{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.03364",
  "author_total": 1,
  "authors": [
    {
      "name": "Hidekazu Yoshioka"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3kq9bvnf5w47b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.03364",
  "fulltext_url": null,
  "id": "3kq9bvnf5w47b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.03364",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "q-bio.QM"
    ],
    [
      "openalex",
      "2303|Environmental DNA in Biodiversity Studies"
    ]
  ],
  "openalex": "W7172507424",
  "pdf_url": "https://arxiv.org/pdf/2608.03364",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3kq9bvnf5w47b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2608.03364",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.03364"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.QM",
      "subfield": "bioinformatics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Stochastic partial differential equation model for environmental DNA dynamics in river environments",
  "title_text": "Stochastic partial differential equation model for environmental DNA dynamics in river environments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:36Z",
  "url": "https://research.draconitic.com/paper/3kq9bvnf5w47b",
  "venue": "arXiv",
  "versions": []
}