The project will develop new mathematical models and tools for the rigorous analysis of very general
stochastic populations that are subject to internal competition and feedback. The mathematical framework is that of measure-valued processes, a setting needed to encompass the complexity and random structure inherent in such systems. Models of this kind have real-world applications in evolutionary biology, cell kinetics and cancer research, and are essential to our understanding of the persistence of endemic disease and of the preservation of endangered species. The results of this project will provide insight into the behaviour and (in-)stabilities of complex stochastic populations, and offer guidance for their management.