  Dominance and subordinate behaviours are important ingredients in the social
organizations of group living animals. Behavioural observations on the two
eusocial species \textit{Ropalidia marginata} and \textit{Ropalidia
cyathiformis} suggest varying complexities in their social systems. The queen
of R. cyathiformis is an aggressive individual who usually holds the top
position in the dominance hierarchy although she does not necessarily show the
maximum number of acts of dominance, while the R. marginata queen rarely shows
aggression and usually does not hold the top position in the dominance
hierarchy of her colony. These differences are reflected in the distribution of
dominance-subordinate interactions among the hierarchically ranked individuals
in both the species. The percentage of dominance interactions decrease
gradually with hierarchical ranks in R. marginata while in R. cyathiformis it
first increases and then decreases. We use an agent-based model to investigate
the underlying mechanism that could give rise to the observed patterns for both
the species. The model assumes, besides some non-interacting individuals, that
the interaction probabilities of the agents depend on their pre-differentiated
winning abilities. Our simulations show that if the queen takes up a strategy
of being involved in a moderate number of dominance interactions, one could get
the pattern similar to R. cyathiformis, while taking up the strategy of very
low interactions by the queen could lead to the pattern of R. marginata. We
infer that both the species follow a common interaction pattern, while the
differences in their social organization are due to the slight changes in queen
as well as worker strategies. These changes in strategies are expected to
accompany the evolution of more complex societies from simpler ones.
