Recent research on computational models of language change and cultural evolution in general has focused on the analytical study of languages as dynamic systems, thus avoiding the difficulties of analysing the complex multi-agent interactions underlying numerical simulations of cultural transmission. The same is true for the examination of the effects of inductive biases on language distributions within the Bayesian Iterated Learning Framework. The aim of this work is to test whether the strong results obtained through analytical methods in this framework also extend to finite populations of Bayesian learners, and to investigate what other effects richer population dynamics have on the results. Small world networks are introduced as a tool to model social structures which are shown to play an important role in the outcome of cultural transmission processes. The assumptions behind a Bayesian approach to language learning and its implications will be studied and compared to previous models of language change. While studying the effects of populations on convergence rates in the Bayesian model, the role of more complex population settings for the future of Iterated Learning will also be explored.