Discrete-time metapopulation dynamics and unidirectional dispersal

Journal of Difference Equations and Applications

Volumn 9, Issue 7, 2003, Pages 633-653

  Yakubu, Abdul Aziz ^a,b  

^a HOWARD UNIVERSITY   (United States)

^b Department of Obstetrics Gynecology   (United States)

Author keywords

Compensatory dynamics; Discrete time models; Intraspecific competition; Metapopulation; Multiple attractors; One way (unidirectional) dispersal; Overcompensatory dynamics

Indexed keywords

EID: 0037505921     PISSN: 10236198     EISSN: None     Source Type: Journal    
DOI: 10.1080/1023619021000042225     Document Type: Conference Paper

References (50)

1. J. C. Alexander, J. A. Yorke, Z. You and I. Kan, Riddled basins, Intern. J. Bifurc. Chaos, 2(4) (1992), 795-813.
2. L. J. Allen, Persistence, extinction, and critical patch number for island populations, J. Math. Biol., 24 (1987), 617-625.
3. M. Begon, J. L. Harper and C. R. Townsend, Ecology: Individuals, Populations and Communities, Blackwell Science, Oxford, 1996.
4. F. Brauer and C. Castillo-Chavez, Mathematical models in population biology and epidemiology, Texts in Applied Mathematics, Springer, New York, Vol. 40, 2001.
5. C. Castillo-Chavez and A. A. Yakubu, Dispersal, disease and life-History evolution, Math. Biosc., 173 (2001), 35-53.
6. C. Castillo-Chavez and A. A. Yakubu, Intraspecific competition, dispersal and disease dynamics in discrete-time patchy environments, In: Carlos Castillo-Chavez, SallyBlower, Paulinevan den Driessche, DeniseYakubu and Abdul-AzizYakubu, eds, Mathematical Approaches For Emerging and Reemerging Infectious Diseases: Part I: An Introduction to Models, Methods and Theory, Series: The IMA Volumes in Mathematics and its Applications, Springer, New York, Vol. 125, 2002.
7. D. Cohen and S.A. Levin, The interaction between dispersal and dormancy strategies in varying and heterogeneous environments, In: E. Teramoto and M. Yamaguti, eds, Mathematical Topics in Population Biology, Morphogenesis and Neurosciences, Proc. Kyoto 1985, Springer, Berlin, pp. 110-122, 1987.
8. M. Doebeli, Dispersal and dynamics, Theor. Popl. Biol., 47 (1995), 82-106.
9. M. Doebeli and G. D. Ruxton, Evolution of dispersal rates in metapopulation model: branching and cyclic dynamics in phenotype space, Evolution, 5(6) (1997), 1730-1741.
10. D. J. Earn, S. A. Levin and P. Rohani, Coherence and conservation, Science, 290 (2000), 1360-1364.
11. S. N. Elaydi, Discrete Chaos, Chapman and Hall/CRC, Boca Raton, FL, 2000.
12. S. N. Elaydi and A. -A. Yakubu, Global stability of cycles: Lotka-Volterra competition model with stocking, J. Diff. Equations Appl., 8(6) (2002), 537-549.
13. P. L. Errington, Some contributions of a fifteen year local study of the northern bobwhite to a knowledge of population phenomena, Ecol. Monogr., 15 (1945), 1 - 34.
14. J. E. Franke and A. -A. Yakubu, Extinction and persistence of species in discrete competitive systems with a safe refuge, J. Math. Anal. Appl., 23 (1996), 746-761.
15. J. E. Franke and A. -A. Yakubu, Geometry of exclusion principles in discrete systems, J. Math. Anal. Appl., 168 (1992), 385-400.
16. J. E. Franke and A. -A. Yakubu, Mutual exclusion versus coexistence for discrete competitive systems, J. Math. Biol., 30 (1991), 161-168.
17. J. L. Gonzalez-Andújar and J. N. Perry, Chaos, metapopulations and dispersal, Ecol. Model., 65 (1993), 255-263.
18. C. Grebogi, E. Ott and J. A. Yorke, Chaos, strange attractors, and fractal basin boundaries in nonlinear dynamics, Science, 228 (1987), 632-638.
19. M. Gyllenberg, G. Söderbacka and S. Ericsson, Does migration stabilize local population dynamics? Analysis of a discrete metapopulation model, Math. Biosc., 118 (1993), 25-49.
20. A. Halanay and V. Rǎsvan, Stability and stable oscillations in discrete time systems, Advances in Discrete Mathematics and Applications, Gordon and Breach Science Publishers, London, 2002.
