Multi-population evolutionary algorithms are, by nature, highly complex and difficult to describe. Even two populations working in concert (or opposition) present a myriad of potential configurations that are often difficult to relate using text alone. Little effort has been made, however, to depict these kinds of systems, relying solely on the simple structural connections (related using ad hoc diagrams) between populations and often leaving out crucial details. In this paper, we propose a notation and accompanying formalism for consistently and powerfully depicting these structures and the relationships within them in an intuitive and consistent way. Using our notation, we examine simple co-evolutionary systems and discover new configurations by the simple process of "drawing on a whiteboard". Finally, we demonstrate that even complex, highly-interconnected systems with large numbers of populations can be understood with ease using the advanced features of our formalism