Advertisement

Theoretical Ecology

, Volume 5, Issue 4, pp 533–544 | Cite as

Impacts of predation on dynamics of age-structured prey: Allee effects and multi-stability

  • Viola Pavlová
  • Luděk BerecEmail author
Original paper

Abstract

With a series of mathematical models, we explore impacts of predation on a prey population structured into two age classes, juveniles and adults, assuming generalist, age-specific predators. Predation on any age class is either absent, or represented by types II or III functional responses, in various combinations. We look for Allee effects or more generally for multiple stable steady states in the prey population. One of our key findings is the occurrence of a predator pit (low-density “refuge” state of prey induced by predation; the chance of escaping predation thus increases both below and above an intermediate prey density) when only one age class is consumed and predators use a type II functional response —this scenario is known to occur for an unstructured prey consumed via a type III functional response and can never occur for an unstructured prey consumed via a type II one. In the case where both age classes are consumed by type II generalist predators, an Allee effect occurs frequently, but some parameters give also rise to a predator pit and even three stable equilibria (one extinction equilibrium and two positive ones—Allee effect and predator pit combined). Multiple positive stable equilibria are common if one age class is consumed via a type II functional response and the other via a type III functional response—here, in addition to the behaviours mentioned above one may even observe three stable positive equilibria—“double” predator pit. Some of these results are discussed from the perspective of population management.

Keywords

Age-specific predation Functional response Generalist predator Population dynamics Predator pit 

Notes

Acknowledgements

LB acknowledges funding by the Institute of Entomology (Z50070508). We also thank two anonymous reviewers for their stimulating comments.

