This Week's Citation Classic

Hamilton, W.D. 1971. Geometry for the selfish herd. Journal of Theoretical Biology 31:296-311.

One of the most difficult things to do in science is come up with an idea that revolutionizes a field. Most biologists fail to do so in their entire careers. I can think of at least six major revolutions inspired by Bill Hamilton: Inclusive Fitness (the so-called Hamilton's Rule; Hamilton 1964), Mate Choice and Good Genes (Hamilton & Zuk 1982), Extraordinary Sex Ratios (Hamilton 1967), the Red Queen Theory and the Evolution of Sex (Hamilton 1980), Tit for Tat and the Evolution of Cooperation (Axelrod & Hamilton 1981) and present paper, Selfish Herds (Hamilton 1971).

Geometry for the Selfish Herd is my personal favorite from Hamilton's oeuvre. With a few pages of text and some simple algebra and geometry, Hamilton explains the behavior of animals wide ranging as elk, herring, starlings, bats, locusts, caterpillars, and sheep. All of these animals, and their brethren, aggregate into groups. Some theorists supposed that this was for the benefit of the species, for better access to mates or to enable members to assess population numbers. Hamilton thought this was nonsense. These animals are aggregating to ensure that their fellows are eaten rather than themselves.

In the first paragraph of the paper, Hamilton writes,

"Imagine a circular lily pond. Imagine that the pond shelters a colony of frogs and a water-snake. The snake preys on the frogs but only does so at a certain time of day-up to this time it sleeps on the bottom of the pond. Shortly before the snake is due to wake up all the frogs climb out onto the rim of the pond. This is because the snake prefers to catch frogs in the water. If it can’t find any, however, it rears its head out of the water and surveys the disconsolate line sitting on the rim-it is supposed that fear of terrestrial predators prevents the frogs from going back from the rim-the snake surveys this line and snatches the nearest one."
So what will the frogs do in such a situation? Will they disperse evenly about the rim of the pond where each frog has an equal chance of being eaten? (See Fig. A).

"No", said Hamilton, "each will have a better chance of not being nearest to the snake if he is situated in a narrow gap between two others." The frogs now bordering a wide gap will have the greatest chance of being eaten (See Fig. B).If the frogs continue to move, they will "quickly collect in heaps", with the outermost individuals selfishly struggling to find a place in the middle. So strong is this urge that animals will experience extreme discomfort at being separated from the herd. Hamilton cites a passage from Sir Francis Galton, Darwin's cousin.

“Yet although the ox has so little affection for, or individual interest in, his fellows, he cannot endure even a momentary severance from his herd. If he be separated from it by stratagem or force, he exhibits every sign of mental agony; he strives with all his might to get back again and when he succeeds, he plunges into its middle, to bathe his whole body with the comfort of closest companionship.”

So there you have it, a superb theory of animal behavior, exceptionally general, expressed cogently and written with verve and enthusiasm. And such a great title. How cool is that?