AI 中文总结
针对河流eDNA建模的不确定性，提出含延迟源输入的随机偏微分方程模型，推导其理论性质与非负离散格式，结合中游河段数据验证并做敏感性分析，为洄游鱼类eDNA动态提供首个数学计算框架。
AI 中文摘要
环境DNA（eDNA）已成为量化水体中水生物种季节性丰度的新型工具，但其数学建模因机制不确定性仍处于萌芽阶段。我们针对洄游鱼类的eDNA动态提出了首个数学与计算框架，该框架基于含延迟源输入的新型随机偏微分方程模型，模型描述河流中eDNA浓度的时空变化，其源项来自鱼类洄游动力学的随机微分方程。模型的仿射特性便于理论分析，包括适定性的保证，且尽管乘性噪声项的比例系数非利普希茨，仍可推导拉普拉斯泛函的闭式解。我们还提出了该模型的离散化格式，其理论上可生成非负数值解。最后，将该模型应用于某河系中游河段采样得到的eDNA浓度数据，并开展了敏感性分析。
英文摘要
Environmental DNA (eDNA) has emerged as a novel tool for quantifying the seasonal abundance of aquatic species in water bodies; however, its mathematical modeling is still at a germinating stage because of its mechanistic uncertainties. We propose a first-step mathematical and computational framework for the eDNA dynamics of migratory fish based on a novel stochastic partial differential equation model with a delayed source input. The model governs spatiotemporal eDNA concentration in rivers where the source comes from a stochastic differential equation for the migration dynamics of the fish. The affine nature of the model facilitates its theoretical analysis, including the guarantee of well-posedness and the closed-form derivation of the Laplace functional despite the proportionality coefficient of the multiplicative noise term being non-Lipschitz. We also propose a discretization scheme for the model that theoretically generates nonnegative numerical solutions. We finally apply the proposed model to eDNA concentration data sampled from midstream reaches of a river system and perform sensitivity analysis.
CommentsProof of Lemma A1 was revised on August 9, 2026
