Analysis of ant foraging algorithms

We consider some models of ant foraging and recruitment behaviour that depend on each individual ant following a simple algorithm. Self-organisation enables the colony as a whole to establish a foraging strategy in the absence of any hierarchical control. In this paper we investigate how the effectiveness of such a foraging strategy depends on the persistence of the signals used by the individual ants and on the errors they make in following such signals. The use of inhibitory as well as excitatory signals is considered, and shown to be extremely effective in certain circumstances. This is interesting, as such signals have never been observed in real ant colonies. Such models are often investigated by simulation, but we approach them from the point of view of statistical mechanics. Looked at another way, which yields some insight, we approximate the stochastic process that models the system by a diffusion process with small diffusion parameter. This approach does not replace simulation, but supplements it. Its advantage is that it can elucidate the role of parameters more clearly and using much less computer time than simulation, but its disadvantage is that many simplifying assumptions must be made before the problem is amenable to analytic treatment.