Models of allee effects and their implications for population and community dynamics

Biophysical Reviews and Letters

Volumn 3, Issue 1-2, 2008, Pages 157-181

  Berec, Luděk ^a  

^a INSTITUTE OF ENTOMOLOGY   (Czech Republic)

Author keywords

Allee effects; Community dynamics; Metapopulation models

Indexed keywords

COMMUNITY DYNAMICS; COMMUNITY ECOLOGY; CONFERENCE PAPER; HOST PARASITE INTERACTION; HUMAN; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; METAPOPULATION; NONHUMAN; POPULATION DENSITY; POPULATION DYNAMICS; POPULATION GROWTH; POPULATION MODEL; POPULATION SIZE; POPULATION STRUCTURE; PREDATOR PREY INTERACTION; PRIORITY JOURNAL; SPECIES INVASION;

EID: 51349106906     PISSN: 17930480     EISSN: None     Source Type: Journal    
DOI: 10.1142/s1793048008000678     Document Type: Conference Paper

References (94)

1. Courchamp F, Clutton-Brock TH and Grenfell BT (1999a). Inverse density dependence and the Allee effect. Trends in Ecology & Evolution, 14, 405-410.
2. Stephens PA and Sutherland WJ (1999). Consequences of the Allee effect for behaviour, ecology and conservation. Trends in Ecology & Evolution, 14, 401-405.
3. Liermann M and Hilborn R (2001). Depensation: Evidence, models and implications. Fish and Fisheries, 2, 33-58.
4. Berec L, Angulo E and Courchamp F (2007). Multiple Allee effects and population management. Trends in Ecology & Evolution, 22, 185-191.
5. Stephens PA, Sutherland WJ and Freckleton R (1999). What is the Allee effect? Oikos, 87, 185-190.
6. Courchamp F, Clutton-Brock TH and Grenfell BT (2000a). Multipack dynamics and the Allee effect in the African wild dog, Lycaon pictus Animal Conservation, 3, 277-285.
7. Pfister CA and Bradbury A (1996). Harvesting red sea urchins: Recent effects and future predictions. Ecological Applications, 6, 298-310.
8. Jonhson DM, Liebhold AM, Tobin PC and Bjornstad ON (2006). Allee effects and pulsed invasion by the gypsy moth. Nature, 444, 361-363.
9. Dennis B (1989). Allee effects: Population growth, critical density and the chance of extinction. Natural Resource Modeling, 3, 481-538.
10. Boukal DS and Berec L (2002). Single-species models of the Allee effect: extinction boundaries, sex ratios and mate encounters. Journal of Theoretical Biology, 218, 375-394.
11. Gascoigne J and Lipcius R (2004a). Allee effects driven by predation. Journal of Applied Ecology, 41, 801-810.
12. Tcheslavskaia K, Brewster CC and Sharov AA (2002). Mating success of gypsy moth (Lepidoptera: Lymantriidae) females in Southern Wisconsin. Great Lakes Entomologist, 35, 1-7.
13. Courchamp F, Berec L, Gascoigne J (2008). Allee effects in ecology and conservation. Oxford University Press, Oxford.
14. Vogel H, Czihak G, Chang P and Wolf W (1982). Fertilization kinetics of sea urchin eggs. Mathematical Biosciences, 58, 189-216.
15. Mosimann JE (1958). The evolutionary significance of rare matings in animal populations. Evolution, 12, 246-261.
16. Rowe S, Hutchings JA, Bekkevold D and Rakitin A (2004). Depensation, probability of fertilization, and the mating system of Atlantic cod ( Gadus morhua L.). ICES Journal of Marine Science, 61, 1144-1150.
17. Barclay H and Mackauer M (1980a). The sterile insect release method for pest control: A density-dependent model. Environmental. Entomology, 9, 810-817.
18. Courchamp F, Angulo E, Rivalan P et al. (2006). Raxity value and species extinction: The anthropogenic Allee effect. Plos Biology, 4, 2405-2410.
19. Skalski GT and Gilliam JF (2001). Functional responses with predator interference: Viable alternatives to the Holling type II model. Ecology, 82, 3083-3092.
20. Stephens PA, Frey-Roos F, Arnold W and Sutherland WJ (2002a). Model complexity and population predictions. The alpine marmot as a case study. Journal of Animal Ecology, 71, 343-361.
