A stochastic model of ant trail formation and maintenance in static and dynamic environments

Colonies of ants can complete complex tasks without the need for centralised control as a result of interactions between individuals and their environment. Particularly remarkable is the process of path selection between the nest and food sources that is essential for successful foraging. We have designed a stochastic model of ant foraging in the absence of direct communication. The motion of ants is governed by two components - a random change in direction of motion that improves ability to explore the environment, and a non-random global indirect interaction component based on pheromone signalling. Our model couples individual-based off-lattice ant simulations with an on-lattice characterisation of the pheromone diffusion. Using numerical simulations we have tested three pheromone-based model alternatives: (1) a single pheromone laid on the way toward the food source and on the way back to the nest; (2) single pheromone laid on the way toward the food source and an internal imperfect compass to navigate toward the nest; (3) two different pheromones, each used for one direction. We have studied the model behaviour in different parameter regimes and tested the ability of our simulated ants to form trails and adapt to environmental changes. The simulated ants behaviour reproduced the behaviours observed experimentally. Furthermore we tested two biological hypotheses on the impact of the quality of the food source on the dynamics. We found that increasing pheromone deposition for the richer food sources has a larger impact on the dynamics than elevation of the ant recruitment level for the richer food sources.