Embracing uncertainty in fisheries stock assessment and management : a comparison of statistical methods for quantifying uncertainty, improving population model parameterization and evaluation of robust harvest strategies

Quantifying and managing the uncertainty associated with the assessment of harvested fish stocks is a key component of the United Nations Food and Agriculture Organization (FAO) code of conduct for responsible fisheries. Failure to incorporate uncertainty into management advice increases the risk of suboptimal yields, lack of a sustainable industry and stock collapse. Despite the proliferation of methods that quantify uncertainty, in practice, it is not always clear which methods are most appropriate, or how to mitigate the risk of this uncertainty in management decisions. The main objectives of this thesis are to present an overview of current methods for quantifying statistical uncertainty in fish stock assessment models and compare alternative methods for managing uncertainty in the context of an important Australian groundfish fishery. This thesis considers technical improvements in the efficiency of Bayesian algorithms (Metropolis-Hastings and No-U-Turn sampler (NUTS)), through to the evaluation of the biological and economic implications of incorporating uncertainty into the control rules for fishery management. In the second chapter we explored frequentist and Bayesian uncertainty measurements in fish stocks that are near the limit reference point (depletion). Here we found that frequentist and Bayesian methods correspond well for simpler models in terms of structure (e.g. with simple functions such as logistic selectivity) and with lower dimensions (e.g. low number of parameters to estimate). However, a Bayesian approach may be better suited to more complex models (specifically in the selectivity functions: Dome-shaped and time-blocked selectivities) with higher dimensions (e.g. larger number of parameters to estimate) and Bayesian approaches can be more robust to poly-modal likelihood surfaces than frequentist methods. In addition, we found frequentist and Bayesian approaches provided slightly different estimates of parameters and quantities of management interest (i.e. spawning biomass, depletion and recruitment). The larger differences occurred in the more complex model (pink ling) and could be explained by a number of reasons (i) the incorporation of a prior for natural mortality (ii) some parameters are highly correlated, and (iii) some parameters did not converge to a stationary distribution under the Bayesian approach. Finally, we also found high levels of correlation among some parameters, including mean unfished recruitment and natural mortality across all species considered. We conclude that highly correlated parameters are likely to degrade the numerical efficiency of both approaches, and the corresponding decrease in the accuracy and precision of key management parameters could have an adverse effect on species that are at risk of over-exploitation. In the third chapter, we evaluate how issues relating to the reliability and efficiency of highly dependent parameters (e.g. unfished recruitment, the ascending and descending limbs of the dome-shaped selectivity curve, and the parameters of the growth model) can be mitigated by re-parameterizing these functions within the stock assessment model. We also considered how the choice of algorithm for sampling the joint posterior distribution (Metropolis-Hasting and NUTS methods) interacts with the parameterization. It was found that the mixing behaviour and efficiency of chains for Metropolis-Hasting and NUTS can be greatly improved by increasing the number of single re-parameterizations of the parameters in a stock assessment model. In addition, NUTS always achieves a larger final effective sample size than Metropolis-Hasting by more effectively sampling the whole space, However, this improved result comes at a cost in time for NUTS, compared to Metropolis-Hasting, by taking longer to achieve this larger effective sample size. We conclude that increasing the orthogonality of model parameterization should improve the efficiency of stochastic Bayesian stock assessments when there are highly correlated parameters. In the fourth chapter, we quantified the level of management risk associated with frequency of assessment, by comparing single or multi-year total allowable catches (TACs) using management strategy evaluation. Single year TACs occur when an assessment of stock status is conducted every year and the harvest control rule (HCR) is used to set a TAC based on each new assessment. Multi-year TACs (MYTACs) occur when an assessment is not conducted annually, and in intermediate years, fixed TACs are set based on the results from the last assessment. We present an evaluation of the biological and economic implications of setting annual TACs compared with setting MYTACs that are held fixed for two or more years for three species with different life histories and current stock status. We found that short-lived species with high variability in recruitment are most at risk of collapse when setting MYTACs in comparison with annually set TACs. Although the difference in risk associated with the TAC setting frequency is relatively small for some relatively long-lived species (tiger flathead) the simulations probably understate the true risk that would be observed if other sources of variability (e.g. recruitment failure) and process and model uncertainty are considered. We conclude that single-year TACs are a higher priority for short-lived stocks, while MYTACs can be applied to longer-lived stocks with lower risk to the stock or economic losses to industry. In the last chapter we investigated options for managing uncertainty in key fisheries parameters by adopting more sophisticated harvest control rules for a specific fishery case study (school whiting). We propose two HCRs that determine future catch by integrating across an ensemble of assessment models with different fixed values of key productivity parameters (natural mortality and steepness of the stock recruitment relationship) that are often poorly estimated in stock assessment. The first proposed HCR approach makes the TAC recommendation on the basis of the likelihood-weighted mean (LW) of TACs from the model ensemble. The second approach uses an adaptative percentile (AP) from the distribution of TACs in the ensemble (a more precautionary percentile is adopted if the stock is highly depleted). We found that the LW harvest strategy maintains the biomass near the target level more effectively than the conventional approach (i.e. applying the HCR to a single preferred assessment model) and the AP approach, thus reducing the risk of breaching biomass limit reference points. The AP harvest strategy performance is very similar to the conventional approach, but allows the user greater control over the degree of precaution applied as biomass approaches the limit reference point. Management strategy evaluation demonstrated that both the likelihood-weighted and adaptive percentile methods approach the management target more consistently and significantly reduce the risk of falling below the limit reference point, compared to the conventional approach used to set the recommended biological catch for this species. For the species explored here, the LW approach consistently outperforms the AP approach for these two-management metrics, and both new approaches outperform the conventional HCR. These new approaches provide a convenient way of incorporating uncertainty from poorly estimated parameters within the design of HCR based on real fisheries data and fisheries management requirements. However, further case-specific investigation is warranted to consider the appropriate level of precaution that is desired for each fishery, as the risk reduction in these examples is associated with a decrease in catch. This thesis provides improvements to the treatment of uncertainty in fisheries models and the estimation of abundance trends. This has the potential to provide better inference and thus better management outcomes both for industry and for the harvested stocks