Self-organization in collective honeybee foraging: emergence of symmetry breaking,cross inhibition and equal harvest-rate distribution

De Vries and Biesmeijer described in 1998 an individual-oriented model that simulates the collective foraging behaviour of a colony of honeybees. Here we report how this model has been expanded and show how, through self-organization, three colony-level phenomena can emerge: symmetry breaking, cross inhibition and the equal harvest-rate distribution. Symmetry breaking is the phenomenon that the numbers of foragers visiting two equally profitable food sources will diverge after some time. Cross inhibition is the phenomenon that, by increasing the profitability of one of two equal food sources, the number of foragers visiting the other source will decrease. In some circumstances, the bees foraging on two sources of different profitabilities will be distributed between these sources such that the two average energy harvest rates are equal. We will refer to this phenomenon as the equal harvest-rate distribution. For each of these three phenomena, we show what the necessary behavioural rules to be followed by the individual forager bees are, and what the necessary circumstances are (that is, what values the model parameters should take) in order for these phenomena to arise. It seems that patch size and forager group size largely determine when each of these phenomena will arise. Experimenting with two types of currency, net gain rate and net gain efficiency, revealed that only gain rate may result in an equal harvest-rate distribution of foragers visiting different food sources.