Ecological regime shifts from clear to turbid water states in shallow temperate lakes are quite well-investigated phenomena but critical time lags from human interaction with the lake and restoration activities are much less understood. This is a complex challenge for institutions who manage lakes but are usually less familiar with non-linear dynamics, slow and fast influences on water quality and how to manage those from a social-ecological perspective. We extend a well-known minimal model of shallow lake regime shifts to enable simulations over time with short- and long-term management measures (nutrient reduction, trawling, planting of aquatic vegetation). While we explore the mathematical conditions for ecological bistability, we also identify the necessary and sufficient extent of measures to restore the clear water state. Restoration scenarios evaluated by trajectories in the state space demonstrate the increased effectiveness from combined measures even when considering countereffective activities such as pike fishing. But, single measures alone may delay or even miss the overall restoration target. Our analysis demonstrates the importance of understanding transient dynamics where stable state analyses alone remain elusive about alternative ways to interact with bistability. We conclude that successful management of bistable systems, and particularly shallow temperate lakes, needs careful balancing between short-term improvements and long-term influence on the systems state.

中文翻译：

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湖泊恢复的短期决策会对水质产生长期影响

在浅温带湖泊中，生态系统从清水状态转变为浑水状态的现象已得到充分研究，但人类与湖泊相互作用和恢复活动的关键时间滞后却鲜为人知。对于管理湖泊但通常不熟悉非线性动力学，对水质的缓慢和快速影响以及如何从社会生态学角度进行管理的机构而言，这是一个复杂的挑战。我们扩展了一个众所周知的浅水湖政权转移的最小模型，以通过短期和长期的管理措施（养分减少，拖网，水生植物种植）进行模拟。在探索生态学双稳态的数学条件的同时，我们还确定了必要和充分程度的措施来恢复清水状态。通过状态空间中的轨迹评估的恢复方案表明，即使考虑使用派克钓鱼等反作用活动，联合措施也能提高有效性。但是，单独采取一项措施可能会延迟甚至错过总体恢复目标。我们的分析表明了理解瞬态动力学的重要性，其中仅靠稳态分析仍无法了解与双稳态交互的其他方法。我们得出的结论是，成功地管理双稳态系统，尤其是浅温带湖泊，需要在短期改善和对系统状态的长期影响之间进行谨慎的平衡。单靠一项措施可能会延迟甚至错过总体恢复目标。我们的分析表明了理解瞬态动力学的重要性，其中仅靠稳态分析仍无法了解与双稳态交互的其他方法。我们得出的结论是，成功地管理双稳态系统，尤其是浅温带湖泊，需要在短期改善和对系统状态的长期影响之间进行谨慎的平衡。单靠一项措施可能会延迟甚至错过总体恢复目标。我们的分析表明了理解瞬态动力学的重要性，其中仅靠稳态分析仍无法了解与双稳态交互的其他方法。我们得出的结论是，成功地管理双稳态系统，尤其是浅温带湖泊，需要在短期改善和对系统状态的长期影响之间进行谨慎的平衡。