References

  1. Begon M, Townsend CR, Harper JL (2006) Ecology: from individuals to ecosystems. Wiley-Blackwell, New YorkGoogle Scholar
  2. Berec L, Angulo E, Courchamp F (2007) Multiple Allee effects and population management. Trends Ecol Evol 22:185–191PubMedCrossRefGoogle Scholar
  3. Bor YJ (1995) Optimal pest management and economic threshold. Agric Syst 49:113–133CrossRefGoogle Scholar
  4. Boukal DS, Berec L (2009) Modelling mate-finding Allee effects and populations dynamics, with applications in pest control. Popul Ecol 51:445–458CrossRefGoogle Scholar
  5. Chen Y, Harvey HH (1994) Maturation of white sucker, Catostomus commersoni, populations in Ontario. Can J Fish Aquat Sci 51:2066–2076CrossRefGoogle Scholar
  6. Chen J-P, Zhang H-D (1986) The qualitative analysis of two species predator–prey model with Holling type III functional response. Appl Math Mech 71:73–80Google Scholar
  7. Chen TY, French JV, Liu OX, Da Grac JV (2006) A Predation of Galendromus helveolus (Acari: Phytoseiidae) on Brevipalpus californicus (Acari: Tenuipalpidae). Biocontrol Sci Technol 16:753–759CrossRefGoogle Scholar
  8. Courchamp F, Macdonald DW (2001) Crucial importance of pack size in the African wild dog Lycaon pictus. Anim Conserv 4:169–174CrossRefGoogle Scholar
  9. Courchamp F, Clutton-Brock TH, Grenfell BT (1999) Inverse density dependence and the Allee effect. Trends Ecol Evol 14:405–410PubMedCrossRefGoogle Scholar
  10. Courchamp F, Berec L, Gascoigne J (2008) Allee effects in ecology and conservation. Oxford University Press, OxfordCrossRefGoogle Scholar
  11. de Roos AM, Persson L, Thieme HR (2003) Emergent Allee effects in top predators feeding on structured prey populations. Proc R Soc Lond B 270:611–619CrossRefGoogle Scholar
  12. Deredec A, Courchamp F (2007) Importance of the Allee effect for reintroductions. Ecoscience 14:440–451CrossRefGoogle Scholar
  13. Dhooge A, Govaerts W, Kuznetsov YA (2003) Matcont: a Matlab package for numerical bifurcation analysis of ODEs. ACM Trans Math Softw 29:141–164CrossRefGoogle Scholar
  14. Erlinge S, Göransson G, Hansson L, Högstedt G, Liberg O, Nilsson I, Nilsson T, von Schantz T, Sylvén M (1983) Predation as a regulating factor on small rodent populations in southern Sweden. Oikos 40:36–52CrossRefGoogle Scholar
  15. Ernande B, Dieckmann U, Heino M (2004) Adaptive changes in harvested populations: plasticity and evolution of age and size at maturation. Proc R Soc Lond B 271:415–423CrossRefGoogle Scholar
  16. Fauvergue X, Malausa J-C, Giuge L, Courchamp F (2007) Invading parasitoids suffer no Allee effect: a manipulative field experiment. Ecology 88:2392–2403PubMedCrossRefGoogle Scholar
  17. Gascoigne JC, Lipcius RN (2004) Allee effects driven by predation. J Appl Ecol 41:801–810CrossRefGoogle Scholar
  18. Grange S, Duncan P, Gaillard JM, Sinclair ARE, Gogan PJP, Packer C, Hofer H, East M (2004) What limits the Serengeti zebra population? Oecologia 140:523–532PubMedCrossRefGoogle Scholar
  19. Grevstad FS (1999) Factors influencing the chance of population establishment: implications for release strategies in biocontrol. Ecol Appl 9:1493–1447CrossRefGoogle Scholar
  20. Hajek A (2004) Natural enemies. Cambridge University Press, CambridgeGoogle Scholar
  21. Hassell MP, Lawton JH, Beddington JR (1976) The components of arthropod predation. 1. The prey death rate. J Anim Ecol 45:135–164CrossRefGoogle Scholar
  22. Hastings A (1983) Age-dependent predation is not a simple process. I. Continuous time models. Theor Popul Biol 23:347–362CrossRefGoogle Scholar
  23. Hastings A (1984a) Simple models for age dependent predation. In: Levin SA, Hallam TG (eds) Mathematical ecology: lecture notes in biomathematics. Springer, Berlin, pp 114–119Google Scholar
  24. Hastings A (1984b) Age-dependent predation is not a simple process, II. Wolves, ungulates and a discrete time model for predation on juveniles with a stabilizing tail. Theor Popul Biol 26:271–282CrossRefGoogle Scholar
  25. Hastings A (1984c) Delays in recruitment at different trophic levels: effects on stability. J Math Biol 21:35–44PubMedCrossRefGoogle Scholar
  26. Hoogland JL, Cannon KE, DeBarbieri LM, Manno TG (2006) Selective predation on Utah prairie dogs. Am Nat 168:546–552PubMedCrossRefGoogle Scholar
  27. Hopper KR, Roush RT (1993) Mate finding, dispersal, number released, and the success of biological control introductions. Ecol Entomol 18:321–331CrossRefGoogle Scholar
  28. Hunter ML Jr, Gibbs JP (2007) Fundamentals of conservation biology. Blackwell, New YorkGoogle Scholar
  29. Jang SR (2007) Allee effects in a discrete-time host parasitoid model with stage structure in the host. Discrete Contin Dyn Syst B 8:145–159CrossRefGoogle Scholar
  30. Jang SR (2010) Discrete host-parasitoid models with Allee effects and age structure in the host. Math Biosci Eng 7:67–81PubMedCrossRefGoogle Scholar
  31. Jarnemo A, Liberg O (2005) Red fox removal and roe deer fawn survival: a 14-year study. J Wildl Manag 69:1090–1098CrossRefGoogle Scholar
  32. Jeschke JM, Kopp M, Tollrian R (2002) Predator functional responses: discriminating between handling and digesting prey. Ecol Monogr 72:95–112CrossRefGoogle Scholar
  33. Kramer AM, Drake JM (2010) Experimental demonstration of population extinction due to a predator-driven Allee effect. J Anim Ecol 79:633–639PubMedCrossRefGoogle Scholar
  34. Krivan V (1996) Optimal foraging and predator-prey dynamics. Theor Popul Biol 49:265–290PubMedCrossRefGoogle Scholar
  35. Liebhold AM, Bascompte J (2003) The Allee effect, stochastic dynamics and the eradication of alien species. Ecol Lett 6:133–140CrossRefGoogle Scholar
  36. Liebhold AM, Tobin PC (2008) Population ecology of insect invasions and their management. Annu Rev Entomol 53:387–408PubMedCrossRefGoogle Scholar
  37. Manca M, Vijverberg J, Polishchuk LV, Voronov DA (2008) Daphnia body size and population dynamics under predation by invertebrate and fish predators in Lago Maggiore: an approach based on contribution analysis. J Limnol 67:15–21Google Scholar
  38. May (1977) Thresholds and breakpoints in ecosystems with a multiplicity of stable states. Nature 269:471–477CrossRefGoogle Scholar
  39. Messier F (1994) Ungulate population models with predation: a case study with the North American moose. Ecology 75:478–488CrossRefGoogle Scholar
  40. Murdoch WW, Briggs CJ (1996) Theory for biological control: recent developments. Ecology 77:2001–2013CrossRefGoogle Scholar
  41. Nishi A, Imamura T, Miyanoshita A, Morimoto S, Takahashi K, Visarathanonth P, Kengkanpanich R, Shazalis MEH, Sato K (2004) Predatory abilities of Amphibolus venator (Klug) (Hemiptera: Reduviidae), a predator of stored-product insect pests. Appl Entomol Zool 39:321–326CrossRefGoogle Scholar
  42. Oaten A, Murdoch WW (1975) Functional response and stability in predator-prey systems. Amer Natur 109:289–298CrossRefGoogle Scholar
  43. Raymond B, Vanbergen A, Watt A (2002) Escape from pupal predation as a potential cause of outbreaks of the winter moth, Operoptera brumata. Oikos 98:219–228CrossRefGoogle Scholar
  44. Tanhuanpaa M, Ruohomaki K, Kaitaniemi P (2003) Influence of adult and egg predation on reproductive success of Epirrita autumnata (Lepidoptera: Geometridae). Oikos 102:263–272CrossRefGoogle Scholar
  45. Tobin PC, Berec L, Liebhold AM (2011) Exploiting Allee effects for managing biological invasions. Ecol Lett 14:615–624PubMedCrossRefGoogle Scholar
  46. Wikan A (2001) From chaos to chaos. An analysis of a discrete age-structured prey predator model. J Math Biol 43:471–500PubMedCrossRefGoogle Scholar
  47. Wittmer HU, Sinclair ARE, McLellan BN (2005) The role of predation in the decline and extirpation of woodland caribou. Oecologia 144:257–267PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Ecosystem Biology, Faculty of ScienceUniversity of South BohemiaČeské BudějoviceCzech Republic
  2. 2.National Environmental Research Institute, Department of Arctic EnvironmentUniversity of AarhusRoskildeDenmark
  3. 3.Department of Biosystematics and Ecology, Institute of EntomologyBiology Centre of the Academy of Sciences of the Czech RepublicČeské BudějoviceCzech Republic
  4. 4.Department of Mathematics and Biomathematics, Faculty of ScienceUniversity of South BohemiaČeské BudějoviceCzech Republic

Personalised recommendations