Interactions between ageing error and selectivity in statistical catch-at-age models: simulations and implications for assessment of the Chilean Patagonian toothfish fishery

In age-structured fisheries stock assessments, ageing errors within age composition data can lead to biased mortality rate and year-class strength estimates. These errors may be further compounded where fishery-dependent age composition data are influenced by temporal changes in fishery selectivity and selectivity misspecification. In this study, we investigated how ageing error within age composition data interacts with time-varying fishery selectivity and selectivity misspecification to affect estimates derived from a statistical catch-at-age (SCA) model that used fishery-dependent data. We tested three key model parameters: average unfished recruitment (R-0), spawning stock depletion (D-final), and fishing mortality in the terminal year (F-terminal). The Patagonian toothfish (Dissostichus eleginoides) fishery in southern Chile was used as a case study. Age composition data used to assess this fishery were split into two sets based on scale (1989-2006) and otolith (2007-2012) readings, where the scale readings show clear age-truncation effects. We used a simulation-estimation approach to examine the bias and precision of parameter estimates under various combinations of ageing error, selectivity type (asymptotic or dome-shaped), selectivity misspecification, and variation in selectivity over time. Generally, ageing error led to overly optimistic perceptions of current fishery status relative to historical reference points. Ageing error generated imprecise and positively biased estimates of R-0 (range 10 to >200%), D-final (range - 20 to >100%), and F-terminal (range - 15 to. 150%). The bias in D-final and R-0 was more severe when selectivity was dome-shaped. Time-varying selectivity (both asymptotic and dome-shaped) increased the bias in D-final and F-terminal, but decreased the bias in R-0. The effect of ageing error was more severe, or was masked, with selectivity misspecification. Correcting the ageing error inside the SCA reduced bias and improved precision of estimated parameters.