Models of Ant Foraging Lines

The objective of this problem is to study ant foraging lines in one and two dimensions in order to understand their dynamics and examine the fitness of ant colonies. A simple model to describe ant traffic is formulated using conservation laws and a behavioral model. In this work, the behavioral model assumes that the concentration of pheromones is simply proportional to the density of ants. This leads to a hyperbolic system for the density and velocity of ants. The system is reduced to a system of second order PDEs which is analyzed using Fourier series. The Fourier analysis predicts the existence of phase speeds in the ants’ motion which can be verified experimentally. The group divided into two teams in order to study the one-dimensional and the twodimensional cases separately. The two-dimensional analysis was done numerically using a stochastic model and simulated using cellular automata. This simulation provided qualitative information to study the formation of foraging lines. In particular, this model shows the importance of large populations. Also, additional constraints on the model were considered in order to make it more realistic. For the one-dimensional analysis, the first goal was to find representative Froude numbers for the ants’ movement from the experimental data. The full hyperbolic system was analyzed and its characteristic speeds identified. Numerical solutions of the problem were obtained using both a Lax-Friedrichs and a Lax-Wendroff scheme.