Noise Induced Bistability of Ants Foraging using Indirect Recruitment

Bistability is usually modeled using a double well potential and simple white noise. There is, however, an alternative mathematical description of bistability utilizing a simple harmonic potential and multiplicative noise. The noise is greatest at the bottom of the well and vanishes at the boundaries, such that dz/dt = -z + s sqrt(1-z²) η, where η is Gaussian noise, z is the bistable quantity and s controls the strength of the noise. Previous studies have shown that when ants directly recruit one another to forage from one of two food sources, the ants exhibit this type of bistability. At small population sizes, the ants will forage bistably from the different food sources, but as the population size is increased over a certain critical population size, they will start to forage from both food sources equally. We extend this model to include indirect recruitment of ants to a food source via a pheromone laid out by other ants. The critical population size of this extended model depends on the ratio of the rates of creation and evaporation of the pheromones. Here we map the phase diagram for the extended model both analytically and through computer simulation. This model makes robust predictions that can be experimentally tested.