Bulletin of Mathematical Biology

, Volume 73, Issue 3, pp 683–699 | Cite as

Kleptoparasitic Melees—Modelling Food Stealing Featuring Contests with Multiple Individuals

Original Article

Abstract

Kleptoparasitism is the stealing of food by one animal from another. This has been modelled in various ways before, but all previous models have only allowed contests between two individuals. We investigate a model of kleptoparasitism where individuals are allowed to fight in groups of more than two, as often occurs in real populations. We find the equilibrium distribution of the population amongst various behavioural states, conditional upon the strategies played and environmental parameters, and then find evolutionarily stable challenging strategies. We find that there is always at least one ESS, but sometimes there are two or more, and discuss the circumstances when particular ESSs occur, and when there are likely to be multiple ESSs.

Keywords

Kleptoparasitism Multiplayer contests ESS Game theory Strategy 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barnard, C. J., & Sibly, R. M. (1981). Producers and scroungers: a general model and its application to captive flocks of house sparrows. Anim. Behav., 29, 543–555. CrossRefGoogle Scholar
  2. Brockmann, H. J., & Barnard, C. J. (1979). Kleptoparasitism in birds. Anim. Behav., 27, 487–514. CrossRefGoogle Scholar
  3. Broom, M., & Ruxton, G. D. (1998). Evolutionarily stable stealing: game theory applied to kleptoparasitism. Behav. Ecol., 9, 397–403. CrossRefGoogle Scholar
  4. Broom, M., & Ruxton, G. D. (2003). Evolutionarily stable kleptoparasitism: consequences of different prey types. Behav. Ecol., 14, 23–33. CrossRefGoogle Scholar
  5. Broom, M., Luther, R. M., & Ruxton, G. D. (2004). Resistance is useless?—extensions to the game theory of kleptoparasitism. Bull. Math. Biol., 66, 1645–1658. MathSciNetCrossRefGoogle Scholar
  6. Broom, M., & Rychtář, J. (2007). The evolution of a kleptoparasitic system under adaptive dynamics. J. Math. Biol., 54, 151–177. MathSciNetMATHCrossRefGoogle Scholar
  7. Grimm, M. P., & Klinge, M. (1996). Pike and some aspects of its dependence on vegetation. In J. F. Craig (Ed.) Pike: biology and exploitation (pp. 125–126). London: Chapman and Hall. Google Scholar
  8. Holling, C. S. (1959). Some characteristics of simple types of predation and parasitism. Can. Entomol., 91, 385–398. CrossRefGoogle Scholar
  9. Jeanne, R. L. (1972). Social biology of the nootropical wasp. Bull. Museum Comp. Zool., 144, 63-1-50. Google Scholar
  10. Kruuk, H. (1972). The spotted hyena: a study of predation and social behaviour. Chicago: University of Chicago Press. Google Scholar
  11. Luther, R. M., & Broom, M. (2004). Rapid convergence to an equilibrium state in kleptoparasitic populations. J. Math. Biol., 48, 325–339. MathSciNetMATHCrossRefGoogle Scholar
  12. Luther, R. M., Broom, M., & Ruxton, G. D. (2007). Is food worth fighting for? ESS’s in mixed populations of kleptoparasites and foragers. Bull. Math. Biol. 69, 1121–1146. MathSciNetMATHCrossRefGoogle Scholar
  13. Maynard Smith, J. (1982). Evolution and the theory of games. Cambridge: Cambridge University Press. MATHGoogle Scholar
  14. Rothschild, M., & Clay, T. (1952). Fleas, Flukes and Cuckoos. Glasgow: Collins. Google Scholar
  15. Ruxton, G. D., & Broom, M. (1999). Evolution of kleptoparasitism as a war of attrition. J. Evol. Biol., 12, 755–759. CrossRefGoogle Scholar
  16. Ruxton, G. D., & Moody, A. L. (1997). The ideal free distribution with kleptoparasitism. J. Theoret. Biol., 186, 449–458. CrossRefGoogle Scholar
  17. Shealer, D. A., & Spendelow, J. A. (2002). Individual foraging strategies of kleptoparasitic Roseate Terns. Waterbirds, 25, 436–441. CrossRefGoogle Scholar
  18. Spear, L. B., Howell, S. N. G., Oedekoven, C. S., Legay, D., & Bried, J. (1999). Kleptoparasitism by brown skuas on albatrosses and giant-petrels in the Indian Ocean. The Auk, 116, 545–548. Google Scholar
  19. Steele, W. K., & Hockey, P. A. R. (1995). Factors influencing rate and success of intraspecific kleptoparasitism among kelp gulls. The Auk, 112, 847–859. Google Scholar
  20. Stillman, R. A., Goss-Custard, J. D., & Caldow, R. W. G. (1997). Modelling interference from basic foraging behaviour. J. Anim. Ecol., 66, 692–703. CrossRefGoogle Scholar
  21. Triplet, P., Stillman, R. A., & Goss-Custard, J. D. (1999). Prey abundance and the strength of interference in a foraging sea-bird. J. Anim. Ecol., 68, 254–265. CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of SussexBrightonUK
  2. 2.Centre for Mathematical ScienceCity UniversityLondonUK
  3. 3.Department of Mathematics and StatisticsThe University of North Carolina at GreensboroGreensboroUSA

Personalised recommendations