Mathematical models for some types of chemical information systems

Abstract

Ant species on a “high evolutionary level” have evolved chemical recruitment systems such as mass recruitment or quality recruitment. The recruitment process from the nest to a food source may be damped by crowding effects at the source. For four patterns of behavior (mass/quality recruitment; with/without damping) we study mathematical models for the time development of the quantity of food at the source. Each of the models can be reduced to a second order time-delayed differential equation which will be studied in the equivalent form of a first order (nonlinear) functional differential equation. We discuss the complete exploitation of a given source. In case of mass recruitment there possibly remains a threshold quantity of food not worth exploiting. However, every source will be exploited completely (in finite time) provided that the volatility of the trail pheromone is small compared with the exploitation activities of the colony and the distance from the nest to the source. In addition, for the damped models the “capacity” of the crowded source must be large compared with the initial quantity of food offered. The efficiency of the exploitation activities of some species allows conclusions on their evolutionary development.