Evaluating the prevalence of early warning signals in palaeoecological time series of state change

在一系列系统中，状态间的突变已成为一种普遍现象。微小的变化可能会推动一个系统越过一个临界点，从而产生一种新的行为模式。改变状态的倾向与面对扰动时对变化的抵抗力和恢复力有关。考虑到对气候变化的预测，更好地了解抵抗力、复原力和生态系统变化之间的关系尤为重要。关键转变可以影响生态系统的管理；生态系统的功能或服务可能在状态变化后从根本上改变甚至丧失，而逆转可能代价高昂。**通过理论数学模型推导出即将发生跃迁的预警信号（ews），包括状态变量的自相关和方差增加、波动的不对称性增加或闪烁。在阈值变化之前识别这些系统响应将使我们能够更好地检测未来变化的EWSs。然而，由于普遍缺乏过渡前的长期观测数据，我们确认自然系统中ews普遍存在的能力受到了阻碍。**湖泊沉积物岩心提供了关于过去生态系统状态的丰富信息，但在充分发挥其潜力之前，需要解决数据性质的一些问题。该计划的主要重点是通过利用湖泊沉积物来了解生态状态的变化。特别是，我将确定解决使用沉积物时间序列困难所需的统计技术，包括不规则采样间隔和沉积物压实。工作将在三个方面取得进展，通过使用经过充分研究的湖泊的理想时间序列和每年的层压化石记录（Baldeggersee，瑞士；Kassjon，瑞典），阿拉斯加、格陵兰和俄罗斯北极湖泊的新的高分辨率序列，以及加拿大北部大平原草原湖泊的新核心。**不同湖泊类型为研究生态系统状态变化提供了新的工具。每年层压序列是一个理想的系统工作，因为他们规避了不规则采样和压实的问题。草原湖泊受到气候变化的强烈影响，气候变化对水分可用性的变化反应迅速。北极湖泊集水区的植被被认为对气候变暖有类似阈值的反应，但北极湖泊的生物地球化学和生态如何对这种变化作出反应在很大程度上是未知的。在每种情况下，我将使用一系列生物和地球化学数据，通过针对快速变化时期的分析，检查阈值响应和ews的证据。**以前，我开发了带有残差时间序列过程的加性模型来模拟古生态数据。这些模型假设变化是平滑的，这就排除了对阈值行为的检查。使用自适应样条提供了一个潜在的解决方案，我也设想通过使用结构时间序列模型来取得进展。由于大多数生物数据都是高维的，因此也需要适合这些数据的方法。我将开发冗余分析与时间变化的多尺度测量相结合，以提取能够检测快速变化和变化模式转移的正交模式。**本项目将促进长期生态和古湖泊数据的定量建模。我将把这些方法应用到ct和ews的理论中。接下来，我希望从古生态学的角度研究宏观生态模式，并从时间上解决随机与生态位划分在生态群落结构中的相对重要性。

Abrupt transition between states has emerged as a common phenomenon in a range of systems. Small changes may push a system past a tipping point resulting in a new mode of behaviour. The propensity to change state is related to resistance to change and resilience in the face of perturbation. A better understanding of the relationships between resistance, resilience and ecosystem change is particularly important considering projections for climate change. Critical transitions can affect the management of ecosystems; ecosystem function or services may be fundamentally altered or even lost following state change and reversal may be prohibitively costly.**Early warning signals (EWSs) of impending transition have been derived through theoretical mathematical models, and include increased autocorrelation and variance of the state variable, increased asymmetry of fluctuations, or flickering. Identifying these system responses prior to threshold changes will allow us to better detect EWSs of future change. Our ability to confirm the ubiquity of EWSs in natural systems is hampered, however, by a general lack of long-term observational data prior to transition.**Lake sediment cores provide a wealth of information on past ecosystem states yet a number of issues with the nature of the data need to be addressed before their potential is fully realized. The main focus of the proposed program is to develop an understanding of ecological state change through the use of lake sediments. In particular I will identify the statistical techniques needed to address difficulties in using sediment time series, which include irregular sampling intervals and compaction of sediments. Work will progress on three fronts through the use of ideal time series from well-studied lakes with annually-laminated fossil records (Baldeggersee, Switzerland; Kassjon, Sweden), new, high-resolution sequences from arctic lakes in Alaska, Greenland, and Russia, and new cores from prairie lakes of the northern Great Plains, Canada.**Different lake types provide a novel apparatus with which to study ecosystem state change. Annually-laminated sequences are an ideal system to work on as they circumvent issues of irregular sampling and compaction. Prairie lakes are strongly impacted by climate variability having been shown to respond rapidly to changes in moisture availability. Vegetation in arctic lake catchments is thought to respond to climate warming with threshold-like behaviour yet how the biogeochemistry and ecology of arctic lakes react to this change is largely unknown. In each case I will examine the evidence for threshold responses and EWSs with analyses targeted at periods of rapid change using a range of biological and geochemical data.**Previously, I developed additive models with residual time series processes for modelling palaeoecological data. These models assume that changes are smooth, which precludes examination of threshold behaviour. The use of adaptive splines offers one potential solution and I also envisage progress via the use of structural time series models. As most biological data are high-dimensional, methods suited to such data are also required. I will develop the combination of redundancy analysis with multi-scale measures of temporal variation to extract orthogonal patterns capable of detecting both rapid change and shifts in modes of variability.**The proposed program will advance the quantitative modelling of long-term ecological and palaeolimnological data. I will apply these approaches to theories of CTs and EWSs. Subsequently, I expect to address the relative importance of stochasticity versus niche partitioning in structuring ecological communities in time and study macroecological patterns from a palaeoecological perspective.