Remarks on metacommunity synchronization with application to prey-predator systems

American Naturalist

Volumn 171, Issue 4, 2008, Pages 430-442

  Colombo, Alessandro ^a   Dercole, Fabio ^a   Rinaldi, Sergio ^a,b  

^a POLITECNICO DI MILANO   (Italy)

^b INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS   (Austria)

Author keywords

Chaos; Dispersal; Lyapunov exponent; Moran effect; Prey predator; Synchronization

Indexed keywords

CHAOTIC DYNAMICS; DISPERSAL; ECOLOGICAL MODELING; EXPERIMENTAL STUDY; POPULATION DYNAMICS; PREDATOR-PREY INTERACTION; SYNCHRONY; TRAJECTORY;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; FOOD CHAIN; PREDATION;

ANIMALS; FOOD CHAIN; MODELS, BIOLOGICAL; PREDATORY BEHAVIOR;

EID: 40949139796     PISSN: 00030147     EISSN: None     Source Type: Journal    
DOI: 10.1086/528959     Document Type: Article

References (61)

1. Blasius, B., A. Huppert, and L. Stone. 1999. Complex dynamics and phase synchronization in spatially extended ecological systems. Nature 399:354-359.
2. Bulmer, M. G. 1974. A statistical analysis of the 10-year cycle in Canada. Journal of Animal Ecology 43:701-718.
3. Cazelles, B., and G. Boudjema. 2001. The Moran effect and phase synchronization in complex spatial community dynamics. American Naturalist 157:670-676.
4. Cazelles, B., S. Bottani, and L. Stone. 2001. Unexpected coherence and conservation. Proceedings of the Royal Society B: Biological Sciences 268:2595-2602.
5. Cushing, J. M., R. F. Costantino, B. Dennis, R. A. Desharnais, and S. M. Henson. 2002. Chaos in ecology: experimental nonlinear dynamics. Academic Press, Amsterdam.
6. Dercole, F., D. Loiacono, and S. Rinaldi. 2007. Synchronization in ecological networks: a byproduct of Darwinian evolution? International Journal of Bifurcation and Chaos 17:2435-2446.
7. Doebeli, M., and G. D. Ruxton. 1997. Evolution of dispersal rates in metapopulation models: branching and cyclic dynamics in phenotype space. Evolution 51:1730-1741.
8. Earn, D. J. D., and S. A. Levin. 2006. Global asymptotic coherence in discrete dynamical systems. Proceedings of the National Academy of Sciences of the USA 103:3968-3971.
9. Earn, D. J. D., P. Rohani, and B. T. Grenfell. 1998. Persistence, chaos and synchrony in ecology and epidemiology. Proceedings of the Royal Society B: Biological Sciences 265:7-10.
10. Earn, D. J. D., S. A. Levin, and P. Rohani. 2000. Coherence and conservation. Science 290:1360-1364.
11. Ellner, S., and P. Turchin. 1995. Chaos in a noisy world: new methods and evidence from time series analysis. American Naturalist 145:343-375.
12. Elton, C. S. 1924. Periodic fluctuations in the numbers of animals. British Journal of Experimental Biology 2:119-163.
13. Elton, C. S., and M. Nicholson. 1942. The ten-year cycle in numbers of the lynx in Canada. Journal of Animal Ecology 11:215-244.
14. Fontaine, C., and A. Gonzalez. 2005. Population synchrony induced by resource fluctuations and dispersal in an aquatic microcosm. Ecology 86:1463-1471.
15. Gragnani, A., and S. Rinaldi. 1995. A universal bifurcation diagram for seasonally perturbed predator-prey models. Bulletin of Mathematical Biology 57:701-712.
16. Grenfell, B. T., K. Wilson, B. F. Finkenstädt, T. N. Coulson, S. Murray, S. D. Albon, J. M. Pemberton, T. H. Clutton-Brock, and M. J. Crawley. 1998. Noise and determinism in synchronized sheep dynamics. Nature 394:674-677.
17. Hanski, I., and I. P. Woiwod. 1993. Spatial synchrony in the dynamics of moth and aphid populations. Journal of Animal Ecology 62:656-668.
