Ecologists have long recognized that ecosystems can exist and function in one state within predictable bounds for extended periods of time and then abruptly shift to an alternate state (1⇓⇓⇓–5). Desertification of grasslands, shrub expansion in the Arctic, the eutrophication of lakes, ocean acidification, the formation of marine dead zones, and the degradation of coral reefs represent real and potential ecological regime shifts marked by a tipping point or threshold in one or more external drivers or controlling variables within the system that when breached causes a major change in the system’s structure, function, or dynamics (6⇓⇓–9). Large or incremental alterations in climate, land use, biodiversity (invasive species or the overexploitation of species), and biogeochemical cycles represent external and internal drivers that when pushed too far cross thresholds that can could lead to regime shifts (Fig. 1). Seeing the tipping point after the fact and ascribing mechanisms to the change is one thing; predicting them using empirical data has been a challenge. The difficulty in predicting tipping points stems from the large number of species and interactions (high dimensionality) within ecological systems, the stochastic nature of the systems and their drivers, and the uncertainty and importance of initial conditions that the nonlinear nature of the systems introduce to outcomes. In PNAS, Jiang et al. (10) confront these issues using a dimension-reduction framework that uses empirical data from 59 complex multidimensional plant–pollinator mutualistic networks, some of which contain scores of species and interactions, to develop simpler 2D models for studying and predicting tipping points.

中文翻译：

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预测复杂环境系统中的临界点

生态学家早已认识到，生态系统可以在可预测的范围内以一种状态存在并运行很长时间，然后突然转变为另一种状态（1-5）。草原的荒漠化，北极的灌木丛扩张，湖泊的富营养化，海洋酸化，海洋死区的形成以及珊瑚礁的退化代表了一个或多个外部的临界点或临界点所标志的真实和潜在的生态系统变化系统中的驱动程序或控制变量，一旦被破坏，将导致系统的结构，功能或动力学发生重大变化（6⇓⇓–9）。气候，土地利用，生物多样性（入侵物种或物种过度开发）的大规模或增量变化，生物和地球化学循环代表了外部和内部驱动力，当推力过大时会越过阈值，从而可能导致政权转移（图1）。在事实发生后看到临界点并确定变化的机制是一回事；使用经验数据来预测它们一直是一个挑战。预测临界点的困难源于生态系统中的大量物种和相互作用（高维），系统及其驱动程序的随机性质以及系统非线性性质引入的初始条件的不确定性和重要性。结果。在PNAS中，Jiang等人。（10）使用降维框架解决这些问题，该框架使用了来自59个复杂的多维植物-授粉媒介互惠网络的经验数据，