Behavioral Ecology and Sociobiology

, Volume 49, Issue 2–3, pp 220–234 | Cite as

A simple spatially explicit ideal-free distribution: a model and an experiment

  • D. W. Stephens
  • J. R. Stevens
Original Article

Abstract 

This investigation presents a simple spatially explicit analysis of the ideal-free distribution. The traditional ideal-free distribution assumes discrete sites with definite boundaries, and predicts how many individuals should occupy each site. In contrast, the present analysis assumes that a forager’s gains gradually decline with distance from a site, and asks where in space individuals ought to be. Although many interesting situations may arise, the analysis asks how individuals should position themselves as the distance between two identical sources increases. Nash equilibrium positions should follow a pitchfork pattern as the distance between sites is increased; that is, an individual should maintain a position between two sources when they are close together but should move nearer one of the sources when they are far apart. In addition, the text describes an experimental study that parallels the theoretical analysis. The experiment supports the predicted pitchfork pattern, and provides somewhat weaker support for the predicted differences in ”individual” and ”paired” pitchforks.

Keywords Ideal-free distribution Spatial models Foraging Starling 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • D. W. Stephens
    • 1
  • J. R. Stevens
    • 1
  1. 1.Department of Ecology, Evolution and Behavior, University of Minnesota, St. Paul, MN 55108, USA e-mail: dws@forager.cbs.umn.edu Tel.: +1-612-6255722, Fax: +1-612-6246777US

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