How barriers to gene flow evolve in space and time and along the genome, and under which conditions they can cause complete reproductive isolation between populations living in contact is a major question in evolutionary biology. The formation of barriers to gene flow, and their spatiotemporal dynamics is influenced by multiple evolutionary processes. How the barriers are distributed in the genome may also be important (e.g., whether or not they are harboured by inversion polymorphism) and is also subject to evolution. In this project, we will use mathematical models to study the dynamics of the barriers to gene flow: in space, time, and along the genome. This project is funded by Vetenskapsrådet, grant number 2021-05243.