Consequences for predators of rescue and Allee effects on prey

Ecological Modelling

Volumn 162, Issue 3, 2003, Pages 233-245

  Kent, Adam ^a   Doncaster, C Patrick ^a   Sluckin, Tim ^a  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

Extinction threshold; Functional response; Lotka Volterra; Open system

Indexed keywords

ALLEE EFFECT; EXTINCTION; IMMIGRATION; LIMITING FACTOR; LOTKA-VOLTERRA MODEL; PREDATOR-PREY INTERACTION;

EID: 0037446297     PISSN: 03043800     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3800(02)00343-5     Document Type: Article

References (55)

1. Abrams, P.A., Roth, J.D., 1994a. The effects of enrichment of three-species food-chains with nonlinear functional responses. Ecology 75, 1118-1130.
2. Abrams, P.A., Roth, J., 1994b. The responses of unstable food-chains to enrichment. Evol. Ecol. 8, 150-171.
3. Abrams, P.A., Walters, C.J., 1996. Invulnerable prey and the paradox of enrichment. Ecology 77, 1125-1133.
4. Abrams, P.A., Namba, T., Mimura, M., Roth, J.D., 1997. The relationship between productivity and population densities in cycling predator-prey systems, Evol. Ecol. 11, 371-373.
5. Allee, W.C., 1931. Animal Aggregations. A Study in General Sociology. University of Chicago Press, Chicago.
6. Alvarez, L.H.R., 1998. Optimal harvesting under stochastic fluctuations and critical depensation. Math. Biosci. 152, 63-85.
7. Amarasekare, P., 1998a, Allee effects in metapopulation dynamics. Am. Nat. 152, 298-303.
8. Amarasekare, P., 1998b. Interactions between local dynamics and dispersal: insights from single species models. Theor. Pop. Biol. 53, 44-59.
9. Arditi, R., Ginzburg, L.R., 1989. Coupling in predator-prey dynamics: ratio-dependence. J. Theor. Biol. 139, 311-326.
10. Armstrong, R.A., 1979. Prey species replacement along a gradient of nutrient enrichment: a graphical approach. Ecology 60, 76-84.
11. Beddington, J.R., 1975. Mutual interference between parasites or predators and its effect on searching efficiency. J. Anim. Ecol. 44, 331-340.
12. Berryman, A.A., 1992. The origins and evolution of predator-prey theory. Ecology 73, 1530-1535.
13. Brown, J.H., Kodric-Brown, A., 1997. Turnover rates in insular biogeography: effect of immigration and extinction. Ecology 58, 445-458.
14. Courchamp, F., Clutton-Brock, T., Grenfell, B., 1999. Inverse density dependence and the Allee effect. Trends Ecol. E 14, 405-410.
15. Deangelis, D.L., Mulholland, P.J., Palumbo, A.V., Steinman, A.D., Huston, M.A., Elwood, J.W., 1989. Nutrient dynamics and food-web stability. Ann. Rev. Ecol. Syst. 20, 71-95.
16. Dennis, B., 1989. Allee effects: population growth, critical density, and the chance of extinction. Nat. Res. Model. 3, 48-538.
17. Gilpin, M.E., 1972. Enriched predator-prey systems: theoretical stability. Science 177, 902-904.
18. Hanski, I.A., 1999. Metapopulation Ecology. Oxford University Press, Oxford.
19. Hassell, M.P., Varley, G.C., 1969. New inductive population model for insect parasites and its bearing on biological control. Nature 223, 1133-1136.
20. Hessen, D.O., Nilssen, J.P., 1986. From phytoplankton to detritus and bacteria: the effects of short-term nutrient and fish perturbations in a eutrophic lake. Archly. Hydrobiol. 105, 273-284.
21. Holling, C.S., 1959. Some characteristics of simple types of predation and parasitism. Can. Entomol. 91, 385-398.
22. Huxel, G., 1999. On the influence of food quality in consumer-resource interactions. Ecol. Lett. 2, 256-261.
23. Jost, C., Arino, O., Arditi, R., 1999. About deterministic extinction in ratio-dependent predator-prey models. Bull. Math. Biol. 61, 19-32.
24. Kenward, R., 1978. Hawks and doves: attack success and selection in Goshawk flights at Wood Pigeons. J. Anim. Ecol. 47, 449-460.
