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.
Bibliographical noteFunding Information:
equilibrium p-values. The solid lines show numerical calculated values. The dashed lines show the approximation A18 Acknowledgements We thank Sandra Knox and Jennifer Ernisse for help with the experiments. We thank Carlos Bernstein, Alex Kacelnik, Kate Lessells, Colleen McLinn, and Tom Tregenza for their comments on the manuscript. The experimental portion of this work was conducted while the authors were members of the Nebraska Behavioral Biology Group. We thank the NBBG for providing a stimulating and supportive environment. This work was supported by grant number IBN-9507668 from the National Science Foundation. This was conducted in accordance with animal use and care protocols approved by the Institutional Animal Use and Care Committee of the University of Nebraska, Lincoln.
- Ideal-free distribution
- Spatial models