This dissertation presents the results of a series of simulations intended to expand the findings of Burkett and Griffiths (2009, 2010), whose model is shown to make a number of assumptions that may be unrealistic with regard to human language learners. These assumptions are modified to create a number of more realistic scenarios. A series of simulations shows that the concentration parameter if continues to affect the outcome of iterated learning with Bayesian learners in these new scenarios. To overcome the need for the concentration parameter to be specified by the modeller, a model is presented where agents learn a complex hypothesis composed of both a distribution of languages within a population and the appropriate value for. The outcome of the simulations based on this model are inconclusive but do hint at the possibility of _ being affected by iterated learning, potentially enabling learners to acquire a complex hypothesis.