A tale of two cycles - Distinguishing quasi-cycles and limit cycles in finite predator-prey populations

Oikos

Volumn 116, Issue 1, 2007, Pages 53-64

  Pineda Krch, Mario ^a,b   J Blok, Hendrik ^a   Dieckmann, Ulf ^c   Doebeli, Michael ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

ECOSYSTEM MODELING; POPULATION CYCLE; POPULATION SIZE; PREDATOR-PREY INTERACTION; STOCHASTICITY;

EID: 33846215107     PISSN: 00301299     EISSN: 16000706     Source Type: Journal    
DOI: 10.1111/j.2006.0030-1299.14940.x     Document Type: Article

References (34)

1. Bartlett, M. S. 1957. Measles periodicity and community size. - J. R. Stat. Soc. A 120: 48-70.
2. Berryman, A.. 2002. Population cycles: cause and analysis. - In: Berryman, A. A. (ed.), Population cycles: the case for trophic interactions. Oxford Univ. Press, pp. 13-28.
3. Bulmer, M. G. 1994. Theoretical evolutionary ecology., Sinauer Ass. Publishers.
4. D'Agostino, R. B., Belanger, A. and D'Agostino Jr., R. B. 1990. A suggestion for using powerful and informative test of normality. - Am. Stat. 44: 316-321.
5. Dallal, G. E. and Wilkinson, L. 1986. An analytical approximation to the distribution of Lilliefors's test statistic for normality. - Am. Stat. 40: 294-296.
6. Elton, C. 1924. Periodic fluctuations in the numbers of animals: their cause and effects. - Brit. J. Exp. Biol. 2: 119-163.
7. Elton, C. 1942. Voles, mice and lemmings: problems in population dynamics. - Claredon Press.
8. Elton, C. and Nicholson, M. 1942. The ten-year cycle in numbers of the lynx in Canada. - J. Anim. Ecol. 11: 215-244.
9. Gilg, O., Hanski, I. and Sittler, B. 2003. Cyclic dynamics in a simple vertebrate predator-prey community. - Science 302: 866-868.
10. Grover, J. P., McKee, D., Young, S. et al. 2000. Periodic dynamics in Daphnia populations: biological interactions and external forcing. - Ecology 81: 2781-2798.
11. Gurney, W. C. S. and Nisbet, R. M. 1998. Ecological dynamics. - Oxford Univ. Press.
12. Hastings, A. 1998. Population biology: concepts and models. - Springer.
13. Higgins, K., Hastings, A., Sarvela, J. N. et al. 1997. Stochastic dynamics and deterministic skeletons: population behavior of Dungeness crab. - Science 276: 1431-1435.
14. Hyndman, R. J. 2005. Time Series Data Library. - [WWW document]. URL: http://www-personal.buseco.monash.edu.au/~hyndman/TSDL/.
15. Kot, M. 2001. Elements of mathematical ecology. - Cambridge Univ. Press.
16. Korpimäki, E., Brown, P. R., Jacob, J. et al. 2004. The puzzle of population cycles and outbreaks of small mammals solved? - BioScience 54: 1071-1079.
17. Krebs, C. J. 1985. Ecology. The experimental analysis of distribution and abundance. - Harper and Row.
18. Krebs, C. J., Boonstra, R., Boutin, S. et al. 2001. What drives the 10-year cycle of snowshoe hares? - BioScience 51: 25-35.
19. Liebhold, A. and Kamata, N. 2000. Are population cycles and spatial synchrony a universal characteristic of forest insect populations? - Popul. Ecol. 42: 205-209.
20. Lilliefors, H. W. 1967. On the Kolmogorov-Smirnov test for normality with mean and variance unknown. - Am. Stat. Ass. J. 62: 399-402.
21. Lindström, J., Ranta, E., Kokko, H. et al. 2001. From arctic lemmings to adaptive dynamics: Charles Elton's legacy in population ecology. - Biol. Rev. 76: 129-158.
22. McKane, A. J. and Newman, T. J. 2005. Predator-prey cycles from resonant amplification of demographic stochasticity. - Phys. Rev. Lett. 94, article no. 218102
23. May, R. M. 1974. Stability and complexity in model ecosystems. - Princeton Univ. Press.
24. Moran, P. A. P. 1953. The statistical analysis of the Canadian lynx cycle. - Aust. J. Zool. 1: 163-173.
25. Nisbet, R. M. and Gurney, W. S. C. 1976. A simple mechanism for population cycles. - Nature 263: 319-320.
26. Nisbet, R. M. and Gurney, W. S. C. 1982. Modelling fluctuating populations. - Blackburn Press, New Jersey.
27. Olarrea, J. and de la Rubia, F. J. 1996. Stochastic Hopf bifurcation: the effect of colored noise on the bifurcation interval. - Phys. Rev. E 53: 268-271.
28. Platt, T. and Denman, K. L. 1975. Spectral analysis in ecology. - Annu. Rev. Ecol. Syst. 6: 189-210.
29. Renshaw, E. 1991. Modelling biological populations in space and time. - Cambridge Univ. Press.
30. Rosenzweig, M. L. and MacArthur, R. H. 1963. Graphical representation and stability conditions of predator-prey interactions. - Am. Nat. 97: 209-223.
31. Sinclair, A. R. E., Gosline, J. M., Holdsworth, G. et al. 1993. Can solar cycles and climate synchronize the snowshoe hare cycle in Canada? Evidence from tree rings and ice cores. - Am. Nat. 141: 173-198.
32. Trujillo-Ortiz, A. and Hernandez-Walls, R. 2003. DagosP-test: D'Agostino-Pearson's K2 test for assessing normality of data using skewness and kurtosis. A MATLAB file. - [WWW document]. URL: http://www.mathworks.com/ matlabcentral/fileexchange/loadFile.do?objectId=3954&objectType=FILE.
33. Turchin, P. and Ellner, S. P. 2000. Living on the edge of chaos: population dynamics of Fennoscandian voles. - Ecology 81: 3099-3116.
34. van Kampen, N. G. 1981. Stochastic processes in physics and chemistry. - North-Holland, Amsterdam.