18. Hanski, I., H. Henttonen, E. Korpimäki, L. Oksanen, and P. Turchin. 2001. Small-rodent dynamics and predation. Ecology 82:1505-1520.
19. Harrison, M. A., Y.-C. Lai, and R. D. Holt. 2001. Dynamical mechanism for coexistence of dispersing species. Journal of Theoretical Biology 213:53-72.
20. Hastings, A., C. L. Hom, S. Ellner, P. Turchin, and H. C. J. Godfray. 1993. Chaos in ecology: is Mother Nature a strange attractor? Annual Review of Ecology and Systematics 24:1-33.
21. Haydon, D., and H. Steen. 1997. The effects of large- and small-scale random events on the synchrony of metapopulation dynamics: a theoretical analysis. Proceedings of the Royal Society B: Biological Sciences 264:1375-1381.
22. Higgins, K., A. Hastings, J. N. Sarvela, and L. W. Botsford. 1997. Stochastic dynamics and deterministic skeletons: population behavior of Dungeness crab. Science 276:1431-1435.
23. Hillary, R. M., and M. A. Bees. 2004. Synchrony and chaos in patchy ecosystems. Bulletin of Mathematical Biology 66:1909-1931.
24. Holling, C. S. 1965. The functional response of predators to prey density and its role in mimicry and population regulation. Memoirs of the Entomological Society of Canada 45:5-60.
25. Holt, R. D., and M. A. McPeek. 1996. Chaotic population dynamics favors the evolution of dispersal. American Naturalist 148:709-718.
26. Izhikevich, E. M. 2000. Phase equations for relaxation oscillators. SIAM Journal on Applied Mathematics 60:1789-1805.
27. Jansen, V. A. A. 2001. The dynamics of two diffusively coupled predator-prey populations. Theoretical Population Biology 59:119-131.
28. Jansen, V. A. A., and A. L. Lloyd. 2000. Local stability analysis of spatially homogeneous solutions of multi-patch systems. Journal of Mathematical Biology 41:232-252.
29. Johst, K., M. Doebeli, and R. Brandl. 1999. Evolution of complex dynamics in spatially structured populations. Proceedings of the Royal Society B: Biological Sciences 266:1147-1154.
30. King, A. A., and W. M. Schaffer. 1999. The rainbow bridge: Hamiltonian limits and resonance in predator-prey dynamics. Journal of Mathematical Biology 39:439-469.
31. _. 2001. The geometry of a population cycle: a mechanistic model of snowshoe hare demography. Ecology 82:814-830.
32. Koenig, W. D. 1999. Spatial autocorrelation of ecological phenomena. Trends in Ecology & Evolution 14:22-26.
33. Kuznetsov, Y. A., S. Muratori, and S. Rinaldi. 1992. Bifurcation and chaos in a periodic predator-prey model. International Journal of Bifurcation and Chaos 2:117-128.
34. Lawton, J. H. 1988. More time means more variation. Nature 334:563.
35. Liebhold, A. M., W. D. Koenig, and O. N. Bjørnstad. 2004. Spatial synchrony in population dynamics. Annual Review of Ecology, Evolution, and Systematics 35:467-490.
36. Lloyd, A. L., and R. M. May. 1999. Synchronicity, chaos and population cycles: spatial coherence in an uncertain world. Trends in Ecology & Evolution 14:417-418.
37. Maggi, S., and S. Rinaldi. 2006. Synchronization and peak-to-peak dynamics in networks of low-dimensional chaotic oscillators. International Journal of Bifurcation and Chaos 16:3631-3642.
38. Moran, P. A. P. 1953. The statistical analysis of the Canadian lynx cycle. II. Synchronisation and meteorology. Australian Journal of Zoology 1:291-298.
39. Pascual, M., F. A. Ascioti, and H. Caswell. 1995. Intermittency in the plankton: a multifractal analysis of zooplankton biomass variability. Journal of Plankton Research 17:1209-1232.
