Simple models for trail-following behaviour; Trunk trails versus individual foragers

Social insects such as ants use trial-marking and trail-following to organize the behaviour and movement patterns of a large population. Since behaviour has to meet needs of the population in a changing environment, the type of trail networks formed must be adaptable. Both solitary foraging as well as mass migration along a system of trunk trails are behaviours essential for survival of the colony, and the population must be able to switch from one behaviour to the other, depending on conditions. Using a mathematical model for trail following we show that subtle changes in individual behaviour can give rise to dramatic differences in the behaviour of the population, including the ability to switch from solitary movement to organized group traffic. The model incorporates biological parameters associated with the organism, the trail-marker, and the population. Ordinary differential equations are formulated for the density of the trails and for the number of individuals following trails or exploring randomly. It is assumed that the followers reinforce trails by pheromone marking, and that individuals respond to the strength of the trails by becoming more efficient followers. The model is analyzed by qualitative phase-plane methods.