Modeling ant foraging lines.

Figure 1: A Big-Headed Ant (Formicidae Pheidole, left) finds food in the MEC Lab at the University of Delaware, and a view of the foraging line (right).

Ant colonies are a classic example of self-organization. When viewing a column of ants invading one's kitchen despite obstacles and barriers, it is easy to assume erroneously that the ants are being directed toward the food source. In fact, there is no centralized coordination of ant foraging. Individual ants are nearly blind organisms that possess little or no memory, and their cognitive ability is limited to a small set of behavioral modes, such as searching for food, being alarmed or carrying food back to the hive. The key to the collective intelligence of ants is a small collection of communication protocols they instinctively use. When ants find and consume food, they know to seek their hive and start laying a pheromone trail as they go. Ants seeking food are drawn toward this chemical trail. Furthermore, encounters with food carrying ants can trigger a regurgitative process that draws ants toward the food source. Meanwhile, ants searching for food carry a pheromone from the hive that helps ants carrying food to find the hive again. All these chemical signals decay with time so shorter routes or routes that are frequently traveled are reinforced. Through foraging lines are often viewed as steady streams of ants flowing to and from the hive, careful observation and measurement reveals that a single foraging line exhibits a rich collection of interacting traveling waves and clumps.

Space-time A Space-time B

Figure 2: Space-time plots of experimental measurements of ant densities along a foraging line. Notice the strong left- and right-moving wave in the left plot. In the right plot, one can see many combinations of waves. The colorbar indicates the ant density.

The success of ant colonies in the wild and in laboratory experiments has inspired a number of investigations and experiments. There are numerous investigations into “swarm intelligence” which focuses on using small cooperating, autonomous algorithms for solving large scale problems. Ant Colony Optimization (ACO) algorithms, which are based on ant behavior, have proven successful against a number of classic mathematical optimization problems including the Traveling Salesman Problem and the Job-Shop Scheduling problem. There has been effort by complexity theorists to study the behavior of ant-inspired continuum and discrete models. Finally, the biology community has an sustained interest in social insects and the role of social behavior in their evolution.

Actual ant behavior is rich and complex, and the fundamental unit of ant colony expression is the foraging line. If ant colonies inspire so much investigation, it is essential that foraging lines and other components of ant colonies be systematically modeled and analyzed. Fundamental questions include:

  1. What are the relevant behavioral parameters governing local interactions between ants?
  2. What are appropriate boundary conditions for foraging lines?
  3. What impact does each parameter have on the macroscopic features of a foraging line?
  4. What outcomes would one expect from a successful model? Is there a definitive experiment that one can design based upon the model?
  5. How do the model parameters effect the quality of solution obtained by the foraging line?
A number of approaches are possible for capturing the motion and behavior and collections of ants.

If you are eager to start reading about ants and ant modeling, here are some good references:

  1. Eric Bonabeau, Guy Theraulaz, Jean-Louis Denebourg, Serge Anon and Scott Camazine. “Self-organization in social insects.” TREE vol 12, no 5, pp 188-193 (1997). A nice user-friendly introduction to some of the broader issues.

  2. I. D. Couzin and N. R. Franks. “Self-organized lane formation and optimized traffic flow in army ants.” Proceedings of the Royal Society B, vol 270, pp 139-146 (2002). A nice modeling piece with measurements and computations.

  3. Bert Hölldobler and Edward O. Wilson. Journey to the Ants. The Belkap Press of Harvard University Press (1994). A friendly book on ant behavior with some cool experiments.