Morozov Andrew, Feudel Ulrike, Hastings Alan, Abbott Karen C, Cuddington Kim, Heggerud Christopher M, Petrovskii Sergei
School of Computing and Mathematical Sciences, University of Leicester, LE1 7RH, UK; Institute of Ecology and Evolution, Russian Academy of Sciences, Moscow, Russia.
Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky University Oldenburg, Oldenburg, Germany.
Phys Life Rev. 2024 Dec;51:423-441. doi: 10.1016/j.plrev.2024.11.004. Epub 2024 Nov 13.
Traditionally, mathematical models in ecology placed an emphasis on asymptotic, long-term dynamics. However, a large number of recent studies highlighted the importance of transient dynamics in ecological and eco-evolutionary systems, in particular 'long transients' that can last for hundreds of generations or even longer. Many models as well as empirical studies indicated that a system can function for a long time in a certain state or regime (a 'metastable regime') but later exhibits an abrupt transition to another regime not preceded by any parameter change (or following the change that occurred long before the transition). This scenario where tipping occurs without any apparent source of a regime shift is also referred to as 'metastability'. Despite considerable evidence of the presence of long transients in real-world systems as well as models, until recently research into long-living transients in ecology has remained in its infancy, largely lacking systematisation. Within the past decade, however, substantial progress has been made in creating a unifying theory of long transients in deterministic as well as stochastic systems. This has considerably accelerated further studies on long transients, in particular on those characterised by more complicated patterns and/or underlying mechanisms. The main goal of this review is to provide an overview of recent research on long transients and related regime shifts in models of ecological dynamics. We pay special attention to the role of environmental stochasticity, the effect of multiple timescales (slow-fast systems), transient spatial patterns, and relation between transients and spatial synchronisation. We also discuss current challenges and open questions in understanding transients with applications to ecosystems dynamics.
传统上，生态学中的数学模型侧重于渐近的长期动态。然而，最近大量研究强调了瞬态动态在生态和生态进化系统中的重要性，特别是可持续数百代甚至更长时间的“长瞬态”。许多模型以及实证研究表明，一个系统可以在某个状态或 regime（“亚稳 regime”）下长时间运行，但随后会突然转变为另一个 regime，且在此之前没有任何参数变化（或者是在转变发生很久之前发生的变化之后）。这种在没有任何明显 regime 转变源的情况下发生翻转的情况也被称为“亚稳定性”。尽管有大量证据表明在现实世界系统以及模型中存在长瞬态，但直到最近，生态学中对长寿命瞬态的研究仍处于起步阶段，在很大程度上缺乏系统性。然而，在过去十年中，在为确定性和随机系统中的长瞬态创建统一理论方面取得了重大进展。这极大地加速了对长瞬态的进一步研究，特别是对那些具有更复杂模式和/或潜在机制的长瞬态的研究。本综述的主要目标是概述生态动力学模型中关于长瞬态及相关 regime 转变的近期研究。我们特别关注环境随机性的作用、多时间尺度（快慢系统）的影响、瞬态空间模式以及瞬态与空间同步之间的关系。我们还讨论了在理解瞬态并将其应用于生态系统动力学方面当前面临的挑战和未解决的问题。
