DISTINGUISHING THE EFFECTS OF DILUTION AND RESTRICTED MOVEMENT ON THEINTRA-NEST TRANSMISSION OF HONEYBEE QUEEN PHEROMONES

This paper develops a simple model for the movement of a non-volatile pheromone through a honey-bee hive. The model is specifically develope d for a pheromone produced by the queen which is thought to regulate c olony swarming. Although the model begins as a system of partial integ ro-differential equations, it is in the end reduced to a system of lin ear, first-order partial differential equations for the average pherom one level per worker, che pheromone level of the hive substrate, and t he pheromone level of the queen. Analysis of this system shows that bo th colony size and hive area have independent effects on the average p heromone levels of the workers, hut that worker congestion can have an even stronger effect on the pheromone distribution. These results est ablish a relationship between colony size, hive area, worker crowding, and queen-pheromone transmission. (C) 1998 Society for Mathematical B iology.