标题： 洛什讲座关于理论生态学：高维模型与极端事件 显示英文标题

标题： Les Houches lectures on Theoretical Ecology: High-dimensional models and extreme events

摘要： 生态系统的研究在现代科学研究中正日益受到重视，这得益于大量实证数据和生物工程技术的进步。然而，在持续的生物多样性危机背景下，全面理解其动态和热力学特性仍是一项艰巨的任务。从理论角度来看，对这些复杂系统内部相互作用进行建模——例如微生物群落中的细菌、森林中的植物-传粉者网络或椋鸟的群体飞行——提出了重大挑战。鉴于数据集的典型高维性，替代的优雅方法采用随机矩阵形式和无序系统的技术。在这些讲座中，我们将探讨理论生态学中的两个核心模型：MacArthur/资源-消费者模型和广义Lotka-Volterra模型，并特别关注由大量相互作用物种组成的系统。在第二部分中，我们将强调及时的研究方向，特别是弥合与实证观察之间的差距并检测宏观生态模式。 显示英文摘要

摘要： The study of ecological systems is gaining momentum in modern scientific research, driven by an abundance of empirical data and advancements in bioengineering techniques. However, a full understanding of their dynamical and thermodynamical properties, also in light of the ongoing biodiversity crisis, remains a formidable endeavor. From a theoretical standpoint, modeling the interactions within these complex systems -- such as bacteria in microbial communities, plant-pollinator networks in forests, or starling murmurations -- presents a significant challenge. Given the characteristic high dimensionality of the datasets, alternative elegant approaches employ random matrix formalism and techniques from disordered systems. In these lectures, we will explore two cornerstone models in theoretical ecology: the MacArthur/Resource-Consumer model, and the Generalized Lotka-Volterra model, with a special focus on systems composed of a large number of interacting species. In the second part, we will highlight timely directions, particularly to bridge the gap with empirical observations and detect macroecological patterns.