Ant Random Walk

If aliens were to visit Earth, it is possible that they would miss us altogether and assume this was a planet of ants (1). Before the belittlement creeps in, understand that ants are some of the most dominant predators in terms of numbers and body mass (once combined, of course). As most creatures, we humans are limited to viewing the world from our own individualistic perspective, but if we can perceive past that, we might consider an ant colony to be a single super-organism, capable of complex and intricate actions, communication, and specialization.

The next time you have the inclination to sit and observe, take a good look towards the ground. If you are outdoors, you will notice ants. See how they wander for some time in a wavering line, and then abruptly turn in a different direction? At first sight, it may seem illogical, especially if you see them headed straight for a piece of food, only to watch them turn away a measly two feet from the target. Although this can seem sporadic, ants have a mighty sense of direction. The apparent disorganization is actually a highly systemized feature of the ant colony. This chaotic behavior may be referred to as hunting -- the beginning strategy in the ant foraging process. Once a scout ant has found a food source and makes the decision to return to the nest, they do so by way of homing, where they determine the most efficient pathway home based off of their own knowledge of the nest's location. In their final mechanism used in the search for food, ants utilize a path-building strategy, which involves individual ants laying down a chemical (pheromone) trail as they walk so that when one ant comes across a pheromone trail of another, it is more likely to follow it (2?). The more ants following the trail, the stronger it attracts other ants to fall in line.

"...the ants go marching..."

If you were to place a piece of food on the ground and wait, the ants would find it with amazing efficiency. Interestingly enough, the way ants forage is called a random walk (3). Now, the next time you find yourself sitting on a park bench, pondering life, and you see an orderly line of ants, place a stick over the line and observe the confusion. You will witness a pheromone trail.

An immortal ant, walking forever would walk over every point on the globe (assuming there are no rivers or oceans), AND it would eventually end up back home. If you had a lot of ants doing this, they could cover the space amazingly quickly. The random walks of ants have been extensively studied, modeled, and imitated for a wide variety of human interests.

Imagine you were planning a trip to Europe, and could only bring one knapsack (4), what would you put in it? Ask the ants! Ants evaluate resources in their walks. In the figure to the left, we see a huge pile of sugar, a concentrated drop of honey, and some water droplets. Ants will go for the honey before the sugar, because the honey is concentrated nutrition, even though there is more sugar. We can model this behavior in our own lives, and leave the blow-drier behind, in favor of the nail clipper.

In computer science, there is an ant colony optimization (ACO) algorithm based on the behavior of ants where simulated "ants" search through 2 dimensional space to maximize efficiency for things like the distribution of "Lyft" vehicles, or police patrols, as well as internet routing (5). There is even a company that uses the ACO algorithm to design its commercial products.

There are so many methods we can learn from random walks. Think of a traveling salesperson (6), who must efficiently cover extensive ground (See Figure below, panel 1), visiting each city once and only once (panel 2). Distant cities are less likely to be visible, and the more traffic on the roads (pheromone trails) the more likely that route will be selected (panel 3). Rules that imitate ant behavior will result in the selection of the best path for the salesperson (panel 4).

Furthermore, we can imitate ants to study the interplay between personality and information sharing (7), optimize circuit design (8) and discounted cash flows (9), estimate population densities (10), and so forth. There truly is so much to learn from these masters of the Earth.

Web Resources

1. BBC article on the rulers of the Earth

2. Paper on ant foraging behavior

3. NBC news on ant foraging

4. Paper about the knapsack problem

5. Wikipedia explanation of Ant Colony Optimization

6. Paper on Ants and the traveling salesman problem

7. Psychological review discussing ants and information-sharing

8. Paper on ACO and circuit design

9. Paper on optimizing cash flows

10. Paper on estimating population densities with ant random walks

Photo Credit

1. Wikipedia commons, open access. Author, Dake.
2. Wikipedia commons, open access. Author, Johann Dréo.