发表机构
Universidad de Valparaíso; Brown University; Pontificia Universidad Católica de Chile; The Santa Fe Institute（瓦尔帕莱索大学; 布朗大学; 智利天主教 Pontificia 大学; 圣塔菲研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用开放系统动力学和随机分析，构建了刻画适应度变化与可预测性关系的理论框架，通过扩散过程分析生物量丰度，并利用正交多项式实现参数估计。
AI 中文摘要
理解生态进化动力学带来了重大的数学挑战，特别是在可预测性、均衡以及适应度的数学表示方面。利用开放系统动力学和随机分析，我们构建了一个理论框架来刻画适应度变化及其与可预测性的关系。我们探索了由随机过程建模的生物量丰度的极限行为，从离散时间模型推导出连续时间的扩散对应物。聚焦于中性性和对均衡的探索，我们在两个不同的状态空间中分析了扩散过程。对于d维单纯形上的相对丰度，我们证明了正交多项式在模型构建中的核心作用。对于d维空间正象限中的非比例丰度，我们详细介绍了两个特定的模型族。最后，我们通过呈现相对丰度的数值示例来处理统计推断，说明正交多项式如何促进最大似然参数估计。
英文摘要
Understanding eco-evolutionary dynamics presents significant mathematical challenges, particularly regarding predictability, equilibrium, and the mathematical representation of fitness. Using Open System Dynamics and Stochastic Analysis, we develop a theoretical framework to characterize fitness change and its relationship with predictability. We explore the limiting behavior of biomass abundances modeled by stochastic processes, deriving continuous-time diffusion counterparts from discrete-time models. Focusing on neutrality and the search for equilibrium, we analyze diffusions in two distinct state spaces. For relative abundances on a d-dimensional simplex, we demonstrate the central role of orthogonal polynomials in model construction. For non-proportional abundances in the positive orthant of d-dimensional space, we detail two specific families of models. Finally, we address statistical inference by presenting numerical examples for relative abundances, illustrating how orthogonal polynomials facilitate maximum likelihood parameter estimation.
Comments39 pages, 1 figure, 79 references. Submitted to the SIAM Journal on Applied Mathematics
