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Foraging Under Competition: Evolutionarily Stable Patch-Leaving Strategies with Random Arrival Times.

Scramble Competition
  • Frédéric Hamelin
  • Pierre Bernhard
  • Philippe Nain
  • Éric Wajnberg
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 9)

Abstract

Our objective is to determine the evolutionarily stable strategy [14] that is supposed to drive the behavior of foragers competing for a common patchily distributed resource [16]. Compared to [18], the innovation lies in the fact that random arrival times are allowed.

In this first part, we investigate scramble competition: the game still yields simple Charnov-like strategies [4]. Thus we attempt to compute the optimal longterm mean rate γ* [11] at which resources should be gathered to achieve the maximum expected fitness: the assumed symmetry among foragers allows us to express γ* as a solution of an implicit equation, independent of the probability distribution of arrival times.

A digression on a simple model of group foraging shows that γ*N can be simply computed via the classical graph associated to the marginal value theorem—N is the size of the group. An analytical solution allows us to characterize the decline in efficiency due to group foraging, as opposed to foraging alone: this loss can be relatively low, even in a “bad world,” provided that the handling time is relatively long.

Back to the original problem, we then assume that the arrivals on the patch follow a Poisson process. Thus we find an explicit expression of γ* that makes it possible to perform a numerical computation: Charnov’s predictions still hold under scramble competition.

Finally, we show that the distribution of foragers among patches is not homogeneous but biased in favor of bad patches. This result is in agreement with common observation and theoretical knowledge [1] about the concept of ideal free distribution [12, 22].

Keywords

Intake Rate Handling Time Interarrival Time Patch Quality Scramble Competition 
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.

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Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  • Frédéric Hamelin
    • 1
  • Pierre Bernhard
    • 1
  • Philippe Nain
    • 2
  • Éric Wajnberg
    • 3
  1. 1.CNRS and University of Nice Sophia Antipolis-I3SÉcole Polytechnique de l’Université de Nice Sophia AntipolisSophia AntipolisFrance
  2. 2.INRIASophia AntipolisFrance
  3. 3.INRASophia Antipolis CedexFrance

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