On the dangers of including demographic analysis in Bayesian surplus production models: A case study for Indian Ocean blue shark

Also available as an information paper IOTC-2021-WPEB17(DP)-INF02.

The Schaefer and Pella-Tomlinson production models (LPM and PTPM) can be used to provide management advice in data poor situations, as they require only a time-series of catches and an index of abundance. These models are commonly fit using Bayesian methods, with the prior for the intrinsic rate of growth (r) set based on the results of a demographic analysis. We used simulations based on blue shark Prionace glauca in the Indian Ocean to evaluate the performances of estimation methods that reflect different assumptions regarding the form of the production function and the basis for the prior for r. Nine age-structured operating models reflected different levels of productivity (determined by the steepness of stock-recruitment relationship [h = 0.4; h = 0.6; h = 0.79] and the pattern of historical catches (increasing, stable and declining). As expected, estimation performance was poorer for greater extents of observation error, and better when there was more ‘contrast’ in biomass. However, the PTPM usually performed worse than the LPM, particularly for high levels of observation error. Surprisingly, the prior for r with mean set to of the estimate of the r inferred from the demographic analysis combined with the LPM performed best for an increasing catch series (a one-way trip in biomass) and high uncertainty in the abundance index. Additional analyses revealed that the poor performance of the PTPM was due to the additional estimation variance associated with the estimation of the shape parameter, while the better performance for the ‘wrong prior’ occurred because the Schaefer model assumes a linear relationship between growth rate and population depletion whereas an age-structured model implies a non-linear relationship. Given poor data, r is not updated much, leading the LPM to overestimate productivity. This paper highlights the dangers of naively integrating demographic analysis into Bayesian surplus production models, and the value of including simulation analysis as a part of the standard set of diagnostics used when selecting an estimation method on which to base stock assessments. We also recommend use of JABBA-Select or a prior for r from a demographic analysis that accounts for the status of the population when the data on which the demographic parameters are based as well as the form of the production function.