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

状态之间的突然转换已经成为一种常见的现象，在一系列的系统。小的变化可能会推动系统通过一个临界点，导致一种新的行为模式。改变状态的倾向与对变化的抵抗力和面对扰动的弹性有关。考虑到气候变化的预测，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。关键的过渡可能会影响生态系统的管理;生态系统的功能或服务可能会在状态改变后发生根本性的改变，甚至丧失，而逆转可能代价高昂。 预警信号（EWS）的即将发生的过渡已经通过理论数学模型，并包括增加的自相关性和方差的状态变量，增加不对称的波动，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EWS。然而，我们确认EWS在自然系统中普遍存在的能力受到了阻碍，因为在过渡之前普遍缺乏长期观测数据。 湖泊沉积物岩心提供了丰富的信息，过去的生态系统状态，但一些问题的性质的数据需要得到解决之前，他们的潜力得到充分实现。该计划的主要重点是通过使用湖泊沉积物来了解生态状态的变化。特别是我将确定所需的统计技术，以解决困难，在使用沉积物的时间序列，其中包括不规则的采样间隔和压实的沉积物。工作将在三个方面取得进展，通过使用理想的时间序列，从经过充分研究的湖泊与年度层压化石记录（Baldeggersee，瑞士; Kassjon，瑞典），新的，高分辨率的序列，从北极湖泊在阿拉斯加，格陵兰岛和俄罗斯，和新的核心，从草原湖泊的北方大平原，加拿大。 不同的湖泊类型为研究生态系统状态变化提供了新的工具。年度分层序列是一个理想的系统，因为它们避免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，已被证明对水分供应的变化迅速作出反应。北极湖泊集水区的植被被认为对气候变暖有阈值反应，但北极湖泊的地球化学和生态学如何对这种变化作出反应在很大程度上是未知的。在每一种情况下，我将检查阈值响应和EWS的证据与分析针对快速变化的时期，使用一系列的生物和地球化学数据。 在此之前，我开发了添加剂模型与剩余的时间序列过程模拟古生态数据。这些模型假设变化是平稳的，这就排除了对阈值行为的检查。自适应样条的使用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的进展。由于大多数生物数据是高维的，因此也需要适合于此类数据的方法。我将开发的冗余分析与时间变化的多尺度措施相结合，以提取正交模式能够检测快速变化和变化模式的转变。 拟议的方案将推进长期生态和古湖沼学数据的定量建模。我将把这些方法应用于CT和EWS的理论。随后，我希望解决的相对重要性，随机性与生态位划分在构建生态群落的时间和研究宏观生态格局从古生态的角度来看。

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.