40. Pecora, L. M., and T. L. Carroll. 1998. Master stability functions for synchronized coupled systems. Physical Review Letters 80:2109-2112.
41. Petchey, O. L., A. Gonzalez, and H. B. Wilson. 1997. Effects on population persistence: the interaction between environmental noise colour, intraspecific competition and space. Proceedings of the Royal Society B: Biological Sciences 264:1841-1847.
42. Pikovsky, A., M. Rosenblum, and J. Kurths. 2001. Synchronization. Cambridge University Press, Cambridge.
43. Post, E., and M. C. Forchhammer. 2002. Synchronization of animal population dynamics by large-scale climate. Nature 420:168-171.
44. Ramasubramanian, K., and M. S. Sriram. 2000. A comparative study of computation of Lyapunov spectra with different algorithms. Physica D 139:72-86.
45. Ranta, E., V. Kaitala, J. Lindström, and E. Helle. 1997. The Moran effect and synchrony in population dynamics. Oikos 78:136-142.
46. Rinaldi, S., and S. Muratori. 1993. Conditioned chaos in seasonally perturbed predator-prey models. Ecological Modelling 69:79-97.
47. Rinaldi, S., S. Muratori, and Y. A. Kuznetsov. 1993. Multiple attractors, catastrophes and chaos in seasonally perturbed predator-prey communities. Bulletin of Mathematical Biology 55:15-35.
48. Ripa, J. 2000. Analysing the Moran effect and dispersal: their significance and interaction in synchronous population dynamics. Oikos 89:175-187.
49. Rosenzweig, M. L., and R. H. MacArthur. 1963. Graphical representation and stability conditions of predator-prey interactions. American Naturalist 97:209-223.
50. Royama, T. 1992. Analytical population dynamics. Chapman & Hall, London.
51. Ruxton, G. D., J. L. Gonzalez-Andujar, and J. N. Perry. 1997. Mortality during dispersal an the stability of a metapopulation. Journal of Theoretical Biology 186:389-396.
52. Scheffer, M., S. Rinaldi, Y. A. Kuznetsov, and E. H. van Nes. 1997. Seasonal dynamics of Daphnia and algae explained as a periodically forced predator-prey system. Oikos 80:519-532.
53. Scheffer, M., S. Rinaldi, and Y. A. Kuznetsov. 2000. Effects of fish on plankton dynamics: a theoretical analysis. Canadian Journal of Fisheries and Aquatic Sciences 57:1208-1219.
54. Schwartz, M. K., L. S. Mills, K. S. McKelvey, L. F. Ruggiero, and F. W. Allendorf. 2002. DNA reveals high dispersal synchronizing the population dynamics of Canadian lynx. Nature 415:520-522.
55. Sinclair, A. R. E., J. M. Goseline, G. Holdsworth, C. J. Krebs, S. Boutin, N. M. Smith, R. Boonstra, and M. Dale. 1993. Can the solar cycle and climate synchronize the snowshoe hare cycle in Canada? evidence from tree rings and ice cores. American Naturalist 141:173-198.
56. Smith, C. H. 1983. Spatial trends in Canadian snowshoe hare Lepus americanus, population cycles. Canadian Field-Naturalist 97:151-160.
57. Somers, D., and N. Kopell. 1993. Rapid synchronization through fast threshold modulation. Biological Cybernetics 68:393-407.
58. Strogatz, S. H. 1994. Nonlinear dynamics and chaos. Addison-Wesley, Reading, MA.
59. Travis, J. M. J. 2001. The color of noise and the evolution of dispersal. Ecological Research 16:157-163.
60. Turchin, P., and A. D. Taylor. 1992. Complex dynamics in ecological time series. Ecology 73:289-305.
61. Vandermeer, J. 1993. Loose coupling of predator-prey cycles: entrainment, chaos, and intermittency in the classic MacArthur consumer-resource equations. American Naturalist 141:687-716.