How do workers of the primitively eusocial wasp Ropalidia marginata detect the presence of their queens?

Queens in primitively eusocial insect societies are morphologically indistinguishable from their workers, and occupy the highest position in the dominance hierarchy. Such queens are believed to use aggression to maintain worker activity and reproductive monopoly in the colony. However, in the primitively eusocial wasp Ropalidia marginata, the queen is a strikingly docile individual, who interacts rarely with her workers. If the queen is experimentally removed, one of the workers becomes extremely aggressive within minutes, and eventually becomes the new queen of the colony. We designate her as the potential queen. Experimental evidence suggests that the queen probably uses a non-volatile pheromone to signal her presence to her workers. Here we attempt to identify the mechanism by which the queen transmits information about her presence to the workers. We designate the time taken for the potential queen to realize the absence of the queen as the realization time and model the realization time as a function of the decay time of the queen's signal and the average signal age. We find that the realization time obtained from the model, considering only direct interactions (193.5 min) is too large compared to the experimentally observed value of 30 min. Hence we consider the possibility of signal transfer through relay. Using the Dijkstra's algorithm, we first establish the effectiveness of relay in such a system and then use experimental data to fit the model. We find that the realization time obtained from the model, considering relay (237.1 min) is also too large compared to the experimentally observed value of 30 min. We thus conclude that physical interactions, both direct and indirect (relay), are not sufficient to transfer the queen's signal in R. marginata. Finally, we discuss the possibility that the queen applies her pheromone on the nest material from where the workers can perceive it without having to physically interact with the queen.