发表机构
Institut Denis Poisson, CNRS, IDP UMR 7013, Université de Tours, Université d’Orléans; Institut de Recherche sur la Biologie de l’Insecte, UMR CNRS 7261, Université de Tours（迪厄尼·普瓦松研究所，法国国家科学研究中心，IDP联合研究单位7013，图尔大学，奥尔良大学; 昆虫生物学研究所，CNRS联合研究单位7261，图尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对生态进化模型多平衡态问题，提出以系统为中心的概率形式体系，量化状态出现与多重性，揭示跨系统汇总所隐藏的群落结构模式。
AI 中文摘要
生态与进化群落并不总是会稳定在一个单一的可预测的构型中。诸如Lotka-Volterra或复制子动力学等模型可能预测出多个可允许的状态。这些状态的多重性对于理解鲁棒性、替代性群落构型、共存以及生物多样性的变化至关重要。然而，标准做法通常是状态为中心的：它们要么关注典型平衡的性质，要么跨系统汇总状态，从而丢失了关于在单个系统中可能产生多少状态（包括不存在任何状态的情况）的信息。在此，我们引入了一个以系统为中心的概率形式体系，该体系能够捕捉这一隐藏的结构，并可应用于广泛的生态与进化动力学模型，其灵感来源于障碍模型和零膨胀模型。每个生态系统被视为在其可能的结果上生成一个分布。这使我们能够联合量化给定状态类型的出现、该类型在每个系统内的多重性，以及在这些状态中共存的物种数量。该形式体系具有通用性，可应用于不同系列的动力学模型。为了说明其适用范围，我们考虑了两个案例研究：具有随机和结构化参数的广义Lotka-Volterra动力学和复制子动力学。这一统一的视角揭示了在单独分析平衡或跨系统汇总平衡时不可见的模式。通过将模型的状态空间转化为可解释的概率量，我们的形式体系为研究群落结构的鲁棒性、在初始条件微小变化下替代性结果的可能性，以及低多样性与高多样性状态之间转变的潜力提供了一种新方法。
英文摘要
Ecological and evolutionary communities do not always settle into a single predictable configuration. Models such as Lotka-Volterra or replicator dynamics may predict several admissible states. The multiplicity of such states is central to understanding robustness, alternative community configurations, coexistence, and shifts in biodiversity. Yet, standard practices are often state-centered: they either focus on the properties of typical equilibria or pool states across systems, losing information about how many states can arise in a single system, including cases where no state exists. Here, we introduce a system-centered probabilistic formalism that captures this hidden structure and could be applied across a wide range of ecological and evolutionary dynamical models, drawing inspiration from hurdle and zero-inflated models. Each ecological system is viewed as generating a distribution over its possible outcomes. This allows us to jointly quantify the occurrence of a given state type, its multiplicity within each system, and the number of species co-existing within these states. The formalism is generic and can be applied to different families of dynamical models. To illustrate its scope, we consider two case studies: the generalized Lotka-Volterra and replicator dynamics with random and structured parameters. This unified perspective reveals patterns that remain invisible when equilibria are analyzed individually or pooled across systems. By turning the state space of a model into interpretable probabilistic quantities, our formalism offers a new way for studying the robustness of community structure, the likelihood of alternative outcomes under small changes in initial conditions, and the potential for shifts between states of low and high diversity.
