Spatial structure, environmental heterogeneity, and population dynamics: Analysis of the coupled logistic map

Theoretical Population Biology

Volumn 54, Issue 1, 1998, Pages 11-37

  Kendall, Bruce E ^a,b   Fox, Gordon A ^c,d  

^a University of Arizona   (United States)

^b NATIONAL CENTER FOR ECOLOGICAL ANALYSIS AND SYNTHESIS   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d SAN DIEGO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

HETEROGENEITY; MODELING; POPULATION DYNAMICS; SPATIAL VARIATION;

ANIMALIA;

EID: 0032146563     PISSN: 00405809     EISSN: None     Source Type: Journal    
DOI: 10.1006/tpbi.1998.1365     Document Type: Article

References (85)

1. Allen J. C. Mathematical models of species interactions in time and space. Am. Nat. 109:1975;319-342.
2. Allen J. C., Schaffer W. M., Rosko D. Chaos reduces species extinction by amplifying local population noise. Nature (London). 364:1993;229-232.
3. Baier G., Klein M. Maximum hyperchaos in generalized Hénon maps. Phys. Lett. A. 151:1990;281-284.
4. Baker G. L., Gollub J. P. Chaotic Dynamics: An Introduction. 1996;Cambridge Univ. Press, Cambridge.
5. Brown J. H., Kodric-Brown A. Turnover rates in insular biogeography: Effect of immigration on extinction. Ecology. 58:1977;445-449.
6. Christiansen E. Fluctuations in some small rodent population in Norway 1971-1979. Holarctic Ecol. 6:1983;24-31.
7. Collet P., Eckmann J.-P. Iterated Maps on the Interval as Dynamical Systems. 1980;Birkhäuser, Basel.
8. Comins H. N., Hassell M. P. Persistence of multispecies host-parasitoid interactions in spatially distributed models with local dispersal. J. Theor. Biol. 183:1996;19-28.
9. Comins H. N., Hassell M. P., May R. M. The spatial dynamics of host-parasitoid systems. J. Anim. Ecol. 61:1992;735-748.
10. Daido H. Coupling sensitivity of chaos. Prog. Theor. Phys. Suppl. 79:1984a;75-95.
11. Daido H. Coupling sensitivity of chaos. Prog. Theor. Phys. 72:1984b;853-856.
12. Day J. R., Possingham H. P. A stochastic metapopulation model with variability in patch size and position. Theor. Popul. Biol. 48:1995;333-360.
13. den Boer P. J. On the survival of populations in a heterogeneous and variable environment. Oecologia. 50:1981;39-53.
14. Doebeli M. Dispersal and dynamics. Theor. Popul. Biol. 47:1995;82-106.
15. Eckmann J.-P., Ruelle D. Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57:1985;617-656.
16. Ferretti A., Rahman N. K. Coupled logistic maps in physico-chemical processes: Coexisting attractors and their implications. Chem. Phys. Lett. 140:1987a;71-75.
17. Ferretti A., Rahmann N. K. A study of coupled logistic maps and their usefulness for modelling physico-chemical processes. Chem. Phys. Lett. 133:1987b;150-153.
18. Ferretti A., Rahman N. K. A study of coupled logistic map and its applications in chemical physics. Chem. Phys. 119:1988;275-288.
19. Frøyland J. Some symmetric, two-dimensional, dissipative maps. Physica D (Amsterdam). 8:1983;423-434.
20. Fujita K. Systems analysis of an acarine predator-prey system. II: Interactions in discontinuous environment. Res. Popul. Ecol. 25:1983;387-399.
21. Gilpin M., Hanski I. Metapopulation Dynamics: Empirical and Theoretical Investigations. 1991;Academic Press, London.
22. Grebogi C., Ott E., Yorke J. A. Crises, sudden changes in strange attractors, and transient chaos. Physica D (Amsterdam). 7:1983;181-200.
23. Gurney W. S. C., Nisbet R. M. Predator-prey fluctuations in patchy environments. J. Anim. Ecol. 47:1978;85-102.
24. Gyllenberg M., Söderbacka G., Ericsson S. Does migration stabilize local population dynamics? Analysis of a discrete metapopulation model. Math. Biosci. 118:1993;25-49.
25. Hanski I., Gilpin M. E. Metapopulation Biology: Ecology, Genetics, and Evolution. 1997;Academic Press, San Diego.
26. Hanski I., Woiwood I. Spatial synchrony in the dynamics of moth and aphid populations. J. Anim. Ecol. 62:1993;656-668.
27. Hassell M. P., Comins H. N., May R. M. Spatial structure and chaos in insect population dynamics. Nature (London). 353:1991;255-258.
