Making sense of transient dynamics Ecological systems can switch between alternative dynamic states. For example, the species composition of the community can change or nutrient dynamics can shift, even if there is little or no change in underlying environmental conditions. Such switches can be abrupt or more gradual, and a growing number of studies examine the transient dynamics between one state and another—particularly in the context of anthropogenic global change. Hastings et al. review current knowledge of transient dynamics, showing that hitherto idiosyncratic and individual patterns can be classified into a coherent framework, with important general lessons and directions for future study. Science, this issue p. eaat6412 BACKGROUND Much of ecological theory and the understanding of ecological systems has been based on the idea that the observed states and dynamics of ecological systems can be represented by stable asymptotic behavior of models describing these systems. Beginning with early work by Lotka and Volterra through the seminal work of May in the 1970s, this view has dominated much of ecological thinking, although concepts such as the idea of tipping points in ecological systems have played an increasingly important role. In contrast to the implied long time scales of asymptotic behavior in mathematical models, both observations of ecological systems and questions related to the management of ecological systems are typically focused on relatively short time scales. A number of models and observations demonstrate possible transient behavior that may persist over very long time periods, followed by rapid changes in dynamics. In these examples, focusing solely on the long-term behavior of systems would be misleading. A long transient is a persistent dynamical regime—including near-constant dynamics, cyclic dynamics, or even apparently chaotic dynamics—that persists for more than a few and as many as tens of generations, but which is not the stable long-term dynamic that would eventually occur. These examples have demonstrated the potential importance of transients but have often appeared to be a set of idiosyncratic cases. What is needed is an organized approach that describes when a transient behavior is likely to appear, predicts what factors enhance long transients, and describes the characteristics of this transient behavior. A theory of long ecological transients is a counterpart to the related question of tipping points, where previous work based on an analysis of simple bifurcations has provided broad insights. ADVANCES Just as ideas based on the saddle-node bifurcation provide a basis for understanding tipping points, a suite of ideas from dynamical systems provides a way to organize a systematic study of transient dynamics in ecological systems. As illustrated in the figure, a relatively small number of ideas from dynamical systems are used to categorize the different ways that transients can arise. Translating these abstract results from dynamical systems into observations about both ecological models and ecological system dynamics, it is possible to understand when transients are likely to occur and the various properties of these transients, with implications for ecosystem management and basic ecological theory. Transients can provide an explanation for observed regime shifts that does not depend on underlying environmental changes. Systems that continually change rapidly between different long-lasting dynamics, such as insect outbreaks, may most usefully be viewed using the framework of long transients. An initial focus on conceptual systems, such as two-species systems, establishes the ubiquity of transients and an understanding of what ecological aspects can lead to transients, including the presence of multiple time scales and particular nonlinear interactions. The influences of stochasticity and more realistic higher-dimensional dynamics are shown to increase the likelihood, and possibly the temporal extent, of transient dynamics. OUTLOOK The development of such a framework for organizing the study of transients in ecological systems opens up a number of avenues for future research and application. The approach we describe also raises important questions for further development in dynamical systems. We have not, for example, emphasized nonautonomous systems, which may be required to understand the implications of a changing environment for transients. Systems with explicit time dependence as well as stochastic nonlinear systems still present great mathematical challenges. Implications for management and basic ecological understanding depend on both the results we describe and future developments. A recognition of the difficulty of prediction caused by long transients, and of the corresponding need to match dynamics to transient behaviors of models, shows that basing either management or interpretation of ecological observations only on long-term dynamics can be seriously flawed. Two ways that long transients arise in ecology, illustrated as a ball rolling downhill. (A) Slow transition away from a ghost attractor: a state that is not an equilibrium, but would be under slightly different conditions. (B) Lingering near a saddle: a state that is attracting from some directions but repelling from others. Additional factors such as stochasticity, multiple time scales, and high system dimension can extend transients. The importance of transient dynamics in ecological systems and in the models that describe them has become increasingly recognized. However, previous work has typically treated each instance of these dynamics separately. We review both empirical examples and model systems, and outline a classification of transient dynamics based on ideas and concepts from dynamical systems theory. This classification provides ways to understand the likelihood of transients for particular systems, and to guide investigations to determine the timing of sudden switches in dynamics and other characteristics of transients. Implications for both management and underlying ecological theories emerge.

