Box 1. Box 1 How ants find the shortest path

Ant colonies can collectively perform tasks and make decisions that appear to require a high degree of co-ordination among the workers: building a nest, feeding the brood, foraging for food, and so on. In the example presented here, the ants collectively discover the shortest path to a food source. In experiments with the ant Linepithaema humile, a food source is separated from the nest by a bridge with two branches^{1, 2}. The longer branch is r times longer than the shorter branch (Fig. 2a).

The shorter branch is selected by the colony in most experiments if r is sufficiently large (r = 2 in Fig. 2b). This is because the ants lay and follow pheromone trails: individual ants lay a chemical substance, a pheromone, which attracts other ants. The first ants returning to the nest from the food source are those who take the shorter path twice (from the nest to the source and back). At choice points 1 and 2, nestmates are recruited toward the shorter branch, which is the first to be marked with pheromone. If, however, the shorter branch is presented to the colony after the longer branch, the shorter path will not be selected because the longer branch is already marked with pheromone (Fig. 2b).

This problem can be overcome in an artificial system, by introducing pheromone decay: when the pheromone evaporates sufficiently quickly, it is more difficult to maintain a stable pheromone trail on a longer path. The shorter branch can then be selected even if presented after the longer branch. This property is particularly desirable in optimization, where one seeks to avoid convergence toward mediocre solutions. In Linepithaema humile, although pheromone concentrations do decay, the lifetime of trail pheromones is too large to allow such flexibility.