This thesis presents a formal empirical anthropological analysis of the Indigenous population of the Central Murray Darling Basin (CMDB) region of South East Australia. The first part of the analysis comprises a review of past theoretical assumptions underlying social anthropological models of Indigenous population dynamics generally. The second part comprises a conventional kinship network analysis of a 3138-person population model, and introduces a newly developed spatiotemporal kinship network analysis of the same population model. Results are compared. The mainstream discipline of social anthropology, especially as practiced in Australia, is not a formal science but rather more closely aligned with philosophy and the humanities. It is nevertheless concerned with a field of study - human sociality - that also concerns a number of scientific disciplines. Despite this overlapping concern there is no disciplinary integration or 'consilience' between social anthropology and these other scientific fields. Irrespective of this lack of consilience, social anthropology has, since the early 1970s, been treated as a forensic science by the Australian judicial system with regard to legislation affecting Indigenous people. The result has been a slowly developing recognition that the discipline of social anthropology lacks a formal paradigmatic basis, and as such, is of limited use in either a forensic application, or in any other field that requires evidence based research, such as health and demography. Historically, social anthropological research into Indigenous Australian sociality has played an important role in the discipline's theoretical development. Since the inception of social anthropology in the 1870s, research conducted with Indigenous Australian people has formed a key feature of all major theoretical texts, and has been used to support key theoretical assumptions. Most important among these assumptions has been a loose collection of tacit mathematical concepts