中文翻译：

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生态学中的瞬态现象

理解瞬态动态 生态系统可以在不同的动态状态之间切换。例如，群落的物种组成可能会发生变化，或者营养动态可能会发生变化，即使基本环境条件几乎没有变化或没有变化。这种转变可以是突然的，也可以是渐进的，越来越多的研究检查了一种状态和另一种状态之间的瞬态动态——尤其是在人为全球变化的背景下。黑斯廷斯等人。回顾当前关于瞬态动力学的知识，表明迄今为止的特殊和个体模式可以分类为一个连贯的框架，具有重要的一般经验教训和未来研究的方向。科学，这个问题 p。eaat6412 背景 许多生态理论和对生态系统的理解都基于这样一种思想，即生态系统的观察状态和动态可以用描述这些系统的模型的稳定渐近行为来表示。从 Lotka 和 Volterra 的早期工作开始，到 1970 年代 May 的开创性工作，这一观点主导了大部分生态思想，尽管生态系统中的临界点等概念已经发挥了越来越重要的作用。与数学模型中隐含的渐近行为的长时间尺度相反，生态系统的观察和与生态系统管理相关的问题通常都集中在相对较短的时间尺度上。许多模型和观察结果表明，可能会持续很长时间的瞬态行为，然后是动力学的快速变化。在这些例子中，只关注系统的长期行为会产生误导。长期瞬态是一种持续的动态状态——包括接近恒定的动态、循环动态，甚至明显的混沌动态——它持续了不止几代甚至几十代，但这不是稳定的长期动态。最终会发生。这些例子证明了瞬态的潜在重要性，但往往看起来是一组特殊的情况。需要一种有组织的方法来描述可能出现瞬态行为的时间，预测哪些因素会增强长瞬态，并描述了这种瞬态行为的特征。长期生态瞬态理论与临界点相关问题相对应，之前基于简单分岔分析的工作提供了广泛的见解。进展 正如基于鞍节点分叉的思想为理解临界点提供了基础，来自动力系统的一套思想提供了一种方法来组织对生态系统中瞬态动力学的系统研究。如图所示，来自动力系统的相对较少的想法被用于对瞬变可能出现的不同方式进行分类。将这些动态系统的抽象结果转化为对生态模型和生态系统动态的观察，可以了解瞬变何时可能发生以及这些瞬变的各种特性，对生态系统管理和基本生态理论有影响。瞬态可以解释观察到的不依赖于潜在环境变化的状态变化。在不同的持久动态（例如昆虫爆发）之间不断快速变化的系统，可以使用长瞬态框架来查看最有用。对概念系统（如两个物种系统）的初步关注确立了瞬变的普遍性，并了解了哪些生态方面会导致瞬变，包括存在多个时间尺度和特定的非线性相互作用。随机性和更现实的高维动力学的影响被证明会增加瞬态动力学的可能性，并可能增加瞬态动力学的时间范围。展望 开发这样一个用于组织生态系统瞬变研究的框架为未来的研究和应用开辟了许多途径。我们描述的方法也为动力系统的进一步发展提出了重要的问题。例如，我们没有强调非自治系统，它可能需要了解瞬态变化环境的影响。具有显式时间相关性的系统以及随机非线性系统仍然存在巨大的数学挑战。对管理和基本生态理解的影响取决于我们描述的结果和未来的发展。认识到由长瞬态引起的预测困难，以及相应需要将动力学与模型的瞬态行为相匹配，表明仅基于长期动力学对生态观察的管理或解释可能存在严重缺陷。生态学中出现长瞬变的两种方式，用滚下坡的球来说明。(A) 远离鬼吸引子的缓慢转变：一种不是平衡的状态，但在稍微不同的条件下。(B) 在马鞍附近徘徊：从某些方向吸引但从其他方向排斥的状态。其他因素，如随机性、多时间尺度和高系统维度，可以扩展瞬态。瞬态动力学在生态系统和描述它们的模型中的重要性已得到越来越多的认可。然而，以前的工作通常单独处理这些动态的每个实例。我们回顾了经验示例和模型系统，并根据动力系统理论的思想和概念概述了瞬态动力学的分类。这种分类提供了了解特定系统瞬变可能性的方法，并指导调查以确定动态和瞬变的其他特征中突然切换的时间。对管理和潜在生态理论的影响出现了。这种分类提供了了解特定系统瞬变可能性的方法，并指导调查以确定动态和瞬变的其他特征中突然切换的时间。对管理和潜在生态理论的影响出现了。这种分类提供了了解特定系统瞬变可能性的方法，并指导调查以确定动态和瞬变的其他特征中突然切换的时间。对管理和潜在生态理论的影响出现了。