Abstract
This paper develops a simple model for the movement of a non-volatile phero-mone through a honey-bee hive. The model is specifically developed for a pheromone produced by the queen which is thought to regulate colony swarming. Although the model begins as a system of partial integro-differential equations, it is in the end reduced to a system of linear, first-order partial differential equations for the average pheromone level per worker, the pheromone level of the hive substrate, and the pheromone level of the queen. Analysis of this system shows that both colony size and hive area have independent effects on the average pheromone levels of the workers, but that worker congestion can have an even stronger effect on the pheromone distribution. These results establish a relationship between colony size, hive area, worker crowding, and queen-pheromone transmission.
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