 193 (1998), 445–463. [CrossRef] [PubMed] [Google Scholar]
  41. C. Neuhauser, S.W. Pacala. An explicit spatial version of the lotka-volterra model with interspecific competition. Ann. Appl. Probab., 9 (1999), 1226–1259. [CrossRef] [MathSciNet] [Google Scholar]
  42. H.G. Othmer, L.E. Scriven. Interactions of reaction and diffusion in open systems. Ind. Eng. Chem. Fund., 8 (1969), 302–313. [CrossRef] [Google Scholar]
  43. K. Parvinen. Evolution of migration in a metapopulation. Bul. Math. Biol., 61 (1999), 531–550. [CrossRef] [Google Scholar]
  44. H. Qian, J. Murray. A simple method of parameter space determination for diffusion-driven instability with three species. Appl. Math. Let., 9 (2001), 405–411. [CrossRef] [Google Scholar]
  45. A. Sasaki, I. Kawaguchi, A. Yoshimori. Spatial mosaic and interfacial dynamics in a Müllerian mimicry system. Theor. Pop. Biol., 61 (2002), 49–71. [CrossRef] [Google Scholar]
  46. L.E. Segel, J.L. Jackson. Dissipative structure: An explanation and an ecological example. J. Theor. Biol., 37 (1972), 545–559. [CrossRef] [PubMed] [Google Scholar]
  47. J. Smoller. Shock waves and reaction-diffusion equations. Springer-Verlag, New York, 1983. [Google Scholar]
  48. T. Takada, J. Kigami. The dynamical attainability of ESS in evolutionary games. J. Math. Biol., 29 (1991), 513–529. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  49. P.D. Taylor. Evolutionary stability in one-parameter models under weak selection. Theor. Pop. Biol., 36 (1989), 125–143. [CrossRef] [Google Scholar]
  50. D. Tilman, P. Kareiva eds. Spatial ecology : the role of space in population dynamics and interspecific interactions. Princeton University Press, Princeton, 1997. [Google Scholar]
  51. A.M. Turing. On the chemical basis of morphogenesis. Phil. Trans. B., 237 (1952), 37–37. [Google Scholar]
  52. G.T. Vickers, Spatial patterns and ESS's. J. Theo. Biol., 140 (1989), 129–135. [Google Scholar]
  53. G.T. Vickers,V.C.L. Hutson, C.J. Budd. Spatial patterns in population conflicts. J. Math. Biol., 31 (1993), 411–430. [CrossRef] [MathSciNet] [Google Scholar]
  54. T. Vincent, Evolutionary games. J. Optim. Theor. Appl., 46 (1985), 605–612. [Google Scholar]
  55. T. Vincent, J. Brown. Evolution under nonequilibrium dynamics. Math. Model., 8 (1987), 766–771. [CrossRef] [Google Scholar]
  56. T.L. Vincent, J. Brown. Evolutionary game theory, natural selection, and Darwinian dynamics. Cambridge University Press, Cambridge, 2005. [Google Scholar]
  57. Vincent, T. Evolutionary stable strategies in differential and difference equation models. Evol. Ecol., 2, (1988), 321–337. [Google Scholar]
  58. T.L. Vincent, Y. Cohen, J.S. Brown. Evolution via strategy dynamics. Theor. Pop. Biol., 44 (1993), 149–176. [CrossRef] [Google Scholar]
  59. T.L. Vincent, M.V. Van, G.S. Goh. Ecological stability, evolutionary stability, and the ESS Maximum Principle. Evol. Ecol., 10 (1996), 567–591. [CrossRef] [Google Scholar]
  60. V. Zakharov, V.S. L'vov, S.S. Starobinets. Spin-wave turbulence beyond the parametric excitation threshold. Soviet Physics Uspekhii, 17 (1975), 896–919. [CrossRef] [Google Scholar]

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