超越平衡的成核：双稳态生态系统中的入侵由前沿控制
Nucleation beyond Equilibrium: Fronts Control Invasion in Bistable Ecosystems
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中文总结 AI 辅助
本文针对具有非守恒矢量序参量的反应扩散系统建立了非平衡成核理论，将其应用于双稳态生态的 Lotka-Volterra 模型，揭示了强种间竞争使入侵难度指数级增加的机制。
中文摘要 AI 辅助
双稳态是指存在两个具有不同吸引域的替代稳定状态，在生态学以及许多其他生物、化学和物理系统中十分常见。在空间扩展系统中，一个状态对另一个状态的入侵通过成核过程进行，即涨落驱动的液滴生长至临界尺寸以上。经典成核理论（CNT）利用能量景观量化这一过程，但该描述依赖于详细平衡——平衡状态下成立的微观可逆性条件。生态动力学通常违反详细平衡，且其描述对象并非单个标量场，而是多个耦合的非守恒丰度，即矢量序参量，目前尚无通用的成核理论。本文针对具有非守恒矢量序参量的反应扩散系统推导了此类理论，该理论在双结点附近（入侵通过传播前沿进行）和旋节线附近（亚稳态失去稳定性）均有效。对拟势的大量数值计算证实了该理论在两种 regime 下的有效性。研究表明，一旦将能量量替换为前沿的动力学性质，经典成核理论的数学结构在非平衡条件下依然成立：前沿速度扮演两相之间体自由能差的角色，扩散率则扮演表面张力的角色。将该理论应用于双稳态生态拮抗的原型系统——两物种 Lotka-Volterra 模型，结果显示，强种间竞争会在前沿内产生明显的耗尽区，其中总丰度远低于环境容纳量。这种矢量结构仅靠基于物种频率的标量描述无法察觉，它使得在固定竞争优势下，随着竞争增强，入侵难度呈指数级增加——这一预测可在微生物系统中进行检验。
英文摘要
Bistability, the existence of two alternative stable states with distinct basins of attraction, is common across ecology and many other biological, chemical, and physical systems. In spatially extended systems, the invasion of one state by the other proceeds through nucleation, the fluctuation-driven growth of a droplet beyond a critical size. Classical Nucleation Theory (CNT) quantifies this process using the energy landscape, but this description relies on detailed balance, the condition of microscopic reversibility that holds at equilibrium. Ecological dynamics generally violate detailed balance and are described not by a single scalar field but by several coupled, non-conserved abundances--a vector order parameter--for which no general nucleation theory exists. Here we derive such a theory for reaction-diffusion systems with a non-conserved vector order parameter, valid both close to the binodal, where invasion proceeds through propagating fronts, and close to the spinodal, where the metastable state loses stability. Extensive numerical computations of the quasipotential confirm the theory in both regimes. We show that the mathematical structure of CNT survives out of equilibrium, once energetic quantities are replaced by dynamical properties of fronts: the front speed plays the role of the bulk free-energy difference between phases, and the diffusivity that of the surface tension. Applied to the two-species Lotka-Volterra model, an archetypal system of bistable ecological antagonism, our theory shows that strong interspecific competition generates a pronounced depletion region within fronts, where the total abundance falls well below carrying capacity. This vectorial structure, invisible to a scalar description based on species frequency alone, makes invasion exponentially harder as competition strengthens at fixed competitive advantage--a prediction testable in microbial systems.