21. I. Hanski, Single-species metapopulation dynamics-concepts, models and observations, Biol. J. Linn. Soc., 42 (1991), 17-38.
22. I. A. Hanski and M. E. Gilpin, Metapopulation biology: ecology, genetics, and evolution, Academic Press, San Diego, CA, 1997.
23. M. P. Hassell, The dynamics of competition and predation, Studies in Biol., Camelot Press, Vol. 72, 1976.
24. M. P. Hassell, J. H. Lawton and R. M. May, Patterns of dynamical behavior in single species populations, J. Anim. Ecol., 45 (1976), 471-486.
25. A. Hastings, Complex interactions between dispersal and dynamics: lessons from coupled logistic equations, Ecology, 75 (1993), 1362-1372.
26. A. Hastings, Dynamics of a single species in a spatially varying environment: The stabilizing role of high dispersal rates, J. Math. Biol., 16 (1982), 49-55.
27. S. M. Henson, R. F. Constantino, J. M. Cushing, B. Dennis and R. A. Desharnais, Multiple attractors, saddles, and population dynamics in periodic habitats, Bull. Math. Biol., 61 (1999), 1121-1149.
28. S. M. Henson and J. M. Cushing, Hierarchical models of intraspecific competition: scramble versus contest, J. Math. Biol., 34 (1996), 755-772.
29. I. Kan, Open sets of diffeomorphisms having two attractors, each with an everywhere dense basin, Bull. AMS, 31(1) (1994), 68-74.
30. V. L. Kocić and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic, Boston, 1993.
31. S. A. Levin, Dispersion and population interactions, Am. Naturalist, 108 (1974), 207-228.
32. S. A. Levin, The problem of pattern and scale in ecology, Ecology, 73 (1992), 1943-1967.
33. S. Levin and R. T. Paine, Disturbance, patch formation, and community structure, Proc. Natl Acad. Sci. USA, 68 (1974), 2744-2747.
34. R. Levins, Some demographic and genetic consequences of environmental heterogeneity for biological control, Bull. Entomol. Soc. Am., 15 (1969), 237-240.
35. R. Levins, The effect of random variation of different types on population growth, Proc. Natl Acad. Sci. USA, 62 (1969), 1061-1062.
36. R. M. May and G. F. Oster, Bifurcations and dynamic complexity in simple ecological models, Am. Naturalist, 110 (1976), 573-579.
37. R. M. May, Simple mathematical models with very complicated dynamics, Nature, 261 (1977), 459-469.
38. R. M. May, Stability and complexity in model ecosystems, Princeton University Press, USA, 1974.
39. R. M. May, M. P. Hassell, R. M. Anderson and D. W. Tonkyn, Density dependence in host-parasitoid models, J. Anim. Ecol., 50 (1981), 855-865.
40. J. Maynard Smith and M. Slatkin, The stability of predator-prey systems, Ecology, 54 (1973), 384-391.
41. J. G. Milton and J. Bélair, Chaos, noise, and extinction in models of population growth, Theor. Popl. Biol., 37 (1990), 273-290.
42. A. J. Nicholson, Compensatory reactions of populations to stresses, and their evolutionary significance, Aust. J. Zool., 2 (1954), 1-65.
43. H. E. Nusse and J. A. Yorke, Dynamics: Numerical Explorations, Springer, New York, 1997.
44. W. E. Ricker, Stock and recruitment, J. Fish. Res. Board Can., II(5) (1954), 559-623.
45. H. L. Smith, Cooperative systems of differential equations with concave nonlinearities, Nonl. Anal. Theor. Methods Appl., 10 (1986), 1037-1052.
46. H. R. Thieme, Convergence results and a Poincare'-Bendixson trichotomy for asymptotically autonomous differential equations, J. Math. Biol., 30 (1992), 755-763.
47. A. Yakubu and C. Castillo-Chavez, Interplay between local dynamics and dispersal in discrete-time metapopulation models, J. Theor. Biol., 218 (2002), 273-288.
48. A. Yakubu, Asynchronous dispersal and discrete-time metapopulation dynamics, J. Math, Biol., Submitted for publication.
49. P. Yodzis, Introduction to Theoretical Ecology, Harper and Row Publishers, New York, 1989.
50. X. -Q. Zhao, Asymptotic behavior for asymptotically periodic semiflows with applications. Comm. Appl. Nonl. Anal., 3 (1996), 43-66.