Integrating Hierarchical Bayesian Models and Hydrodynamic Simulations for eDNA Dynamics in Adaptive Ecosystem Management under Global Change

Environmental DNA (eDNA) methodologies—encompassing metabarcoding, metagenomics, metatranscriptomics, and digital PCR—herald a paradigm shift in non-invasive biodiversity surveillance amid escalating global stressors like climate change. This conceptual framework synthesizes advanced multi-dimensional mathematical modeling, Bayesian hierarchical inference, rigorous sensitivity analyses, and Python-driven hydrodynamic simulations to translate eDNA signals into falsifiable, actionable strategies for ecosystem resilience. We derive detailed equations for eDNA fate, transport, decay, and detection, incorporating power-law removal kinetics and inhibition effects, validated against empirical parameters (e.g., decay half-lives of 4--5 hours from riverine studies). Reproducible simulations leverage datasets from UNESCO marine expeditions and catchment-scale surveys, quantifying uncertainties via credible intervals and adhering to Popperian falsifiability criteria. Bolstered by quantitative statistics, Bayesian evidence ratios, and integrations with remote sensing, this self-contained framework addresses standardization gaps, stressor-induced microbial shifts, and policy translation, providing a blueprint for scalable conservation in aquatic, terrestrial, and polar realms facing existential threats.