Identifying cues for self-organized nest wall-building behaviour in the rock ant, Temnothorax rugatulus, using hidden Markov models

European Temnothorax albipennis and its American counterpart Temnothorax rugatulus build circular walls to limit their nest area within a rock crevice. To determine wall position, workers are thought to rely on a distance template (from the cluster of brood and nurses at the nest centre) and on indirect social (i.e. stigmergic) information found in the aggregations of already-deposited building material. Analytical and simulation models of this behaviour predict that the combination of these two mechanisms can produce the observed wall structure, but there is so far no empirical evidence of either mechanism. Here, we find statistical evidence in support of the stigmergic relationship between stone density and deposition behaviour. We apply hidden Markov models (HMMs) to analyse wall-building data from four colonies of T. rugatulus. We show that material deposition activity changes following a parabolic relationship with the density of building material at building sites, different from the linear relationship hypothesized previously. This parabolic curve is similar to behavioural response curves identified in the nest enlargement process of several ant species. In addition, HMM analysis indicates the existence of two distinct states in T. rugatulus building activity. These states are associated with different mean building rates (that is, the two states can be described as a high and a low activity state) and might be caused by changes in task priorities during the colony process of settling into a new nest. This study updates one of the earliest models of self-organized animal behaviour.