Stochastic partial differential equation model for environmental DNA dynamics in river environments
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.
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BibTeX
@misc{yoshioka2026stochastic,
title = {{Stochastic partial differential equation model for environmental DNA dynamics in river environments}},
author = {Hidekazu Yoshioka},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.03364},
eprint = {2608.03364},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.03364},
}
RIS
TY - UNPB
TI - Stochastic partial differential equation model for environmental DNA dynamics in river environments
AU - Hidekazu Yoshioka
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2608.03364
UR - https://arxiv.org/abs/2608.03364
AB - 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.
ER -