A Bayesian State-Space Framework for Reconciling Heterogeneous, Sparse Fishery Data in Age-Structured Stock Assessment: An Exploratory Case Study for the Kapchagay Reservoir

Traditional deterministic fish stock assessment methods, such as the swept-area and Kushnarenko techniques, show extreme volatility and numerical 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 fixed-shape NetCDF4 tensor built on a consensus reference field constructed from 8 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. Kapchagay was selected as a representative single-reservoir case study given the material's scope; the broader four-reservoir programme (Zhaysan, Kapchagay, Balkhash, and Lake Samarkand) involves substantially more material and is addressed in separate work. The sampler achieved robust convergence for all species (R̂ ≤ 1.0047, ESS > 750), and comparison against alternative predation specifications evaluated by leave-one-out cross-validation (LOO-CV) showed that the choice of functional form had little effect on estimated stock (within approximately 1% for two of the three alternatives) but materially affected sampler efficiency, favoring the adopted threshold formulation on computational rather than biological grounds. A temporal hold-out test 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 and treated here as a central, unresolved limitation. The algorithm reconciles divergent deterministic stock estimates into a single state-estimation output that may inform, but does not by itself validate, total allowable catch analysis; both the biological necessity of the predation mechanism and multi-year forecasting accuracy remain open limitations for future work.