21. Wertheim B, Marchais J, Vet LEM and Dicke M (2002). Allee effect in larval resource exploitation in Drosophila: An interaction among density of adults, larvae, and microorganisms. Ecological Entomology, 27, 608-617.
22. Taylor CM, Davis HG, Civille JC, Grevstad FS and Hastings A (2004). Consequences of an Allee effect in the invasion of a pacific estuary by Spartina alterniflora. Ecology, 85, 3254-3266.
23. Rohlfs M and Hoffmeister TS (2003). An evolutionary explanation of the aggregation model of species coexistence. Proceedings of the Royal Society of London Series B-Biological Sciences, 270, S33-S35.
24. Gascoigne J and Lipcius RN (2005). Periodic dynamics in a two-stage Allee effect model are driven by tension between stage equilibria. Theoretical Population Biology, 68, 237-241.
25. Cushing JM (1994). Oscillations in age-structured population models with an Allee effect. Journal of Computational and Applied Mathematics, 52, 71-80.
26. Kulenovic MRS and Yakubu AA (2004). Compensatory versus overcompensatory dynamics in density-dependent Leslie models. Journal of Difference Equations and Applications, 10, 1251-1265.
27. Hopper KR and Roush RT (1993). Mate finding, dispersal, number released, and the success of biological-control introductions. Ecological Entomology, 18, 321-331.
28. Ashih AC and Wilson WG (2001). Two-sex population dynamics in space: effects of gestation time on persistence. Theoretical Population Biology, 60, 93-106.
29. Berec L, Boukal DS and Berec M (2001). Linking the Allee effect, sexual reproduction, and temperature-dependent sex determination via spatial dynamics. American Naturalist, 157, 217-230.
30. Berec L and Boukal DS (2004). Implications of mate search, mate choice and divorce rate for population dynamics of sexually reproducing species. Oikos, 104, 122-132.
31. de Roos AM, Persson L and Thieme HR (2003). Emergent Allee effects in top predators feeding on structured prey populations. Proceedings of the Royal Society of London Series B-Biological Sciences, 270, 611-618.
32. Gascoigne J and Lipcius R (2004b). Allee effects in marine systems. Marine Ecology Progress Series, 269, 49-59.
33. Gascoigne J and Lipcius RN (2004c). Conserving populations at low abundance: Delayed functional maturity and Allee effects in reproductive behaviour of the queen conch Strombus gigas. Maxine Ecology-Progress Series, 284, 185-194.
34. Taylor CM and Hastings A (2004). Finding optimal control strategies for invasive species: A density-structured model for Spartina alterniflora. Journal of Applied Ecology, 41, 1049-1057.
35. Schreiber SJ (2004). On Allee effects in structured populations. Proceedings of the American Mathematical Society, 132, 3047-3053.
36. South AB and Kenward RE (2001). Mate finding, dispersal distances and population growth in invading species: A spatially explicit model. Oikos, 95, 53-58.
37. Hanski I and Gaggiotti OE (2004). Ecology, genetics, and evolution of metapopulations. Elsevier Academic Press.
38. Gruntfest Y, Arditi R and Dombrovsky Y (1997). A fragmented population in a varying environment. Journal of Theoretical Biology, 185, 539-547.
39. Amarasekare P (1998b). Interactions between local dynamics and dispersal: Insights from single species models. Theoretical Population Biology, 53, 44-59.
40. Gyllenberg M, Hemminki J and Tammaru T (1999). Allee effects can both conserve and create spatial heterogeneity in population densities. Theoretical Population Biology, 56, 231-242.
41. Greene CM (2003). Habitat selection reduces extinction of populations subject to Allee effects. Theoretical Population Biology, 64, 1-10.
42. Padrón V and Trevisan MC (2000). Effect of aggregating behavior on population recovery on a set of habitat islands. Mathematical Biosciences, 165, 63-78.
43. Amarasekare P (1998a). Allee effects in metapopulation dynamics. American Naturalist, 152, 298-302.
44. Zhou SR and Wang G (2004). Allee-like effects in metapopulation dynamics. Mathematical Biosciences, 189, 103-113.
