  Blue mussels (Mytilus edulis) are an important keystone species that have
been declining in the Gulf of Maine. This could be attributed to a variety of
complex factors such as indirect effects due to invasion by epibionts, which
remains unexplored mathematically. Based on classical optimal foraging theory
and anti-fouling defense mechanisms of mussels, we derive an ODE model for
crab-mussel interactions in the presence of an invasive epibiont, Didemnum
vexillum. The dynamical analysis leads to results on stability, global
boundedness and bifurcations of the model. Next, via optimal control methods we
predict various ecological outcomes. Our results have key implications for
preserving mussel populations in the advent of invasion by non-native
epibionts. In particular they help us understand the changing dynamics of local
predator-prey communities, due to indirect effects that epibionts confer.
