Dynamics, statistics, and task allocation of foraging ants

Ant foraging is one of the most fascinating examples of cooperative behavior observed in nature. It is well studied from an entomology viewpoint, but there is currently a lack of mathematical synthesis of this phenomenon. We address this by constructing an ant foraging model that incorporates simple behavioral rules within three task groups of the ant colony during foraging (foragers, transporters, and followers), pheromone trails, and memory effects. The motion of an ant is modeled as a discrete correlated random walk, with a characteristic zigzag path that is congruent with experimental data. We simulate the foraging cycle, which consists of ants searching for food, transporting food, and depositing chemical trails to recruit and orient more ants (en masse) to the food source. This allows us to gain insights into the basic mechanism of the cooperative interactions between ants and the dynamical division of labor within an ant colony during foraging to achieve optimal efficiency. We observe a disorder-order phase transition from the start to the end of a foraging process, signaling collective motion at the population level. Finally, we present a set of time delay ODEs that corroborates with numerical simulations.