Collective defence in honeybees: Extracting individual behaviour from population data

Collective behaviour emerges from the aggregated behaviours of many individuals - be that cells, bees, or humans. Individuals react to both their environment and the behaviour of others, and this interdependence makes it intrinsically difficult to provide a mechanistic description of collective phenomena. This is particularly true in dynamic systems, in which individuals may modify their environment over time. Here, we provide computational methods that allow the evaluation of individual behaviour from population data, given a probabilistic model and repeated steady-state experimental data. In particular, we develop a model of the collective defence system of honeybees against vertebrates. Honeybees protect their colony against vertebrates by mass stinging and coordinate their actions during this crucial event thanks to an alarm pheromone carried directly on the stinger, which is therefore released upon stinging. This pheromone typically recruits nearby bees so that more and more bees participate in the defence, but understanding its quantitative action during the course of an attack remains challenging. We first propose a biologically plausible model of this phenomenon, fully parametrised by the stinging probabilities of an individual bee at each alarm pheromone concentration level. Second, we provide methods for inferring the parameters of the model from experimental data. As a result, we can evaluate how the individual probability to sting changes during the course of a defensive event. Our methodology could be applied to a number of biological questions with similar probabilistic chains of actions. In the context of honeybee defence, for example, it will be useful to compare the strategies adopted by bees under different social contexts (e.g. varying group sizes).