Economists have relied on convexity assumptions for a long time but many natural resources that stem from ecosystems have non-convexities in their dynamics. This project studies some of the consequences of relaxing convexity assumptions for management and the role of fast and slow variables. We present a general framework to handle systems with fast and slow variables, and illustrates the method using a model of coral reefs subject to fishing pressure. We also present a MATLAB toolbox for handling these optimal control problems with non convexities and illustrate how it works with slow and fast variables. The insights obtained can be used to discuss alternative management strategies.