Advertisement

Bulletin of Mathematical Biology

, Volume 66, Issue 6, pp 1645–1658 | Cite as

Resistance is useless?—Extensions to the game theory of kleptoparasitism

  • Mark Broom
  • Roger M. Luther
  • Graeme D. Ruxton
Article

Abstract

We extend the game theoretic model of kleptoparasitism introduced by Broom and Ruxton (1998, Behav. Ecol.9, 397–403) in two ways: we allow for asymmetric contests, where the probability α of the challenger winning can take any value from 0 to 1; and we allow the handler to choose not to resist the challenge, but to immediately concede and relinquish its food to the challenger. We find, in general, three possible evolutionarily stable strategies—challenge-and-resist (Hawk), challenge-but-do-not-resist (Marauder) and do-not-challenge-but-resist (Retaliator). When α = 1/2, we find that Hawk and Marauder are the only ESS’s, in contrast to the result of the original model; we also find an overlap region, in parameter space, where two different ESS’s are possible, depending on initial conditions. For general α, we see that all three ESS are possible, depending on different values of the environmental parameters; however, as the average time of a contest over food becomes long, then the Marauder strategy becomes more and more prevalent. The model makes a potentially significant prediction about animal behaviour in the area of kleptoparasitism, that a searcher, when it meets a handler, will only decline to attack that handler when α < 1/2 i.e.when the defender is more likely to win. One possible converse of this statement, that a handler whose probability of success is greater than 1/2 should always resist a challenge, is not true.

Keywords

Food Item Prey Item Buffer Zone Broom Stable Strategy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barnard, C. J. and R. M. Sibly (1981). Producers and scroungers: a general model and its application to captive flocks of house sparrows. Anim. Behav. 29, 543–555.CrossRefGoogle Scholar
  2. Beddington, J. R. (1975). Mutual interference between parasites or predators and its effect on searching efficiency. J. Anim. Ecol. 44, 331–340.Google Scholar
  3. Brockman, H. J. and C. J. Barnard (1979). Kleptoparasitism in birds. Anim. Behav. 27, 487–514.CrossRefGoogle Scholar
  4. Broom, M. and G. D. Ruxton (1998). Evolutionarily stable stealing: game theory applied to kleptoparasitism. Behav. Ecol. 9, 397–403.Google Scholar
  5. Broom, M. and G. D. Ruxton (2003). Evolutionarily stable kleptoparasitism: consequences of different prey types. Behav. Ecol. 14, 23–33.CrossRefGoogle Scholar
  6. Furness, R. W. (1987). Kleptoparasitism in seabirds, in Seabirds: Feeding Ecology and Role in Marine Ecosystems, J. P. Croxall (Ed.), Cambridge University Press.Google Scholar
  7. Holmgren, N. (1995). The ideal free distribution of unequal competitors: predictions from a behaviour-based functional response. J. Anim. Ecol. 64, 197–212.Google Scholar
  8. Mesterton-Gibbons, M. and E. S. Adams (1998). Animal contests as evolutionary games. Am. Sci. 86, 334–341.CrossRefGoogle Scholar
  9. Ruxton, G. D., W. S. C. Gurney and A. M. de Roos (1992). Interference and generation cycles. Theor. Popul. Biol. 42, 235–253.CrossRefGoogle Scholar
  10. Ruxton, G. D. and A. L. Moody (1997). The ideal free distribution with kleptoparasitism. J. Theor. Biol. 186, 449–458.CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2004

Authors and Affiliations

  • Mark Broom
    • 1
  • Roger M. Luther
    • 1
  • Graeme D. Ruxton
    • 2
  1. 1.Department of MathematicsUniversity of SussexFalmer, BrightonUK
  2. 2.Division of Environmental and Evolutionary BiologyUniversity of GlasgowGlasgowUK

Personalised recommendations