45. May RM (1977a) Togetherness among Schistosomes: Its effects on the dynamics of the infection. Mathematical Biosciences, 35, 301-343.
46. Garrett KA and Bowden RL (2002). An Allee effect reduces the invasive potential of Tilletia indica. Phytopathology, 92, 1152-1159.
47. Taylor CM and Hastings A (2005). Allee effects in biological invasions. Ecology Letters, 8, 895-908.
48. Hadjiavgousti D and Ichtiaroglou S (2004). Existence of stable localized structures in population dynamics through the Allee effect. Chaos, Solitons & Fractals, 21, 119-131.
49. Kot M, Lewis MA and van den Driessche P (1996). Dispersal data and the spread of invading organisms. Ecology, 77, 2027-2042.
50. Veit RR and Lewis MA (1996). Dispersal, population growth, and the Allee effect: Dynamics of the house finch invasion of eastern North America. American Naturalist, 148, 255-274.
51. Wang MH, Kot M and Neubert MG (2002). Integrodifference equations, Allee effects, and invasions. Journal of Mathematical Biology, 44, 150-168.
52. Lewis MA and Kareiva P (1993). Allee dynamics and the spread of invading organisms. Theoretical Population Biology, 43, 141-158.
53. Lewis MA and van den Driessche P (1993). Waves of extinction from sterile insect release. Mathematical Biosciences, 116, 221-247.
54. Wang MH and Kot M (2001). Speeds of invasion in a model with strong or weak Allee effects. Mathematical Biosciences, 171, 83-97.
55. Petrovskii SV and Li BL (2003). An exactly solvable model of population dynamics with density- dependent migrations and the Allee effect. Mathematical Biosciences, 186, 79-91.
56. Soboleva TK, Shorten PR, Pleasants AB and Rae AL (2003). Qualitative theory of the spread of a new gene into a resident population. Ecological Modelling, 163, 33-44.
57. Hastings A (1996). Models of spatial spread: A synthesis. Biological Conservation, 78, 143-148.
58. Almeida RC, Delphim SA and da S Costa MI (2006). A numerical model to solve single-species invasion problems with Allee effects. Ecological Modelling, 192, 601-617.
59. Shi JP and Shivaji R (2006). Persistence in reaction diffusion models with weak Allee effect. Journal of Mathematical Biology, 52, 807-829.
60. Keitt TH, Lewis MA and Holt RD (2001). Allee effects, invasion pinning, and species borders. American Naturalist, 157, 203-216.
61. Hadjiavgousti D and Ichtiaroglou. S (2006). Allee effect in population dynamics: Existence of breather-like behavior and control of chaos through dispersal. International Journal of Bifurcation and Chaos, 16, 2001-2012.
62. Liebhold A and Bascompte J (2003). The Allee effect, stochastic dynamics and the eradication of alien species. Ecology Letters, 6, 133-140.
63. Tobin PC, Whitmire SL, Johnson DM, Bjornstad ON and Liebhold AM (2007). Invasion speed is affected by geographical variation in the strength of Allee effects. Ecology Letters, 10, 36-43.
64. Petrovskii SV, Morozov AY and Venturino E (2002). Allee effect makes possible patchy invasion in a predator-prey system. Ecology Letters, 5, 345-352.
65. Morozov A, Petrovskii S and Li BL (2004). Bifurcations and chaos in a predatorprey system with the Allee effect. Proceedings of the Royal Society of London Series B-Biological Sciences, 271, 1407-1414.
66. Courchamp F, Grenfell BT and Clutton-Brock TH (2000b). Impact of natural enemies on obligately cooperative breeders. Oikos, 91, 311-322.
67. Boukal DS, Sabelis MW and Berec L (2007). How predator functional responses and Allee effects in prey affect the paradox of enrichment and population collapses. Theoretical Population Biology, in press.
68. Zhou SR, Liu YF and Wang G (2005). The stability of predator-prey systems subject to the Allee effects. Theoretical Population Biology, 67, 23-31.
69. Kent A, Doncaster CP and Sluckin T (2003). Consequences for predators of rescue and Allee effects on prey. Ecological Modelling, 162, 233-245.