28. Hassell M. P., Miramontes O., Rohani P., May R. M. Appropriate formulations for dispersal in spatially structured models: Comments on Bascompte & Solé J. Anim. Ecol. 64:1995;662-664.
29. Hastings A. Age dependent dispersal is not a simple process: Density dependence, stability, and chaos. Theor. Popul. Biol. 41:1992;388-400.
30. Hastings A. Complex interactions between dispersal and dynamics: Lessons from coupled logistic equations. Ecology. 74:1993;1362-1372.
31. Heino M., Kaitala V., Ranta E., Lindström J. Synchronous dynamics and rates of extinction in spatially structured populations. Proc. Roy. Soc. London B. 264:1997;481-486.
32. Hilborn R. The effect of spatial heterogeneity on the persistence of predator-prey interactions. Theor. Popul. Biol. 8:1975;346-355.
33. Hogg T., Huberman B. A. Generic behavior of coupled oscillators. Phys. Rev. A. 29:1984;275-281.
34. Holt R. D., Hassell M. P. Environmental heterogeneity and the stability of host-parasitoid interactions. J. Anim. Ecol. 62:1993;89-100.
35. Holyoak M., Lawler S. P. The role of dispersal in predator-prey metapopulation dynamics. J. Anim. Ecol. 65:1996;640-652.
36. Huffaker C. B. Experimental studies on predation: Dispersion factors and predator-prey oscillations. Hilgardia. 27:1958;343-383.
37. Iwasa Y., Roughgarden J. Interspecific competition among metapopulations with space-limited subpopulations. Theor. Popul. Biol. 30:1986;194-214.
38. Kaneko K. Transition from torus to chaos accompanied by frequency lockings with symmetry breaking. Prog. Theor. Phys. 69:1983;1427-1442.
39. Kaneko K. Spatial period-doubling in open flow. Phys. Lett. A. 111:1985;321-325.
40. Kaneko K. Pattern competition intermittency and selective flicker noise in spatiotemporal chaos. Phys. Lett. A. 125:1987;25-31.
41. Kaneko K. Chaotic but regular posi-nega switch among coded attractors by cluster-size variation. Phys. Rev. Lett. 63:1989a;219-223.
42. Kaneko K. Spatiotemporal chaos in one- and two-dimensional coupled map lattices. Physica D (Amsterdam). 37:1989b;60-82.
43. Kaneko K. Supertransients, spatiotemporal intermittency and stability of fully developed spatiotemporal chaos. Phys. Lett. A. 149:1990;105-112.
44. Kaneko K. The coupled map lattice: introduction, phenomenology, Lyapunov analysis, thermodynamics and applications. Theory and Applications of Coupled Map Lattices. 1993;Wiley, Chichester. p. 1-49.
45. Kendall B. E., Schaffer W. M., Tidd C. W. Transient periodicity in chaos. Phys. Lett. A. 177:1993;13-20.
46. Kishimoto K. Coexistence of any number of species in the Lotka-Volterra competitive system over two patches. Theor. Popul. Biol. 38:1990;149-158.
47. Klein M., Baier G. Hierarchies of dynamical systems. Baier G., Klein M. A Chaotic Hierarchy. 1991;1-23 World Scientific, Singapore.
48. Kook K., Ling F. H., Schmidt G. Universal behavior of coupled nonlinear systems. Phys. Rev. A. 43:1991;2700-2708.
49. Levin S. A. Dispersion and population interactions. Am. Nat. 108:1974;207-228.
50. Lindström J., Ranta E., Lindén H. Large-scale synchrony in the dynamics of capercaillie, black grouse and hazel grouse populations in Finland. Oikos. 76:1996;221-227.
51. Lloyd A. L. The coupled logistic map: A simple model for the effects of spatial heterogeneity on population dynamics. J. Theor. Biol. 173:1995;217-230.
52. López-Ruiz R., Pérez-García C. Dynamics of maps with a global multiplicative coupling. Chaos Solitons Fractals. 1:1991;511-528.
53. López-Ruiz R., Pérez-García C. Dynamics of two logistic maps with a multiplicative coupling. Int. J. Bifurcations Chaos. 2:1992;421-425.
54. Losson J., Mackey M. C. Coupling induced statistical cycling in two diffusively coupled maps. Physica D (Amsterdam). 72:1994;324-342.
55. May R. M. Simple mathematical models with very complicated dynamics. Nature (London). 261:1976;459-467.
56. Myrberget S. Geographical synchronism of cycles of small rodents in Norway. Oikos. 24:1973;220-224.
