Theoretical Ecology

, Volume 5, Issue 4, pp 605–610 | Cite as

Behavioral states of predators stabilize predator–prey dynamics

  • Toshinori OkuyamaEmail author
Original Paper


This study considers a common community model (i.e., Rosenzweig–MacArthur model) with an explicit consideration of the behavioral states of predators. Following a mechanistic interpretation of the functional response model in the model, a fraction of predator individuals are assumed searching for prey while the rest are assumed handling prey at any given time. How the explicit consideration of the behavioral states affects the model dynamics with respect to environmental enrichment is considered. The analysis shows that the explicit consideration of the behavioral states can substantially increase the stability of predator–prey dynamics.


Behavioral variation Individual variation Functional response Paradox of enrichment 



I thank two anonymous reviewers for their insightful comments that imported the manuscript. The study was financially supported by the National Science Council of Taiwan (99-2628-B-002-051-MY3).


  1. Abrams PA (1992) Predators that benefit prey and prey that harm predators: unusual effects of interacting foraging adaptations. Am Nat 140:573–600CrossRefGoogle Scholar
  2. Abrams PA (2010) Implications of flexible foraging for interspecific interactions: lessons from simple models. Funct Ecol 24:7–17CrossRefGoogle Scholar
  3. Abrams PA, Roth J (1994) The responses of unstable food chains to enrichment. Evol Ecol 8:150–171CrossRefGoogle Scholar
  4. Alcock J (1998) Animal behavior, 6th edn. Sinauer Associates, SunderlandGoogle Scholar
  5. Barcellos LJG, Ritter F, Kreutz LC, Cericato L (2010) Can zebrafish Danio rerio learn about predation risk? The effect of a previous experience on the cortisol response in subsequent encounters with a predator. J Fish Biol 76:1032–1038CrossRefGoogle Scholar
  6. Bolker B, Holyoak M, Křivan V, Rowe L, Schmitz O (2003) Connecting theoretical and empirical studies of trait-mediated interactions. Ecology 84:1101–1114CrossRefGoogle Scholar
  7. Edelstein-Keshet L (1988) Mathematical models in biology. McGraw-Hill, New YorkGoogle Scholar
  8. Holling CS (1959) Some characteristics of simple types of predation and parasitism. Can Entomol 91:385–398CrossRefGoogle Scholar
  9. Kisdi E, Liu S (2006) Evolution of handling time can destroy the coexistence of cycling predators. J Evol Biol 19:49–58PubMedCrossRefGoogle Scholar
  10. Klepac P, Neubert MG, van den Driessche D (2007) Dispersal delays, predator–prey stability, and the paradox of enrichment. Theor Popul Biol 71:436–444PubMedCrossRefGoogle Scholar
  11. Krebs JR, Davies NB (1993) An introduction to behavioural ecology. Blackwell Scientific, LondonGoogle Scholar
  12. Křivan V, Diehl S (2005) Adaptive omnivory and species coexistence in tri-trophic food webs. Theor Popul Biol 67:85–99PubMedCrossRefGoogle Scholar
  13. Liebhold A, Sork V, Peltonen M, Koenig W, Bjornstad ON, Westfall R, Knops JMH (2004) Predator-avoidance behavior extends trophic cascade to refuge habitat. Oikos 104:156–164CrossRefGoogle Scholar
  14. Luttbeg B, Schmitz O (2000) Predator and prey models with flexible individual behavior and imperfect information. Am Nat 155:669–683PubMedCrossRefGoogle Scholar
  15. Magurran AE (1990) The inheritance and development of minnow anti-predator behaviour. Anim Behav 39(5):834–842CrossRefGoogle Scholar
  16. Mougi A, Nishimura K (2007) A resolution of the paradox of enrichment. J Theor Biol 248:194–201PubMedCrossRefGoogle Scholar
  17. Murdoch WW, Briggs CJ, Nisbet RM (2003) Consumer-resource dynamics. Monographs in population biology. Princeton University Press, PrincetonGoogle Scholar
  18. Okuyama T (2008) Individual behavioral variation in predator–prey models. Ecol Res 23:665–671CrossRefGoogle Scholar
  19. Okuyama T (2009) Local interactions between predators and prey call into question commonly used functional responses. Ecol Model 220:1182–1188CrossRefGoogle Scholar
  20. Okuyama T (2010) Prey density-dependent handling time in a predator–prey model. Community Ecol 11:91–96CrossRefGoogle Scholar
  21. Okuyama T (2011a) Biphasic activity of a jumping spider. Naturwissenschaften 98:15–22PubMedCrossRefGoogle Scholar
  22. Okuyama T (2011b) Individual variation in prey choice in a predator–prey community. Theor Popul Biol 79:64–69PubMedCrossRefGoogle Scholar
  23. Okuyama T (2011c) Flexible components of functional responses. J Anim Ecol. doi: 10.1111/j.1365-2656.2011.01876.x PubMedGoogle Scholar
  24. Rosenzweig ML (1971) Paradox of enrichment: destabilization of exploitation ecosystems in ecological time. Science 171:385–387PubMedCrossRefGoogle Scholar
  25. Schuett W, Dall SR, Baeumer J, Kloesener MH, Nakagawa S, Beinlich F, Eggers T (2011) Personality variation in a clonal insect: the pea aphid, Acyrthosiphon pisum. Dev Psychobiol 53:631–640CrossRefGoogle Scholar
  26. Sih A (1987) Prey refuges and predator–prey stability. Theor Popul Biol 31:1–12CrossRefGoogle Scholar
  27. Turchin P (2003) Complex population dynamics: a theoretical/empirical synthesis. Monographs in population biology, vol 35. Princeton University Press, PrincetonGoogle Scholar
  28. Vos M, Flik BJG, Vijverberg J, Ringelberg J, Mooij WM (2002) From inducible defences to population dynamics: modelling refuge use and life history changes in Daphnia. Oikos 99:386–396CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of EntomologyNational Taiwan UniversityTaipeiTaiwan

Personalised recommendations