70. Petrovskii SV, Morozov AY and Li BL (2005a). Regimes of biological invasion in a predator-prey system with the Allee effect. Bulletin of Mathematical Biology, 67, 637-661.
71. Petrovskii SV, Malchow H, Hilker FM and Venturino E (2005b). Patterns of patchy spread in deterministic and stochastic models of biological invasion and biological control. Biological Invasions, 7, 771-793.
72. Fagan W, Lewis M, Neubert M and van den Driessche P (2002). Invasion theory and biological control. Ecology Letters, 5, 148-157.
73. Brown DH, Ferris H, Fu S and Plant R (2004). Modeling direct positive feedback between predators and prey. Theoretical Population Biology, 65, 143-152.
74. de Roos AM and Persson L (2002). Size-dependent life-history traits promote catastrophic collapses of top predators. Proceedings of the National Academy of Sciences of the United States of America, 99, 12907-12912.
75. van Kooten T, de Roos AM and Persson M (2005). Bistability and an Allee effect as emergent consequences of stage-specific predation. Journal of Theoretical Biology, 237, 67-74.
76. Hethcote HW (2000). The mathematics of infectious diseases. SIAM Review, 42, 599-653.
77. Shea K, Thrall PH and Burdon JJ (2000). An integrated approach to management in epidemiology and pest control. Ecology Letters, 3, 150-158.
78. Courchamp F and Cornell SJ (2000). Virus-vectored immunocontraception to control feral cats on islands: A mathematical model. Journal of Applied Ecology, 37, 903-913.
79. McCallum H, Barlow N and Hone J (2001), How should pathogen transmission be modelled? Trends in Ecology & Evolution, 16, 295-300.
80. Regoes RR, Ebert D and Bonhoeffer, S (2002). Dose-dependent infection rates of parasites produce the Allee effect in epidemiology. Proceedings of the Royal Society of London Series B-Biological Sciences; 269, 271-279.
81. Deredec A and Courchamp F (2003). Extinction thresholds in host-parasite dynamics. Annales Zoologici Fennici, 40, 115-130.
82. May RM and Anderson RM (1979). Population biology of infectious diseases: Part I. Nature, 280, 361-367.
83. Deredec A and Courchamp F (2006). Combined impacts of Allee effects and parasitism. Oikos, 112, 667-679.
84. Hilker FM, Lewis MA, Seno H, Langlais M and Malchow H (2005). Pathogens can slow down or reverse invasion fronts of their hosts. Biological Invasions, 7, 817-832.
85. Devi KU and Rao CUM (2006). Allee effect in the infection dynamics of the entomopathogenic fungus Beauveria bassiana (Bats) Vuill. on the beetle, Mylabris pustulata. Mycopathologia, 161, 385-394.
86. Ebert D, Zschokke-Rohringer CD and Carius HJ (2000). Dose effects and density-dependent regulation of two microparasites of Daphnia magna Oecologia, 122, 200-209.
87. Turelli M and Hoffmann AA (1991). Rapid spread of an inherited incompatibility factor in California Drosophila. Nature, 353, 440-442.
88. Turelli M and Hoffmann AA (1995). Cytoplasmic incompatibility in Drosophila simulans: Dynamics and paxameter estimates from natural populations. Genetics, 140, 1319-1338.
89. Keeling MJ, Jiggins FM and Read JM (2003). The invasion and coexistence of competing Wolbachia strains. Heredity, 91, 382-388.
90. Schofield P (2002). Spatially explicit models of Turelli-Hoffmann Wolbachia invasive wave fronts. Journal of Theoretical Biology, 215, 121-131.
91. Rohlf FJ (1969). The effect of clumped distributions in sparse populations. Ecology, 50, 716-721.
92. Cornell SJ, Isham VS and Grenfell BT (2004). Stochastic and spatial dynamics of nematode parasites in farmed ruminants. Proceedings of the Royal Society of London Series B-Biological Sciences, 271, 1243-1250.
93. Dennis B (2002). Allee effects in stochastic populations. Oikos, 96, 389-401.
94. Allen LJS, Fagan JF, Högnäs G and Fagerholm H (2005). Population extinction in discrete-time stochastic population models with an Allee effect. Journal of Difference Equations and Applications, 11, 273-293.