Abstract
our objective is to determine the evolutionarily stable strategy [13] that is supposed to drive the behavior of foragers competing for a common patchily distributed resource [15]. Compared to [17], the innovation lies in the fact that random arrival times are allowed.
In this second part, we add interference to the model: it implies that a “passive” Charnov-like strategy can no longer be optimal. A dynamic programming approach leads to a sequence of wars of attrition [13] with random end times. This game is solved in Appendix A. Under some conditions that prevail in our
model, the solution is independent of the probability law of the horizon. As a consequence, the solution of the asynchronous foraging problem investigated here, expressed as a closed loop strategy on the number of foragers, is identical to that of the synchronous problem [17].
Finally, we discuss the biological implications such as a possible connection with the genetic variability in the susceptibility to interference observed in [22].
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References
Bishop D.T., Cannings C.: A generalized war of attrition. Journal of Theoretical Biology, 70:85–124, 1978.
Bishop D.T., Cannings C., Maynard Smith J.: The war of attrition with random rewards. Journal of Theoretical Biology, 74:377–388, 1978.
Cressman R.: Stability of the replicator equation with continuous strategy space. Mathematical Social Sciences, 50:127–147, 2005.
Cressman R., Hofbauer J.: Measure dynamics on a one-dimensional trait space: theoretical foundations for adaptive dynamics. Theoretical Population Biology, 67:47–59, 2005.
Doebeli M., Hauert C.: Models of cooperation based on the prisonner’s dilemma and the snowdrift game. Ecology Letters. 8:748–766, 2005.
Dubois F., Giraldeau L.-A.: The forager’s dilemma: food sharing and food defense as risk-sensitive foraging options. The American Naturalist, 162:768–779, 2003.
Goubault M., Outreman Y., Poinsot D., Cortesero A.M.: Patch exploitation strategies of parasitic wasps under intraspecific competition. Behavioral Ecology, 16: 693–701, 2005.
Haigh J., Cannings: Then-person warof attrition. Acta Applicandae Mathematicae, 14:59–74, 1989.
Hamelin F., Bernhard P., Nain P., Wajnberg E.: Foraging under competition: evolutionarily stable patch-leaving strategies with random arrival times. 1. Scramble competition. Annals of Dynamics Games, this volume, Birkhauser, pp. 327–348, 2007.
Hofbauer J., Sigmund K.: Evolutionary games and population dynamics. Cambridge University Press, Cambridge, UK, 1998.
Kuhn H.W.: Contribution to the theory of games. Volume 24 of Annals in Mathematics Studies, Princeton University Press, Princeton, New Jersey, USA, 1950.
McNamaraJ. M., Houston A.I., Collins E.J.: Optimality models in behavioral biology. SI AM Review. 43: 413–466, 2001.
Maynard Smith J.: Evolution and the theory of games. Cambridge University Press, Cambridge, UK, 1982.
Maynard Smith J., Price G.R.: The logic of animal conflict. Nature, 246: 15–18, 1973.
Parker G.A., Stuart. R.A.: Animal behaviour as a strategy optimizer: evolution of resource assessment strategies and optimal emigration thresholds. The American Naturalist, 110:1055–1076, 1976.
Samuelson L.: Evolutionary games and equilibrium selection. MIT Press, Cambridge, Massachusetts, USA, 1997.
Sjerps M., Haccou P.: Effects of competition on optimal patch leaving: a war of attrition. Theoretical Population Biology, 3:300–318, 1994.
Van Der Meer J., Ens B.J.: Models of interference and their consequences for the spatial distribution of ideal and free predators. Journal of Animal Ecology, 66:846–858, 1997.
Vincent T.: Evolutionary games. Journal of Optimization Theory and Applications, 46:605–612, 1985.
Vincent T., Fisher M.E.: Evolutionary stable strategies in differential and differences equations models. Evolutionary Ecology, 2:321–337, 1988.
Von Neumann J., Morgenstern O.: The theory of games and economic behaviour. Princeton University Press, Princeton, New Jersey, USA, 1944.
Wajnberg E., Curty C., Colazza S.: Genetic variation in the mechanisms of direct mutual interference in a parasitic wasp: consequences in terms of patch-time allocation. Journal of Animal Ecology, 73:1179–1189, 2004.
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Hamelin, F., Bernhard, P., Shaiju, A.J., Wajnberg, É. (2007). Foraging Under Competition: Evolutionarily Stable Patch-Leaving Strategies with Random Arrival Times. In: Jørgensen, S., Quincampoix, M., Vincent, T.L. (eds) Advances in Dynamic Game Theory. Annals of the International Society of Dynamic Games, vol 9. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4553-3_17
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