My research lies at the interface of ecology and evolution and is focused around two key questions in evolutionary ecology: 'What determines species diversity?' and 'How did cooperative behaviour evolve?' These questions are among 25 unsolved problems facing the scientific community over the coming decade highlighted in the 125th anniversary issue of Science. The Science issue also stressed that the advancement of our understanding of the issues relating to the above questions requires a 'major interdisciplinary' effort and this is precisely what my fellowship will address. The fellowship is a collaboration between myself as a mathematical modeller and a group of experimental microbial population biologists namely Dr A Buckling, University of Oxford; Dr T Ferenci, University of Sydney; Professor P Rainey, University of Auckland; and Dr C MacLean, Imperial College London. I will be based at the University of Bath where I will work on the development of mathematical models for a range of projects designed to explore ecological mechanisms involved in the evolution of diversity and cooperation. The studies will be conducted by bringing to bare modern techniques of mathematical analysis and computation on the microbial evolutionary experiments of my collaborators.