Lakes are dynamic ecosystems that can transition among stable states. Since ecosystem-scale transitions can be detrimental and difficult to reverse, being able to predict impending critical transitions in state variables has become a major area of research. However, not all transitions are detrimental, and there is considerable interest in better evaluating the success of management interventions to support adaptive management strategies. Here, we retrospectively evaluated the agreement between time series statistics (i.e., standard deviation, autocorrelation, skewness, and kurtosis-also known as early warning indicators) and breakpoints in state variables in a lake (Lake Simcoe, Ontario, Canada) that has improved from a state of eutrophication. Long-term (1980 to 2019) monitoring data collected fortnightly throughout the ice-free season were used to evaluate historical changes in 15 state variables (e.g., dissolved organic carbon, phosphorus, chlorophyll a) and multivariate-derived time series at three monitoring stations (shallow, middepth, deep) in Lake Simcoe. Time series results from the two deep-water stations indicate that over this period Lake Simcoe transitioned from an algal-dominated state toward a state with increased water clarity (i.e., Secchi disk depth) and silica and lower nutrient and chlorophyll a concentrations, which coincided with both substantial management intervention and the establishment of invasive species (e.g., Dreissenid mussels). Consistent with improvement, Secchi depth at the deep-water stations demonstrated expected trends in statistical indicators prior to identified breakpoints, whereas total phosphorus and chlorophyll a revealed more nuanced patterns. Overall, state variables were largely found to yield inconsistent trends in statistical indicators, so many breakpoints were likely not reflective of traditional bifurcation critical transitions. Nevertheless, statistical indicators of state variable time series may be a valuable tool for the adaptive management and long-term monitoring of lake ecosystems, but we call for more research within the domain of early warning indicators to establish a better understanding of state variable behavior prior to lake changes.

中文翻译：

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应用预警指标来预测发生多重变化的湖泊中的关键转变。

湖泊是动态的生态系统，可以在稳定状态之间转换。由于生态系统规模的转变可能是有害的且难以逆转，因此能够预测状态变量中即将发生的关键转变已成为一个主要的研究领域。然而，并不是所有的转变都是有害的，人们对更好地评估管理干预的成功与否以支持适应性管理策略非常感兴趣。在这里，我们回顾性地评估了时间序列统计数据（即标准差、自相关、偏度和峰态 - 也称为早期预警指标）与湖（加拿大安大略省锡姆科湖）状态变量断点之间的一致性，该湖已有所改善从富营养化状态。在整个无冰季节每两周收集一次长期（1980 年至 2019 年）监测数据，用于评估三个监测站 15 个状态变量（例如，溶解有机碳、磷、叶绿素 a）和多变量衍生时间序列的历史变化（浅、中、深）在锡姆科湖。两个深水站的时间序列结果表明，在此期间，Simcoe 湖从藻类为主的状态转变为水透明度增加（即 Secchi 盘深度）和二氧化硅以及较低的养分和叶绿素 a 浓度的状态，这与大量的管理干预和入侵物种的建立（例如，德莱森贻贝）。与改进一致，深水站的 Secchi 深度显示了确定断点之前统计指标的预期趋势，而总磷和叶绿素 a 显示出更微妙的模式。总体而言，状态变量在很大程度上被发现会在统计指标中产生不一致的趋势，因此许多断点可能无法反映传统的分叉关键转变。尽管如此，状态变量时间序列的统计指标可能是湖泊生态系统适应性管理和长期监测的宝贵工具，但我们呼吁在预警指标领域进行更多研究，以更好地了解状态变量行为之前到湖泊的变化。状态变量在很大程度上被发现会在统计指标中产生不一致的趋势，因此许多断点可能无法反映传统的分叉关键转变。尽管如此，状态变量时间序列的统计指标可能是湖泊生态系统适应性管理和长期监测的宝贵工具，但我们呼吁在预警指标领域进行更多研究，以更好地了解状态变量行为之前到湖泊的变化。状态变量在很大程度上被发现会在统计指标中产生不一致的趋势，因此许多断点可能无法反映传统的分叉关键转变。尽管如此，状态变量时间序列的统计指标可能是湖泊生态系统适应性管理和长期监测的宝贵工具，但我们呼吁在预警指标领域进行更多研究，以更好地了解状态变量行为之前到湖泊的变化。