The ARC centre of excellence for the Dynamics of language is offering a number of PhD positions, including on the topic of language evolution. The positions are hosted at ANU in Canberra, the University of Melbourne and the University of Queensland. These are on top of the Wellsprings of Diversity positions.
From the website:
The Evolution program will engage with central questions about the evolution of language across scales that range from the whole span of human evolution to the adaptations that occur as speech capacities are lost in speech-impaired individuals. This program will explore what possible structures languages can develop, how learning and processing biases shape the direction of evolution, what is the role of the speech community in language evolution, and how insights from language evolution can help develop more flexible ways of robots learning speech.
Details can be found in the pdfs below.