Physics–Guided Advection–Diffusion–Reaction Model for the Environmental Dynamics of Bigeye Tuna in the Eastern Pacific

Bigeye tuna (Thunnus obesus) are ecologically important pelagic predators in the eastern Pacific and support valuable international fisheries. Their distribution responds sensitively to the El Niño–Southern Oscillation (ENSO) and to multiscale changes in upper‑ocean structure. However, existing statistical or machine‑learning models often fail to distinguish between environmental suitability and advective redistribution, while complex ecosystem models often face parameter identifiability challenges. To bridge this gap we develop a Physics‑Guided Advection‑Diffusion‑Reaction (PhyG‑ADR) model. The model represents the time‑varying biomass density C(x,y,t) by a partial differential equation where advection describes large‑scale movement, diffusion represents mixing and sub‑mesoscale dispersion, and the reaction term implements environment‑dependent growth and density limitation. A non‑linear habitat selection function combines sea‑surface temperature, mixed‑layer depth, dissolved oxygen, and ocean‑heat content to provide physiological realism. To constrain poorly known parameters, we used a Bayesian inference framework and estimated posterior parameter distributions from a 19-year record of monthly catch-per-unit-effort (CPUE) indices (1994–2012) using Markov chain Monte Carlo (MCMC). The posterior analysis suggests that habitat selection dominates the formation of spatial aggregation, while climate‑driven advection plays a key role in inter‑annual shifts associated with ENSO. Parameter uncertainty is explicitly quantified, and sensitivity experiments demonstrate that the inferred habitat-preference structure of bigeye tuna is robust across carrying‑capacity scenarios. PhyG‑ADR therefore combines predictive skill with mechanistic insight and can inform dynamic fisheries management and spatial conservation planning.