Time delays in density dependence are often not destabilizing

Journal of Theoretical Biology

Volumn 191, Issue 1, 1998, Pages 95-101

  Rodríguez, Diego J ^a  

^a UNIVERSIDAD CENTRAL DE VENEZUELA   (Venezuela)

Author keywords

[No Author keywords available]

Indexed keywords

DENSITY DEPENDENCE; MODELLING; POPULATION SIZE;

ARTICLE; BODY SIZE; LIFE CYCLE; MATHEMATICAL MODEL; MORTALITY; POPULATION DENSITY; POPULATION DYNAMICS; PRIORITY JOURNAL;

EID: 0344936539     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.1997.0569     Document Type: Article

References (40)

1. AGRELL, P., ERLINGE, S., NELSON, J., NILSSON, C. & PERSSON, I. (1995). Delayed density-dependence in a small-rodent population. Proc. R. Soc. Lond. B262, 65-70.
2. BECKER, N. (1989). Life strategies of mosquitoes as an adaptation to their habitats. Bull. Soc. Vector. Ecol. 14, 6-25.
3. BELL, W. J. (1990). Searching behavior patterns in insects. Annu. Rev. Entomol. 35, 447-467.
4. BELLOWS, T. S., JR. (1981). The descriptive properties of some models for density dependence. J. Anim. Ecol. 50, 139-156.
5. BLYTHE, S. P., NISBET, R. M. & GURNEY, W. S. C. (1982). Instability and complex dynamic behavior in population models with long time delays. Theor. Pop. Biol. 22, 147-176.
6. BLYTHE, S. P., GURNEY, W. S. C., MASS, P. & NISBET, R. M. (1990). SOLVER. Applied Physics Industrial Consultants. User Guide 40. Glascow: University of Strathclyde.
7. CHRISTIANSEN, F. B. (1984). Evolution in a temporally varying environment: Density and composition dependent genotypic fitnesses. In: £2Population Biology and Evolution (Wöhrmann, K. & Loeschke, V., eds), pp. 115-124. Berlin: Springer-Verlag.
8. CUNNINGHAM, W. J. (1954). A nonlinear differential-difference equation of growth. Proc. Natl. Acad. Sci. U.S.A. 40, 708-713.
9. CUSHING, J. M. (1980). Model stability and instability in age structured populations. J. theor. Biol. 86, 709-730.
10. CUSHING, J. M. (1981). Stability and maturation periods in age structured populations. In: Differential Equations and Applications in Ecology, Epidemics and Population Dynamics (Busenberg, S. & Cooke, K., eds), pp. 163-181. New York: Academic Press.
11. CUSHING, J. M. & SALEEM, M. (1982). A predator prey model with age structure. J. Math. Biology 14, 231-250.
12. FRYXELL, J. M., HUSSELL, D. J. T., LAMBERT, A. B. & SMITH, P. C. (1991). Time lags and population fluctuations in white-tailed deer. J. Wildl. Manage. 55, 377-385.
13. GURNEY, W. S. C., BLYTHE, S. P. & NISBET, R. M. (1980). Nicholson's blowflies revisited. Nature 287, 17-21.
14. GURNEY, W. S. C., NISBET, R. M. & LAWTON, J. H. (1983). The systematic formulation of tractable single-species population models incorporating age structure. J. Anim. Ecol. 52, 479-495.
15. GURNEY, W. S. C. & NISBET, R. M. (1985). Fluctuation periodicity, generation separation, and the expression of larval competition. Theor. Pop. Biol. 28, 150-180.
16. HASSELL, M. P. (1975). Density dependence in single-species populations. J. Anim. Ecol. 44, 283-295.
17. HASTINGS, A. (1983). Age-dependent predation is not a simple process. I. Continuous time models. Theor. Popul. Biol. 23, 347-362.
18. HÖRNFELDT, B. (1994). Delayed density dependence as a determinant of vole cycles. Ecology 75, 791-806.
19. HUTCHINSON, G. E. (1948). Circular causal systems in ecology. Ann. N.Y. Acad. Sci. 50, 221-245.
20. JANSEN, V. A. A., NISBET, R. M. & GURNEY, W. S. C. (1990). Generation cycles in stage structured populations. Bull. Math. Biol. 52, 375-396.
21. KEITH, L. B., CARY, J. R., RONGSTAD, O. J. & BRITTINGHAM, M. C. (1984). Demography and ecology of a declining snowshoe hare population. Wildl. Monogr. 90, 1-43.
22. MACDONALD, N. (1989). Biological Delay Systems: Linear Stability Analysis. Cambridge: Cambridge University Press.
23. MAY, R. M. (1974). Stability and Complexity in Model Ecosystems. Monographs in Population Biology Nr. 6. Princeton: Princeton University Press.
24. MAY, R. M. & OSTER, G. F. (1976). Bifurcations and dynamic complexity in simple ecological models. Amer. Natur. 110, 573-599.
25. MAYNARD SMITH, J. (1974). Models in Ecology. Cambridge: Cambridge University Press.
26. NICHOLSON, A. J. (1948). Competition for food amongst Lucilia cuprina larvae. Proc. VIII Int. Cong. Entomol. pp. 277-281.
27. NICHOLSON, A. J. (1954). An outline of the dynamics of animal populations. Aust. J. Zool. 2, 9-65.
28. NICHOLSON, A. J. (1957). The self-adjustment of populations to change. Cold Spring Harbour Symp. Quant. Biol. 22, 153-173.
29. NISBET, R. M. & GURNEY, W. S. C. (1982). Modelling Fluctuating Populations. New York: Wiley.
30. NISBET, R. M. & GURNEY, W. S. C. (1983). The systematic formulation of population models for insects with dynamically varying instar duration. Theor. Pop. Biol. 23, 114-135.
31. POULSEN, E. T. (1979). A model for population regulation with density-and frequency-dependent selection. J. Math. Biol. 8, 325-343.
32. PRATT, D. M. (1943). Analysis of population development in Daphnia at different temperatures. Biol. Bull. 85, 116-140.
33. PRESS, W. H., FLANNERY, B. P., TEUKOLSKY, S. A. & VETTERING, W. T. (1989). Numerical Recipes in Pascal. Cambridge: Cambridge University Press.
34. PROKOPY, R. J. & ROITBERG, B. D. (1984). Foraging behavior of true fruit flies. Am. Sci. 72, 41-49.
35. RENWICK, J. A. A. & CHEW, F. S. (1994). Oviposition behavior in Lepidoptera. Annu. Rev. Entomol. 39, 377-400.
36. RODRÍGUEZ, D. J. (1989). A model of population dynamics for the fruit fly Drosophila melanogaster with density dependence in more than one life stage and delayed density effects. J. Anim. Ecol. 58, 349-365.
37. STENSETH, N. C. & ANTONSEN, B. J. (1988). Density dependence and the microtine cycle. I. A continuous time model with delay due to development. Oikos 52, 197-206.
38. TAYLOR, C. E. & SOKAL, R. R. (1976). Oscillations in housefly population sizes due to time lags. Ecology 57, 1060-1067.
39. THOMPSON, J. N. & PELLMYR, O. (1991). Evolution of oviposition behavior and host preference in Lepidoptera. Annu. Rev. Entomol. 36, 65-89.
40. WELLINGTON, W. G. (1960). Qualitative changes in natural populations during changes in abundance. Canad. J. Zool. 38, 289-314.