Dynamic models for fish stock productivity: state-space hidden Markov models and mixture models

Abstract

Hidden Markov models (HMMs) and state-space models (SSMs) are complementary methodologies for capturing discrete (regime-like) and continuous variations, respectively, in the sense that HMMs typically use separate parameter sets for each regime, whereas SSM parameters evolve continuously and are often correlated over time. In this work, we combine the strengths of both approaches by developing HMMs with serial correlation and implementing them efficiently. Resolving recruitment productivity changes is crucial to effective fisheries management as shifts in the stock-recruitment (SR) relationship redefines levels of sustainable removals. To account for interactions between SR parameters and other components of stock assessment models, we embed hidden Markov SR models within the broader stock assessment framework. Additionally, we incorporate covariates into the transition probabilities of the HMM to address nonstationarity and substantially reduce model complexity. Simulation and case studies demonstrate the strong performance of this novel methodology. This study also investigates temporal changes in the maturation dynamics of American plaice using three modeling approaches: an SSM, an HMM, and an additive logistic mixture model (ALMM). Fisheries management is usually focused on maintaining the mature component of a stock at a level expected to maximize egg production and future stock productivity. The mature stock is typically measured using the spawning stock size, which depends on the proportion mature-at-age or length (i.e., maturity). Many stocks in the Newfoundland and Labrador region have experienced large changes in maturity over time. The SSM captures strong temporal dependence and gradual shifts in the age at 50% maturity. The HMM identifies eight discrete regimes representing abrupt changes in maturation parameters, while the ALMM, with five regimes, provides the best fit, capturing distinct maturation patterns across regimes. Collectively, these models reveal both continuous and regime-like changes in maturation, offering valuable insights into life-history variability and its implications for population dynamics.