Universal power laws govern intermittent rarity in communities of interacting species

Ecology

Volumn 80, Issue 5, 1999, Pages 1505-1521

  Ferriere, Regis ^a,b   Cazelles, Bernard ^a,c  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS   (Austria)

^c UNIVERSITÉ PARIS DESCARTES   (France)

Author keywords

Chaos; Community dynamics; Competition; Criticality; Franke Yakubu model; Gatto model; Hochberg Hawkins model; Intermittent rarity; Invasibility; Power law; Universal scaling

Indexed keywords

COMMUNITY STRUCTURE; ECOLOGICAL MODELING; INTERSPECIFIC COMPETITION; POWER LAW; RARITY;

EID: 0032820438     PISSN: 00129658     EISSN: None     Source Type: Journal    
DOI: 10.1890/0012-9658(1999)080[1505:UPLGIR]2.0.CO;2     Document Type: Article

References (78)

1. Anderson, R. M., and R. M. May. 1992. Infectious diseases of humans, dynamic and control. Oxford University Press, Oxford, UK.
2. Back, C. H., Ch. Würsch, A. Vaterlaus, U. Ramsperger, U. Maier, and D. Pescia. 1995. Experimental confirmation of universality for a phase transition in two dimensions. Nature (London) 378:597-600.
3. Bak, P. 1994. Self-organized criticality: a holistic view of Nature. Pages 477-496 in G. Cowan, D. Pines, and D. Meltzer, editors. Complexity: metaphors, models, and reality. Addison-Wesley, New York, New York, USA.
4. Baumgartner, T. R., A. Soutar, and V. Ferreira-Bartrina. 1992. Reconstruction of the history of Pacific sardine and northern anchovy populations over the past two millennia from sediments of the Santa Barbara basin, California. Californian Cooperative Oceanic Fishery Investment Report 33: 24-40.
5. Baxter, R. J. 1982. Exactly solved models in statistical mechanics. Academic Press, London, UK.
6. Chesson, P. L., and S. Ellner. 1989. Invasibility and stochastic boundedness in monotonic competition models. Journal of Mathematical Biology 27:117-138.
7. Crowe, K. M. 1994. A nonlinear ergodic theorem for discrete systems. Journal of Mathematical Biology 32:179-191.
8. _. 1997. Nonlinear ergodic theorems and symmetric vs. asymmetric competition. Pages 515-532 in S. Tuljapurkar and H. Caswell, editors. Structured-population models in marine, terrestrial, and freshwater systems. Chapman and Hall, New York, New York, USA.
9. Csilling, A., I. M. Janosi, G. Pasztor, and I. Scheuring. 1994. Absence of chaos in a self-organized critical coupled map lattice. Physical Review E 50:1083-1092.
10. Cury, P. 1988. Pressions sélectives et nouveautés évolutives: une hypothèse pour comprendre certains aspects des fluctuations à long terme des poissons pélagiques côtiers. Canadian Journal of Fisheries and Aquatic Sciences 45:1099-1107.
11. Cushing, J. M. 1989. A strong ergodic theorem for some nonlinear matrix models for structured population growth. Natural Resource Modeling 3:331-357.
12. De Feo, O., and R. Ferriere. 1999. Bifurcation analysis of population invasion: on-off intermittency and basin riddling. International Journal of Bifurcation and Chaos, in press.
13. De Feo, O., and S. Rinaldi. 1997. Yield and dynamics of tritrophic food chains. The American Naturalist 150:328-345.
14. Dellnitz, M., M. Field, M. Golubitsky, J. Ma, and A. Hohmann. 1995. Cycling chaos. International Journal of Bifurcation and Chaos 5:1243-1247.
15. Dennis B., R. A. Desharnais, J. M. Cushing, and R. F. Costantino. 1995. Nonlinear demographic dynamics: mathematical models, statistical methods, and biological experiments. Ecological Monographs 65:261-281.
16. DeVries, T. J., and W. G. Pearcy. 1982. Fish debris in sediments of the upwelling zone off central Peru: a late Quaternary record. Deep-Sea Research 28:87-109.
17. Dieckmann, U., R. Law, and J. A. J. Metz, editors. 1999. The geometry of spatial interactions. Cambridge University Press, Cambridge, UK.
18. Durrett, R., and S. Levin. 1994. The importance of being discrete (and spatial). Theoretical Population Biology 46: 363-394.
19. Ferriere, R., and M. Gatto. 1995. Lyapunov exponents and the mathematics of invasion in oscillatory or chaotic populations. Theoretical Population Biology 48:126-171.
20. Franke, J. E., and A.-A. Yakubu. 1991. Mutual exclusion vs. coexistence for discrete competitive systems. Journal of Mathematical Biology 30:161-168.
21. Gaston, K. J. 1994. Rarity. Chapman and Hall, London, UK.