57. Nachman G. Temporal and spatial dynamics of an acarine predator-prey system. J. Anim. Ecol. 50:1981;435-451.
58. Nachman G. Systems analysis of acarine predator-prey interactions. II. The role of spatial processes in system stability. J. Anim. Ecol. 56:1976;267-281.
59. Nakamura K., Ohgushi T. Studies on the population dynamics of a thistle-feeding lady beetle,Henosepilachna pustulosa. Res. Popul. Ecol. 25:1983;1-19.
60. Nee S., May R. M. Dynamics of metapopulations: Habitat destruction and competitive coexistence. J. Anim. Ecol. 61:1992;37-40.
61. Pollard E. Synchrony of population fluctuations: The dominant influence of widespread factors on local butterfly populations. Oikos. 60:1991;7-10.
62. Pomeau Y., Manneville P. Intermittent transition to turbulence in dissipative dynamical systems. Commun. Math. Phys. 74:1980;189-197.
63. Pulliam H. R. Sources, sinks, and population regulation. Am. Nat. 132:1988;652-661.
64. Pulliam H. R. Sources and sinks: Empirical evidence and population consequences. Rhodes O. E., Chesser R. K., Smith M. H. Population Dynamics in Ecological Space and Time. 1996;45-69 Univ. of Chicago Press, Chicago.
65. Ranta E., Kaitala V., Lindström J., Lindén H. Synchrony in population dynamics. Proc. Roy. Soc. London B. 262:1995a;113-118.
66. Ranta E., Lindström J., Lindén H. Synchrony in tetraonid population dynamics. J. Anim. Ecol. 64:1995b;767-776.
67. Reeve J. D. Environmental variability, migration, and persistence in host-parasitoid systems. Am. Nat. 132:1988;810-836.
68. Rohani P., May R. M., Hassell M. P. Metapopulations and equilibrium stability: The effects of spatial structure. J. Theor. Biol. 181:1996;97-109.
69. Rohani P., Miramontes O. Host-parasitoid metapopulations: The consequences of parasitoid aggregation on spatial dynamics and searching efficiency. Proc. Roy. Soc. London B. 260:1995;335-342.
70. Rössler O. E. An equation for hyperchaos. Phys. Lett. A. 71:1979;155-157.
71. Ruxton G. D. Density-dependent migration and stability in a system of linked populations. Bull. Math. Biol. 58:1996;643-660.
72. Ruxton G. D., Doebeli M. Spatial self-organization and persistence of transients in a metapopulation model. Proc. Roy. Soc. London B. 263:1996;1153-1158.
73. Ruxton G. D., Rohani P. The consequences of stochasticity for self-organized spatial dynamics, persistence and coexistence in spatially extended host-parasitoid communities. Proc. Roy. Soc. London B. 263:1996;625-631.
74. Sabelis M. W., Diekmann O. Overall population stability despite local extinction: The stabilizing influence of prey dispersal from predator-invaded patches. Theor. Pop. Biol. 34:1988;169-176.
75. Sakaguchi H., Tomita K. Bifurcations of the coupled logistic map. Prog. Theor. Phys. 78:1987;305-315.
76. Smith C. H. Spatial trends in Canadian snowshoe hare, Lepus americanus, population cycles. Can. Field-Naturalist. 97:1983;151-160.
77. Sutcliffe O. L., Thomas C. D., Moss D. Spatial synchrony and asynchrony in butterfly population dynamics. J. Anim. Ecol. 65:1996;85-95.
78. Thomson J. M. T., Stewart H. B. Nonlinear Dynamics and Chaos. 1986;Wiley, Chichester.
79. Van Buskirk R., Jeffries C. Observation of chaotic dynamics of coupled nonlinear oscillators. Phys. Rev. A. 31:1985;3332-3357.
80. Waller I., Kapral R. Spatial and temporal structure in systems of coupled nonlinear oscillators. Phys. Rev. A. 30:1984;2047-2055.
81. Wang X., Lowenstein J. H. Scaling relations for thermodynamic functions of circle maps. Phys. Rev. A. 41:1990;5721-5724.
82. Wang X., Maineri R., Lowenstein J. H. Circle-map scaling in a two-dimensional setting. Phys. Rev. A. 40:1989;5382-5389.
83. Wiggins S. Global Bifurcations and Chaos: Analytical Methods. 1988;Springer-Verlag, New York.
84. Wiggins S. Introduction to Applied Nonlinear Dynamical Systems and Chaos. 1990;Springer-Verlag, New York.
85. Yamada T., Fujisaka H. Stability theory of synchronized motion in coupled-oscillator systems. II. The mapping approach. Prog. Theor. Phys. 70:1983;1240-1248.