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

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.