22. Gaston, K. J. 1997. What is rarity? Pages 30-47 in W. E. Kunin and K. J. Gaston, editors. The biology of rarity. Chapman and Hall, London, UK.
23. Gatto, M. 1993. The evolutionary optimality of oscillatory and chaotic dynamics in simple population models. Theoretical Population Biology 43:310-336.
24. Gavrilets, S., and A. Hastings. 1995. Intermittency and transient chaos from simple frequency-dependent selection. Proceedings of the Royal Society B 261:233-238.
25. Gragnani, A., and S. Rinaldi. 1995. A universal bifurcation diagram for seasonally perturbed predator-prey models. Bulletin of Mathematical Biology 57:701-712.
26. Griggs, R. F. 1940. The ecology of rare plants. Bulletin of the Torrey Botanical Club 67:575-594.
27. Hadeler, K. P., and I. Gerstmann. 1990. The discrete Rosenzweig model. Mathematical Biosciences 98:49-72.
28. Hanski, I. 1985. Single-species spatial dynamics may contribute to long-term rarity and commonness. Ecology 66: 335-343.
29. Hastings, A., and T. Powell. 1991. Chaos in three-species food chain. Ecology 72:896-903.
30. Heagy, J. F., N. Platt, and S. M. Hammel. 1994. Characterization of on-off intermittency. Physical Review E 49: 1140-1150.
31. Heino, M., J. A. J. Metz, and V. Kaitala. 1997. Evolution of mixed maturation strategies in semelparous life histories: the crucial role of dimensionality of feedback environment. Philosophical Transactions of the Royal Society of London B 352:1647-1655.
32. Hochberg, M. E., and B. A. Hawkins. 1992. Refuges as a predictor of parasitoid diversity. Science 255:973-976.
33. Hofbauer, J. 1994. Heteroclinic cycles in ecological differential equations. Tatra Mountains Mathematical Publications 4:105-116.
34. Hofbauer, J., V. Hutson, and W. Jansen. 1987. Coexistence for systems governed by difference equations of Lotka-Volterra type. Journal of Mathematical Biology 25:553-570.
35. Keitt, T. H., and H. E. Stanley. 1998. Dynamics of North American breeding bird populations. Nature 393:257-260.
36. Kondô, K. 1987. Relationships between long term fluctuations in the Japanese sardine (Sardinops melanosticus) and oceanographic conditions. International Symposium on Long Term Changes in Marine Fish Populations, 18-21 November 1986, Vigo, Spain.
37. Krupa, M. 1997. Robust heteroclinic cycles. Journal of Nonlinear Sciences 7:129-176.
38. May, R. M., editor. 1984. Exploitation of marine communities. Life Sciences Research Report 32. Springer Verlag, Berlin, Germany.
39. Maynard Smith, J. 1974. Models in ecology. Cambridge University Press, Cambridge, UK.
40. Meszéna, G., and J. A. J. Metz. In press. The role of effective environmental dimensionality. In U. Dieckmann and J. A. J. Metz, editors. An introduction to adaptive dynamics. Cambridge University Press, Cambridge, UK.
41. Metz, J. A. J., S. D. Mylius, and O. Diekmann. 1996. When does evolution optimise? On the relation between types of density-dependence and evolutionarily stable life history parameters. International Institute for Applied Systems Analysis (IIASA) preprint 96-04. Laxenburg, Austria.
42. Metz, J. A. J., R. M. Nisbet, and S. A. H. Geritz. 1992. How should we define 'fitness' for general ecological scenarios? Trends in Ecology and Evolution 7:198-202.
43. Mikkola, K. 1979. Vanishing and declining species of Finnish Lepidoptera. Notulae Entomologicae 59:1-9.
44. Mikkola, K., and I. Jalas. 1979. Finnish Lepidoptera: Noctuidae 2. Otava, Helsinki, Finland.
45. Mira, C. 1987. Chaotic Dynamics. World Scientific, Singapore, Singapore.
46. Muratori, S., and S. Rinaldi. 1992. Low- and high-frequency oscillations in three-dimensional food chain systems. Society for Industrial and Applied Mathematics Journal of Applied Mathematics 52:1688-1706.
47. Neubert, M. G., and M. Kot. 1992. The subcritical collapse of predator populations in discrete-time predator-prey models. Mathematical Biosciences 110:45-66.
48. Nisbet, R. M., and W. S. C. Gurney. 1982. Modelling fluctuating populations. Wiley, New York, New York, USA.
49. Olsen, L., and W. M. Schaffer. 1990. Chaos vs. noisy periodicity: alternative hypothesis for childhood epidemics. Science 249:499-504.
50. Pomeau, Y., and P. Manneville. 1980. Intermittent transition to turbulence in dissipative dynamical systems. Communications in Mathematical Physics 74:189-
