A Multi-Species Bayesian State-Space Algorithm for Fisheries Stock Assessment with Non-Linear Heaviside Predation Constraints

Source abstract

Traditional deterministic fish stock assessment methods, such as the swept-area and Kushnarenko techniques, show extreme volatility and coordinate singularities under sparse data. This paper presents a multi-species stochastic Bayesian state-space algorithm that fuses heterogeneous catch data across species, years, and age cohorts into a structurally invariant NetCDF4 tensor built on a consensus prior from 18 deterministic methods, jointly models recruitment, mortality, and removal dynamics for several species through an age-structured cohort architecture, and embeds a discrete Heaviside threshold into the population-balance equations to represent age-dependent predation vulnerability. The model was fitted with the No-U-Turn Sampler in PyMC on a 10-year (2015–2024) dataset for four species in the Kapchagay Reservoir, Kazakhstan. The sampler achieved robust convergence for all species (R̂ ≤ 1.0047, ESS > 750), and comparison against alternative predation specifications supported the adopted formulation. A temporal hold-out test, however, showed that forecasting accuracy two to three years ahead remains substantially lower than the in-sample fit (mean absolute percentage error 59–91%), a gap not resolved by correcting an identified age-1 initialization artifact. The algorithm reliably reconciles divergent deterministic stock estimates, providing a state-estimation input for total allowable catch analysis, while multi-year forecasting accuracy remains an open limitation for future work.