Stochastic partial differential equation model for environmental DNA dynamics in river environments
Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Yoshioka, Hidekazu
Institution: Japan Advanced Institute of Science and Technology
Language: English
Subfield: Ecology
Field: Environmental Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7172507424