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Abstract

I study the problem of self-organized pattern formation by groups of organisms. "Self-organized" groups are coordinated by interactions between all individuals in the group rather than by a leader or hierarchical organization. The information and stimuli necessary to coordinate individual activities are communicated through the group by these interactions. I begin by describing a modelling philosophy where as many details of the individual behaviours are included in the model as are necessary for both biological and mathematical completeness, but no group behaviours are fed into the model. Two specific phenomena are addressed using this approach. The first phenomenon is honey bee cluster thermoregulation. I address the question "can cluster thermoregulation be explained using only the observed behaviours of individual bees?" and show that a temperature dependent behaviour of the bees is sufficient to produce the observed global thermoregulation of the cluster. Previous models of cluster thermoregulation are discussed in light of this modelling approach. The model also is able to make testable predictions about the density profiles of the cluster. The second phenomenon modelled is the transmission of a pheromone through a honey bee colony. The problem is of interest to beekeepers, since the pheromone is known to suppress swarming. I answer the question "How does congestion within a honey bee colony affect the transmission of a pheromone through the hive?" This question is central to a current hypothesis on the connection between the queen's ability to produce pheromones, colony size and congestion, and swarming. The cluster thermoregulation model involves a behavioural dependence on the cluster temperature. In contrast, the transmission model involves a direct exchange of a chemical pheromone between the bees. Thus, with the thermoregulation model I examine interactions mediated through an environmental state, and with the transmission model I examine direct interactions between individuals. I study these models using both Eulerian and Lagrangian models. The Lagrangian model is studied using cellular automata simulation. The Eulerian model consists of a system of partial integro-differential equations and is studied using a combination of numerical simulations and mathematical analysis. The results of the models suggest that the two interactions produce similar group properties. In the thermoregulation model, information about the global structure of the group diffuses through the cluster as thermal energy. In the transmission model, pheromone diffuses through the colony by the random motions of the bees.