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 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 popluation dynamics of local predator–prey communities, due to indirect effects that epibionts confer.

中文翻译：

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侵入性 EPIBITIONS 对螃蟹-贻贝群落的影响：理解贻贝种群下降的理论方法

蓝贻贝 (Mytilus edulis) 是缅因湾一直在减少的重要基石物种。这可能归因于多种复杂因素，例如由于外生生物入侵造成的间接影响，这在数学上仍未得到探索。基于经典的最佳觅食理论 (OFT) 和贻贝的防污防御机制，我们推导出了一个 ODE 模型，用于在存在侵入性外生生物 Didemnum vexillum 的情况下蟹-贻贝相互作用。动力学分析导致​​模型的稳定性、全局有界性和分岔的结果。接下来，通过最优控制方法，我们预测各种生态结果。我们的研究结果对在非本地外生生物入侵到来时保护贻贝种群具有重要意义。特别是，