Free Access
Math. Model. Nat. Phenom.
Volume 4, Number 6, 2009
Ecology (Part 1)
Page(s) 54 - 90
Published online 27 November 2009
  1. P.A. Abrams. Adaptive dynamics: Neither F nor G. Evol. Ecol. Res., 3 (2001), 369–373.
  2. P.A. Abrams, H. Matsuda. Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits. Evol. Ecol., 7 (1993), 465–487. [CrossRef]
  3. D. Alonso, F. Bartumeus, J. Catalan. Mutual interference between predators can give rise to Turing spatial patterns. Ecology, 83 (2002), 28–34. [CrossRef]
  4. H. Anton.and C. Rorres. Elementary linear algebra: applications version. 8th Edition. John Wiley & Sons, New York, 2000.
  5. J. Apaloo. Revisting strategic models of evolution: The concept of neighborhood invader strategies. Theor. Pop. Biol.,52 (1997), 71–77.
  6. N.F. Britton. Reaction-diffusion equations and their applications to biology. Academic Press, New York, 1986.
  7. J.S. Brown, N.B. Pavlovic. Evolution in heterogeneous environments - effects of migtation on habitat specialization. Evol. Ecol. 6 (1992),360–382.
  8. J.S. Brown, T.L. Vincent. A theory for the evolutionary game. Theor. Pop. Biol., 31 (1987), 140–166. [CrossRef]
  9. J.S. Brown, T.L. Vincent. Organiztion of predator-prey communities as an evolutionary game. Evolution, 46 (1992), 1269–1283. [CrossRef] [PubMed]
  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.
  11. Y. Cohen, J. Pastor, T.L. Vincent. Evolutionary strategies and nutrient cycling in ecosystems. Evol. Ecol. Res., 2 (2000), 719–743.
  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.
  13. R. Cressman, G.T. Vickers. Spatial and density effects in evolutionary game theory. Math. Biol., 184 (1997), 359–369.
  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]
  15. R. Durrett, S. Levin. The importance of being discrete (and spatial). Theor. Pop. Biol., 46 (1994), 363–394. [CrossRef]
  16. R. Durrett, S. Levin. Allelopathy in spatially distributed populations. J. Theor. Biol., 185 (1997), 165–171. [CrossRef] [PubMed]
  17. I. Eshel. Evolutionary and continuous stability. J. Theor. Biol. 108 (1983), 99–111.
  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.
  19. I. Eshel, U. Motro. Kin selection and strong evolutionary stability of mutual help. Theor. Pop. Biol. 19 (1981), 420–433.
  20. G. Gause. The struggle for existence. Williams and Wilkins, Baltimore, 1934.
  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]
  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]
  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.
  24. A. Gorban. Selection theorem for systems with inheritance. Math. Model. Nat. Phenom., 2 (2007), 1–45. [CrossRef] [EDP Sciences] [MathSciNet]
  25. P. Grindrod. The theory and applications of reaction-diffusion equations: patterns and waves. 2nd Edition. Clarendon press, Oxford, 1996.
  26. M. Gyllenberg, J.A. Metz. On fitness in structured metapopulations. J. Math. Biol., 43 (2001), 545–560. [CrossRef] [MathSciNet] [PubMed]
  27. K.P. Hadeler. Diffusion in Fisher's population model. Rocky Mountain J. Math., 11 (1981), 39–45. [CrossRef] [MathSciNet]
  28. J. Haldane. The causes of evolution. Princeton University Press, 1932.
  29. W.G.S. Hines. Evolutionary stable strategies: A review of basic theory. Theor. Pop. Biol., 31 (1987), 195–272. [CrossRef]
  30. V. C.L. Hutson, G.T. Vickers. Travelling waves and dominance of ESS's. J. Math. Biol., 30 (1992), 457–471. [CrossRef] [MathSciNet]
  31. N. Kalev-Kronik. Evolutionary games in space. Ph.D. Thesis, University of Minneosta, 2006.
  32. W. Kaplan. Advanced calculus. Addison-Wesley, Reading, 1952.
  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.
  34. J.L. Lions. Equations differentielles operationelles. Springer-Verlag, New-York, 1961.
  35. S. Lipschutz. Linear algebra. McGraw-Hill, New York, 1991.
  36. J. Maynard-Smith. Evolution and the theory of games. Cambridge University Press, Cambridge, 1982.
  37. J. Maynard-Smith, G. Price. The logic of animal conflict. Nature, 246 (1973), 15–18. [CrossRef]
  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. [CrossRef]
  39. J. Murray. Mathematical biology, 2nd Edition, Springer-Verlag, Berlin, 1993.
  40. C. Neuhauser. Habitat destruction and competitive coexistence in spatially explicit models with local interactions. J. Theor. Biol., 193 (1998), 445–463. [CrossRef] [PubMed]
  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]
  42. H.G. Othmer, L.E. Scriven. Interactions of reaction and diffusion in open systems. Ind. Eng. Chem. Fund., 8 (1969), 302–313. [CrossRef]
  43. K. Parvinen. Evolution of migration in a metapopulation. Bul. Math. Biol., 61 (1999), 531–550. [CrossRef]
  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]
  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]
  46. L.E. Segel, J.L. Jackson. Dissipative structure: An explanation and an ecological example. J. Theor. Biol., 37 (1972), 545–559. [CrossRef] [PubMed]
  47. J. Smoller. Shock waves and reaction-diffusion equations. Springer-Verlag, New York, 1983.
  48. T. Takada, J. Kigami. The dynamical attainability of ESS in evolutionary games. J. Math. Biol., 29 (1991), 513–529. [CrossRef] [MathSciNet] [PubMed]
  49. P.D. Taylor. Evolutionary stability in one-parameter models under weak selection. Theor. Pop. Biol., 36 (1989), 125–143. [CrossRef]
  50. D. Tilman, P. Kareiva eds. Spatial ecology : the role of space in population dynamics and interspecific interactions. Princeton University Press, Princeton, 1997.
  51. A.M. Turing. On the chemical basis of morphogenesis. Phil. Trans. B., 237 (1952), 37–37. [CrossRef]
  52. G.T. Vickers, Spatial patterns and ESS's. J. Theo. Biol., 140 (1989), 129–135.
  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]
  54. T. Vincent, Evolutionary games. J. Optim. Theor. Appl., 46 (1985), 605–612.
  55. T. Vincent, J. Brown. Evolution under nonequilibrium dynamics. Math. Model., 8 (1987), 766–771. [CrossRef]
  56. T.L. Vincent, J. Brown. Evolutionary game theory, natural selection, and Darwinian dynamics. Cambridge University Press, Cambridge, 2005.
  57. Vincent, T. Evolutionary stable strategies in differential and difference equation models. Evol. Ecol., 2, (1988), 321–337.
  58. T.L. Vincent, Y. Cohen, J.S. Brown. Evolution via strategy dynamics. Theor. Pop. Biol., 44 (1993), 149–176. [CrossRef]
  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]
  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]

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