Abstract: Mussels are present in a vast array of ecosystems throughout the world. These ”ecosystem engineers” can have either an extremely beneficial or a devastatingly detrimental impact on their surroundings. Thus, mussels are influential not only in that they are food source, but also in that they can severely harm their environment. Understanding the underlying nature of mussel populations is vital both to mussel farmers and to those trying to destroy populations of parasitic mussels. Liu, Weerman, Herman, Olff and van de Koppel formulated a mathematical model which describes the way mussels and algae interact with sediment and each other. We seek to perform an in-depth analysis of this model to determine how beneficial mussel populations can best be sustained and how harmful mussel populations can best be controlled.