The evolution of dispersal rates in a heterogeneous time-periodic environment

Journal of Mathematical Biology

Volumn 43, Issue 6, 2001, Pages 501-533

  Hutson, V ^a   Mischaikow, K ^b   Polacik P ^c  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^c Physics and Informatics   (Slovakia)

Author keywords

Evolution of dispersal; Migration modification; Periodic parabolic eigenvalue; Reaction diffusion

Indexed keywords

ANIMAL; ARTICLE; EVOLUTION; GENETIC SELECTION; MUTATION; PHENOTYPE; POPULATION DYNAMICS; THEORETICAL MODEL;

ANIMALS; EVOLUTION; MODELS, THEORETICAL; MUTATION; PHENOTYPE; POPULATION DYNAMICS; SELECTION (GENETICS);

EID: 0035747963     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002850100106     Document Type: Article

References (38)

1. Chesson, P.: General theory of competitive coexistence in spatially-varying environments, Theor. Pop. Bio. 58, 211-237 (2000)
2. Dancer, E.N.: Upper and lower stability and index theory for positive mappings and applications, Nonlinear Anal., Theory Methods Appl., 17(3), 205-217 (1991)
3. Dancer, E.N., Hess, P.: Stable subharmonic solutions in periodic reaction-diffusion equations, J. Differential Equations., 108(1), 190-200 (1994)
4. Dieckman, U., O'Hara, B., Weisser, W.: The evolutionary ecology of dispersal, Trends Ecol. Evol. 14(3), 88-90 (1999)
5. Dockery, J., Hutson, V., Mischaikow, K., Pernarowski, M.: The evolution of slow dispersal rates: a reaction-diffusion model, J. Math. Biol., 37(1), 61-83 (1998)
6. Doebeli, M., Ruxton, G.: Evolution of dispersal rates in metapopulation models: branching and cyclic dynamics in phenotype space, Evolution, 51(6), 1730-1741 (1997)
7. Durrett, R., Levin, S.: Spatial aspects of interspecific competition, Theoretical Population Biology 53, 30-43 (1998)
8. Ferriere, R., Belthoff, J., Olivieri, I., Krackow, S.: Evolving dispersal: where to go next? Trends Ecol. Evol., 15(1), 5-7 (2000)
9. Hale, J.K., Sakamoto, K.: Shadow systems and attractors in reaction-diffusion equations, Appl. Anal., 32(3-4), 287-303 (1989)
10. Hale, J.K., Verduyn Lunel, S.M.: Averaging in infinite dimensions, J. Integral Equations., 2(4), 463-494 (1990)
11. Hastings, A.: Can spatial variation alone lead to selection for dispersal? Theor. Pop. Biol., 24, 244-251 (1983)
12. Henry, D.: Geometric theory of semilinear parabolic equations, Springer, New York, (1981)
13. Hess, P.: Periodic-parabolic boundary value problems and positivity, Longman Scientific & Technical, Harlow, (1991)
14. Hess, P., Poláčik, P.: Boundedness of prime periods of stable cycles and convergence to fixed points in discrete monotone dynamical systems, SIAM J. Math. Anal., 24(5), 1312-1330 (1993)
15. Hutson, V., Shen, W., Vickers, G.T.: Estimates for the principal spectrum point for certain time-dependent parabolic operators, Proc. A.M.S. 129, 1669-1679 (2000)
16. Hetzer, G., Shen, W.: Convergence in Almost Periodic Competition Diffusion Systems, preprint (1999)
17. Holt, R., McPeek, M.: Chaotic population dynamics favors the evolution of dispersal, The American Naturalist 148, 709-718 (1996)
18. Johnson, M., Gaines, M.: Evolution of Dispersal: Theoretical Models and Empirical Tests Using Birds and Mammels, Ann. Rev. Ecol. Syst. 21, 449-480 (1990)
19. Jiang, J.-F., Yu, S.-X.: Stable cycles for attractors of strongly monotone discrete-time dynamical systems, J. Math. Anal. Appl., 202, 349-362 (1996)
20. Keeling, M.: Spatial models of interacting populations, Advanced Ecological Theory: Principles and Applications, J. McGlade, ed. Blackwell Science, Oxford, (1999)
21. Kendall, B., Fox, G.: Spatial structure, environmental heterogeneity, and population dynamics: analysis of the coupled logistic map, Theoretical Population Biology, 54, 11-37 (1998)
22. Kato, T.: Perturbation Theory for Linear Operators. Springer. Berlin, (1966)
23. Lunardi, A.: Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser, Berlin, (1995)
24. McGlade, J. ed.: Advanced Ecological Theory: Principles and Applications, Blackwell Science, Oxford, (1999)
25. McPeek, M., Holt, R.: The evolution of dispersal in spatially and temporally varying environments, The American Naturalist 140, 1010-1027 (1992)
26. Mueller, L.: Theoretical and empirical examination of density-dependent selection, Annu. Rev. Ecol. Syst. 28, 269-88 (1997)
27. Nagylaki, T.: The diffusion model for migration and selection, Some Mathematical Questions in Biology: Models in Population Biology (A. Hastings, ed.) Lect. Math. Life Sciences, 20 AMS, (1989)
28. Parvinen, K.: Evolution of migration in a metapopulation, Bull. Math. Biol. 61, 531-550 (1999)
29. Poláčik, P., Tereščák, I.: Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems, Arch. Rational Mech. Anal., 116(4), 339-360 (1992)
30. Poláčik, P., Tereščák., I.: Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations, J. Dynamics Differential Equations., 5(2), 279-303 (1993)
31. Poláčik, P., Yanagida, E.: Existence of stable subharmonic solutions for reaction diffusion equations, J. Differential Equations., to appear.
32. Smith, H.L., Thieme, H.R.: Quasi convergence and stability for strongly order-preserving semiflows. SIAM J. Math. Anal., 21(3), 673-692 (1990)
33. Takáč, P.: Linearly stable subharmonic orbits in strongly monotone time-periodic dynamical systems, Proc. Amer. Math. Soc., 115(3), 691-698 (1992)
34. Takáč, P.: A construction of stable subharmonic orbits in monotone time-periodic dynamical systems, Monatsh. Math., 115(3), 215-244 (1993)
35. 1 smooth strongly monotone discrete-time dynamical systems, preprint.
36. Tilman, D., Kareiva, P.: Spatial Ecology: The role of Space in Population Dynamics and Interspecific Interactions, Monographs in Population Biology, 30 Princeton Univ. Press, (1997)
37. Travis, J.M.J., Dytham, C.: Habitat persistence, habitat availability and the evolution of dispersal, Proc. Roy. Soc. London B. 266, 723-728 (1999)
38. Zelenyak, T.I., Lavrentiev, M.M., Vishnevskii, M.P.: Qualitative theory of parabolic equations, Part 1. VSP, Utrecht, (1997)