Allee effects, extinctions, and chaotic transients in simple population models

Theoretical Population Biology

Volumn 64, Issue 2, 2003, Pages 201-209

  Schreiber, Sebastian J ^a  

^a The College of William and Mary   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALLEE EFFECT; DENSITY DEPENDENCE; EXTINCTION; POPULATION MODELING; PREDATION; PREDATOR-PREY INTERACTION;

GOES;

EID: 0347598161     PISSN: 00405809     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0040-5809(03)00072-8     Document Type: Article

References (47)

1. Arditi R., Akcakaya H.R. Underestimation of mutual interference of predators. Oecologia. 83:1990;358-361.
2. Bellows T.S. The descriptive properties of some models for density dependence. J. Anim. Ecol. 50:1981;139-156.
3. Costantino R.H., Desharnais R.A., Cushing J.M., Dennis B. Chaotic dynamics in an insect population. Science. 275:1997;389-391.
4. Courchamp F., Clutton-Brock T., Grenfell B. Inverse density dependence and the Allee effect. TREE. 14:1999;405-410.
5. Crawley M.J., Long C.R. Alternate bearing, predator saturation and seedling recruitment in Quercus robur L. J. Ecol. 83:1995;683-696.
6. Cushing J.M., Constantino R.F., Dennis B., Desharnais R.A., Henson S.M. Nonlinear population dynamics. models, experiments, and data J. Theor. Biol. 194:1998;1-9.
7. Dennis B. Allee effects. population growth, critical density, and the chance of extinction Nat. Res. Model. 3:1989;481-538.
8. Ehrlich P.R. The population biology of coral reef fishes. Annu. Rev. Ecol. Sys. 6:1975;211-247.
9. Fowler C.W., Baker J.D. A review of animal population dynamics at extremely reduced population levels. Rep. Int. Whal. Comm. 41:1991;545-554.
10. Fox L.R. Cannibalism in natural populations. Annu. Rev. Ecol. Syst. 6:1975;87-106.
11. Getz W.M. A hypothesis regarding the abruptness of density dependence and the growth rate of populations. Ecology. 77:1996;2014-2026.
12. Goodman D. The demography of chance extinction. Soulé M.E. Viable Populations for Conservation. 1987;11-34 Cambridge University Press, Cambridge, Great Britain.
13. Grenfell B.T., Price O.F., Albon S.D., Clutton-Brock T.H. Overcompensation and population cycles in an ungulate. Nature. 355:1992;823-826.
14. Groom M.J. Allee effects limit population viability of an annual plant. Am. Nat. 151:1998;487-496.
15. Gyllenberg M., Osipov A.V., Söderbacka G. Bifurcation analysis of a metapopulation model with sources and sinks. J. Nonlinear Sci. 6:1996;329-366.
16. Harrison S., Cappuccino N. Using density-manipulation experiments to study population regulation. Cappuccino N., Price P.W. Population Dynamics: New Approaches and Synthesis. 1995;131-147 Academic Press, San Diego, CA.
17. Hassell M.P., Lawton J.H., Beddington J.R. The components of arthropod predation. I. The prey death-rate J. Anim. Ecol. 45:1976;135-164.
18. Hastings A., Higgins K. Persistence of transients in spatially structured ecological models. Science. 263:1994;1133-1136.
19. Jones C.G., Lawton J.H., Shachak M. Positive and negative effects of organisms as physical ecosystem engineers. Ecology. 78:1997;1946-1957.
20. Knowlton N. Thresholds and multiple steady states in coral reef community dynamics. Am. Zool. 32:1992;674-682.
21. Lande R., Engen S., Sæther B.E. Stochastic population dynamics in ecology and conservation. 2003;Oxford University Press, Oxford.
22. Levitan, D.R., McGovern, T.M., in press. The Allee effect in the sea. In: Norse, E.A., Crowder, L.B. (Eds.), Marine Conservation Biology. The Science of Maintaining the Seas Biodiversity. Island Press, Washington, DC.
23. Levitan D.R., Sewell M.A., Chia F. How distribution and abundance influence fertilization success in the sea urchin Strongylocentotus franciscanus. Ecology. 73:1992;248-254.
24. Mangel M., Tier C. Four facts every conservation biologists should know about persistence. Ecology. 75:1994;607-614.
25. May R.M. Stability and Complexity in Model Ecosystems. 2nd Edition:1975;Princeton University Press, Princeton, NJ.
26. May R.M. Thresholds and breakpoints in ecosystems with a multiplicity of stable states. Nature. 269:1977;471-477.
27. McCann K., Yodzis P. Nonlinear dynamics and population disappearances. Amer. Nat. 144:1994;873-879.
28. McCarthy M.A. The Allee effect, finding mates and theoretical models. Ecol. Model. 103:1997;99-102.
29. Noy-Meir I. Stability of grazing systems. an application of predator-prey graphs J. Ecol. 63:1975;459-481.
30. Pianigiani G., Yorke J.A. Expanding maps on sets which are almost invariant. Decay and chaos. Trans. Amer. Math. Soc. 252:1979;351-366.
31. Ricker W.E. Stock and recruitment. J. Fish. Res. Board. Can. 11:1954;559-623.
32. Rosenzweig M.L. Paradox of enrichment: destabilization of paradox of enrichment. destabilization of exploitation ecosystems in ecological time Science. 171:1971;385-387.
33. Scheuring I. Allee effect increases dynamical stability in populations. J. Theor. Biol. 199:1999;407-414.
34. Schreiber S.J. Chaos and sudden extinction in simple ecological models. J. Math. Biol. 42:2001;239-260.
35. Sinha S., Parthasarathy S. Unusual dynamics of extinction in a simple ecological model. Proc. Natl. Acad. Sci. USA. 93:1996;1504-1508.
36. Stephens P.A., Sutherland W.J. Consequences of the Allee effect for behavior, ecology, and conservation. TREE. 14:1999;401-405.
37. Stephens P.A., Sutherland W.J., Freckleton R.P. What is the Allee effect? Oikos. 87:1999;185-190.
38. Stone L. Period-doubling reversals and chaos in simple ecological models. Nature. 365:1993;617-620.
39. Symonides E., Silvertown J., Andreasen V. Population cycles caused by overcompensating density-dependence in an annual plant. Oecologia. 71:1986;156-158.
40. Tilman, D., 1982. Resource Competition and Community Structure. Monographs in Population Biology, Vol. 17. Princeton University Press, Princeton, NJ.
41. Turchin P. Chaos and stability in rodent population dynamics. evidence from nonlinear time-series analysis Oikos. 68:1993;289-305.
42. Turchin P. Population regulation: old arguments, new synthesis. Cappuccino N., Price P.W. Population Dynamics: New Approaches and Synthesis. 1995;19-40 Academic Press, San Diego, CA.
43. Turchin P., Taylor A.D. Complex dynamics in ecological time series. Ecology. 73:1992;289-305.
44. Vandermeer J., Yodzis P. Basin boundary collision as a model of discontinuous change in ecosystems. Ecology. 80:1999;1817-1827.
45. Wiklund C.G., Andersson M. Natural selection on colony size on a passerine bird. J. Anim. Ecol. 63:1994;765-774.
46. Williams K.S., Smith K.G., Stephen F.M. Emergence of 13 year periodical cicadas (Cicadae: Magicada). phenology, mortality, and predator saturation Ecology. 74:1993;1143-1152.
47. Wolda H., Dennis B. Density dependence tests, are they? Oecologia. 95:1993;581-591.