My research focus is dynamical systems, especially those derived from models from ecology. In particular, I am concerned with the existence of invariant manifolds, their geometry, and how this geometry can be used to study the long-term dynamics of the system. Much of my work involves systems that enjoy an ordering property, such as monotone or competitive systems. Originally I worked with continuous time models, but increasingly I have treated models with discrete time. In my work some form of balance is in operation. For example, in ecology growth balances decline along a manifold known as the carrying simplex. In genetics, there is a balance between recombination and selection along a manifold which is close to the well-known Hardy-Weinberg manifold. The identification of processes that balance in models is an important step towards simplifying the model and analysing its behaviour.