As at the end of 2009, 50 million scholarly papers were in existence, and changes in the global higher education sector are seeing this number grow rapidly. With the impact of university ranking schemes, dramatic changes have occurred in the academic publication system; both the number of publications, and the number of scholars, are increasing rapidly. In this research, we conduct a focused study on the quantitative relationships in Australian academic science. Sample data is selected from three institutions, representing three types of universities in Australia: a leading university, a middle-tier university, and a non-comprehensive university. For our analysis, bibliometric data for 32,056 scholars and 353,334 publications are downloaded. The results show that varying growth rates for scholars (5.6%, 6.1%, and 7.7%) and journal publications (6.7%, 7.4%, and 9.7%) for the leading university, the middle-tier university, and the non-comprehensive university respectively. We also evaluate how scholarly publications differ across these three Australian universities types from six aspects: average number of publications per scholar, percentage of first-authored publications, collaboration pattern, average SJR score of publishing journals, percentage of Quartile category of publishing journals, and average citation per publication. Lastly, we consider how the scholarship life-cycle varies in Australian universities in terms of publishing age, thus establishing the quantitative relationship between scholarship life-cycle and publishing performance in Australian universities.