Ants and agents: a process algebra approach to modelling ant colony behaviour.

Process algebras are widely used in the analysis of distributed computer systems. They allow formal reasoning about how the various components of a system contribute to its overall behaviour. In this paper we show how process algebras can be usefully applied to understanding social insect biology, in particular to studying the relationship between algorithmic behaviour of individual insects and the dynamical behaviour of their colony. We argue that process algebras provide a useful formalism for understanding this relationship, since they combine computer simulation, Markov chain analysis and mean-field methods of analysis. Indeed, process algebras can provide a framework for relating these three methods of analysis to each other and to experiments. We illustrate our approach with a series of graded examples of modelling activity in ant colonies.

Gaseous templates in ant nests.

We apply a diffusion model to the atmosphere of ant nests. With particular reference to carbon dioxide (CO2), we explore analytically and numerically the spatial and temporal patterns of brood- or worker-produced gases in nests. The maximum concentration within a typical one-chamber ant nest with approximately 200 ants can reach 12.5 times atmospheric concentration, reaching 95% of equilibrium concentrations within 15 min. Maximum concentration increases with increasing number of ants in the nest (or production rate of the gas), distance between the centre of the nest ants and the nest entrance, entrance length, wall thickness, and with decreasing entrance width, wall permeability and diffusion coefficient. The nest can be divided into three qualitatively distinct regions according to the shape of the gradient: a plateau of high concentration in the back half of the nest; an intermediate region of increasingly steep gradient towards the entrance; and a steep linear gradient in the entrance tunnel. These regions are robust to changes in gas concentrations, but vary with changes in nest architecture. The pattern of diffusing gases contains information about position and orientation relative to gas sources and sinks, and about colony state, including colony size, activity state and aspects of nest architecture. We discuss how this diffusion pattern may act as a "dynamic template", providing local cues which trigger behavioural acts appropriate to colony needs, which in turn may feed back to changes in the gas template. In particular, wall building occurs along lines of similar concentration for a variety of nest geometries; there is surprising convergence between the period of cycles of synchronously active ants and the time taken for CO2 levels to equilibrate; and the qualitatively distinct regions of the "dynamic template" correspond to regions occupied by different groups of ants.