25. Kretschmar, M., Nisbet, R.M., McCauley, E., 1993. A predator-prey model for zooplankton grazing on competition algal populations. Theor. Pop. Biol. 44, 32-66.
26. Lande, R., 1987. Extinction thresholds in demographic models of territorial populations. Am. Nat, 130, 624-635.
27. Leibold, M., 1989. Resource edibility and the effects of predators and productivity on the outcome of trophic interactions. Am. Nat. 134, 922-949.
28. Lewis, M.A., Kareiva, P., 1993. Allee dynamics and the spread of invading organisms. Theor. Pop. Biol. 43, 141-158.
29. Lotka, A.J., 1925. Elements of Physical Biology. Williams and Wilkins, Baltimore.
30. Luckinbill, L.S., 1974. The effects of space and enrichment on a predator-prey system. Ecology 55, 1142-1147.
31. Lunberg, P., Fryxell, J.M., 1995. Expected population density versus productivity in ratio-dependent and prey-dependent models. Am. Nat. 146, 153-161.
32. May, R.M., 1972. Limit cycles in predator-prey communities. Science 177, 900-902.
33. May, R.M., 1973. Mathematical models and stability, In: May, R.M. (Ed.), Stability and Complexity in Model Ecosystems. Princeton University Press, Princeton, pp. 13-36.
34. McAllister, C.D., LeBrasseur, R.J., Parsons, T.R., 1972. Stability of enriched aquatic ecosystems. Science 175, 562-564.
35. McCarthy, M.A., 1997. The Allee effect, finding mates and theoretical models. Ecol. Model. 103, 99-102.
36. McCauley, E., Murdoch, W.M., 1987. Cyclic and stable populations: plankton as a paradigm. Am. Nat. 129, 98-121.
37. McCauley, E., Murdoch, W.M., 1990. Predator-prey dynamics in environments rich and poor in nutrients. Nature 343, 455-457.
38. Murray, J.D., 1993. Mathematical Biology. Springer, Berlin.
39. Nee, S., 1994. How populations persist. Nature 367, 123-124.
40. Nisbet, R.M., De Roos, A.M., Wilson, W.G., Snyder, R.E., 1998. Discrete consumers, small scale resource heterogeneity, and population stability. Ecol. Lett, 1, 34-37.
41. Riebesell, J.F., 1974. Paradox of enrichment in competitive systems. Ecology 55, 183-187.
42. Rosenzweig, M.L., 1969. Why the prey curve has a hump. Am. Nat. 103, 81-87.
43. Rosenzweig, M.L., 1971. Paradox of enrichment: destabilization of exploitation ecosystems in ecological time. Science 171, 385-387.
44. Rousi, M., Tahvanainen, J., Henttonen, H., Uotila, I., 1993. Effects of shading and fertilization on resistance of winter dormant birch (Betula pendula) to voles and hares. Ecology 74, 30-38.
45. Scheffer, M., De Boer, R.J., 1995. Implications of spatial heterogeneity for the paradox of enrichment. Ecology 76, 2270-2277.
46. Scheuring, I., 1999. Allee effect increases the dynamical stability of populations. J. Theor. Biol. 199, 407-414.
47. Schwinning, S., Parsons, A.J., 1996. Analysis of the coexistence mechanisms for grasses and legumes in grazing systems. J. Ecol. 84, 799-813.
48. Stephens, P.A., Sutherland, W.J., 1999. Consequences of the Allee effect for behaviour, ecology and conservation. Trends Ecol. E 14, 401-405.
49. Tanner, J.T., 1975. The stability and intrinsic growth rates of prey and predator populations. Ecology 56, 855-867.
50. Veilleux, B.G., 1979. An analysis of the predatory interaction between Paramecium and Disinium. J. Anim. Ecol. 48, 787-803.
51. Volterra, V., 1926. Fluctuations in the abundance of a species considered mathematically. Nature 118, 558-560.
52. Walde, S.J., 1994. Immigration and the dynamics of a predator-prey interaction in biological control. J. Anim. Ecol. 63, 337-346.
53. Wang, G., Liang, X., Wang, F., 1999. The competitive dynamics of populations subject to an Allee effect. Ecol. Model. 124, 183-192.
54. Way, M., Banks, C., 1967. Intra-specific mechanisms in relation to the natural regulation of numbers of Aphis fabae. Ann. Appl. Biol. 59, 189-205.
55. Yodzis, P., Innes, S., 1992. Body size and consumer-resource dynamics. Am. Nat. 139, 1151-1175.