度量策略空间上Moran过程的标度极限：纯复制子与Fleming--Viot测度值PDE的欧拉推导
Scaling limits for Moran processes on metric strategy spaces: an Eulerian derivation of pure replicator and Fleming--Viot measure-valued PDEs
- Department of Mathematics and Applications “R. Caccioppoli”, University of Naples Federico II（那不勒斯费德里科二世大学应用数学系）
- Dipartimento di Scienze Matematiche “G. L. Lagrange”, Politecnico di Torino（都灵理工大学数学科学系）
- Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari（巴里理工大学机械、数学与管理系）
- Dipartimento di Scienze e Tecnologie Biologiche ed Ambientali Centro Ecotekne（莱切大学生物与环境科学与技术学院生态技术中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究度量策略空间上Moran过程的大种群极限，通过欧拉坐标和紧性论证，推导出纯复制子方程或扩散增强PDE，后者包含Fleming--Viot算子与Kimura方程。
AI中文摘要：
我们研究了离散时间Moran过程的大种群极限，该过程具有多种策略，这些策略取自一个可能无限的策略空间$\mathcal{V}$（一个度量空间），并在弱选择和强选择下进行。在欧拉密度表述中，极限动力学关键依赖于种群大小、突变率和选择强度的相对标度。根据这些标度，极限行为要么由纯确定性的复制子型连续性方程控制，要么由扩散增强的偏微分方程控制。在后一种情况下，扩散算子作为特例恢复了经典的Fleming--Viot算子和Kimura方程。在方法上，我们通过将离散过程在欧拉坐标中重新解释，构造满足近似PDE的插值曲线，并在$\mathcal{V}$上的概率测度空间上的合适拓扑中通过紧性论证建立收敛性，从而推导出极限。
英文摘要：
We study the large-population limit of a discrete-time Moran process featuring multiple strategies, drawn from a possibly infinite strategy space $\mathcal{V}$ (a metric space), under both weak and strong selection. In the Eulerian density formulation, the limiting dynamics depend critically on the relative scaling of population size, mutation rate, and selection intensity. Depending on these scalings, the limit behavior is governed either by a purely deterministic replicator-type continuity equation or by a diffusion-enhanced PDE. In the latter case, the diffusion operator recovers the classical Fleming--Viot operator and the Kimura equation as special instances. Methodologically, we derive the limit by reinterpreting the discrete process in Eulerian coordinates, constructing interpolating curves that satisfy an approximate PDE, and establishing convergence via a compactness argument in a suitable topology on the space of probability measures over probabilities over $\mathcal{V}$.
