The effects of invasive epibionts on crab-mussel communities: a theoretical approach to understand mussel population decline. (English) Zbl 1445.92246
Summary: Blue mussels (Mytilus edulis) are 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 (OFT) and anti-fouling defense mechanisms of mussels, we derive an ODE model for crab-mussel interactions in the presence of an invasive epibiont, Didemnum vellum. 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 population dynamics of local predator-prey communities, due to indirect effects that epibionts confer.
MSC:
| 92D25 | Population dynamics (general) |
| 92D40 | Ecology |
| 34C11 | Growth and boundedness of solutions to ordinary differential equations |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 49J15 | Existence theories for optimal control problems involving ordinary differential equations |
Keywords:
predator-prey system; stability and bifurcation; optimal control; biological invasion; epibiontReferences:
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