51. Radowich, J. 1981. The collapse of the California sardine fishery - what have we learned? Pages 107-136 in M. H. Glantz and J. D. Thompson, editors. Resource management and environmental uncertainty. Wiley-Interscience, New York, New York, USA.
52. Rahel, F. J. 1990. The hierarchical nature of community persistence: a problem of scale. The American Naturalist 136: 328-344.
53. Rand, D. A., H. B. Wilson, and J. M. McGlade. 1994. Dynamics and evolution: evolutionarily stable attractors, invasion exponents, and phenotype dynamics. Philosophical Transactions of the Royal Society of London B 343:261-283.
54. Rhodes, C. J., and R. M. Anderson. 1996a. Dynamics in a lattice epidemic model. Physics Letters A 210:183-188.
55. Rhodes, C. J., and R. M. Anderson. 1996b. Power laws governing epidemics in isolated populations. Nature 381:600-602.
56. Rinaldi, S., S. Muratori, and Y. A. Kuznetsov. 1993. Multiple attraetors, catastrophes, and chaos in periodically forced predator-prey communities. Bulletin of Mathematical Biology 55:15-35.
57. Rogers, T. D. 1984. Rarity and chaos. Mathematical Biosciences 72:13-17.
58. Rosenzweig, M. L., and M. V. Molino. 1997. Who gets the short bits of the broken stick? Pages 63-90 in K. Gaston and W. E. Kunin, editors. Rarity in biological systems. Chapman and Hall, London, UK.
59. Rothschild, B. J. 1986. Dynamics of marine fish populations. Harvard University Press, Cambridge, Massachusette, USA.
60. Royama, T. 1992. Analytical population dynamics. Chapman and Hall, London, UK.
61. Ruelle, D. 1989. Chaotic evolution and strange attractors. Cambridge University Press, Cambridge, UK.
62. Schoener, T. W. 1987. The geographical distribution of rarity. Oecologia (Berlin) 74:161-173.
63. Schonewald-Cox, C., and M. Buechner. 1991. Housing viable populations in protected habitats: the value of a coarse-grained geographic analysis of density patterns and available habitat. Pages 99-115 in A. Seitz, and V. Loeschcke, editors. Species conservation: a population-biological approach. Birkhauser Verlag, Basel, Switzerland.
64. Schuster, H. G. 1989. Deterministic chaos. Second edition. VCH, Weinheim, Germany.
65. Soutar, A., and J. D. Isaacs. 1974. Abundance of pelagic fish during the 19th and 20th centuries as recorded in anaerobic sediment off California. Fishery Bulletin 72:257-274.
66. Southwood, T. R. E., and H. N. Comins. 1976. A synoptic population model. Journal of Animal Ecology 45:949-965.
67. Stanley, H. E. 1971. Introduction to phase transitions and critical phenomena. Oxford University Press, Oxford, UK.
68. _. 1995. Power laws and universality. Nature 378:554.
69. Stanley, H. E., and N. Ostrowky, editors. 1990. Correlations and connectivity: geometric aspects of physics, chemistry, and biology. Kluwer, Dordrecht, the Netherlands.
70. Tilman, D. and P. Kareiva, editors. 1997. Spatial ecology. Princeton University Press, Princeton, New Jersey, USA.
71. Tsuboi, M. 1984. Marine resources trends of purse seines -as main aims of sardine and mackerel fisheries - economical structure of purse seine fishery. Progress Report of Synthesis Investigations of the Japanese Fisheries, 1983 Project. Dai-Nihon Suisankai, Japan, March 1984.
72. Tuljapurkar, S. 1990. Population dynamics in variable environments. Springer-Verlag, New York, New York, USA.
73. Turelli, M. 1978. Does environmental variability limit niche overlap? Proceedings of the National Academy of Sciences USA 75:5085-5089.
74. Vandermeer, J. 1982. To be rare is to be chaotic. Ecology 63:1167-1168.
75. _. 1993. Loose coupling of predator-prey cycles: entrainment, chaos, and intermittency in the classic MacArthur consumer-resource equations. The American Naturalist 141:687-716.
76. Venkataramani, S. C., T. M. Antonsen Jr., E. Ott, and J. C. Sommerer. 1995. Characterization of on-off intermittent time series. Physics Letters A 207:173-179.
77. Venkataramani, S. C., T. M. Antonsen Jr., E. Ott, and J. C. Sommerer. 1996. On-off intermittency: power spectrum and fractal properties of times series. Physica D 96:66-99.
78. Warner, R. R., and P. L. Chesson. 1985. Coexistence mediated by recruitment fluctuations: a field guide to the storage effect. The American Naturalist 125:769-787.