Selfish herd theory

The selfish herd theory states that individuals within a population attempt to reduce their predation risk by putting other conspecifics between themselves and predators. Such behavior inevitably results in aggregations. The theory was proposed by W. D. Hamilton in 1971 to explain the gregarious behavior observed in a variety of animals. It contrasted the popular hypothesis that evolution of such social behavior was based on mutual benefits to the population. The basic principle governing the selfish herd theory is that in aggregations, predation risk is greatest on the periphery and decreases toward the center. More dominant animals within the population are proposed to obtain low-risk central positions, whereas, subordinate animals will be forced into higher risk positions. Many researchers have used this hypothesis to explain why populations at higher predation risks often form larger, more compact groups. It also may explain why these aggregations are often sorted by phenotypic characteristics such as strength.

W.D. Hamilton proposed his theory in an article titled "Geometry for the Selfish Herd." To date, this article has been cited in over 2000 sources. To illustrate his theory, Hamilton asked readers to imagine a circular lily pond which sheltered a population of frogs and a . Upon appearance of the water snake, the frogs scattered to the rim of the pond and the water snake attacked the nearest one. Hamilton proposed that in this model, each frog had a better chance of not being closest to, and thus vulnerable, to attack by the water snake if he was between other frogs. As a result, modeled frogs jumped to smaller gaps between neighboring frogs.

This simple example was based on what Hamilton identified as each frog’s domain of danger, the area of ground in which any point was nearer to that individual than it was to any other individual. The model assumed that frogs were attacked from random points and that if an attack was initiated from within an individual’s domain of danger, he would be attacked and likely killed. The risk of predation to each individual was, therefore, correlated to the size of his domain of danger. Frog jumping in response to the water snake was an attempt to lower the domain of danger.

Hamilton also went on to model predation in two-dimensions, using a lion as an example. Movements that Hamilton proposed would lower an individual’s domain of danger were largely based on the theory of marginal predation. This theory states that predators attack the closest prey, who are typically on the outside of an aggregation. From this, Hamilton suggested that in the face of predation, there should be a strong movement of individuals toward the center of an aggregation.

A domain of danger may be measured by constructing a Voronoi diagram around the group members. Such construction forms a series of convex polygons surrounding each individual in which all points within the polygon are closer to that individual than to any other.

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