The present study explores the idea that human linguistic communication co-opted a pre-existing population-wide behavioural system that was shared among social group members and whose structure reflected the structure of the environment. This system is hypothesized to have emerged from interactions among individuals who had evolved the capacity to imitate arbitrary, functionless behaviour. A series of agent-based computer simulations test the separate and joint effects of imitation, pattern completion behaviour, environment structure and level of social interaction on such a population-wide behavioural system. The results support the view that a system that could be co-opted for linguistic communication might arise in a population of agents equipped with arbitrary imitation for the purposes of pattern completion interacting in certain kinds of structured environments. Such pre-linguistic behavioural system could have bootstrapped communication and paved the way for biological capacities widely believed to be necessary for communication, such as shared intentionality and symbolicity, to evolve.