Modelling Complexity and Uncertainty in Fisheries Stock Assessment

Stock assessment models are used to determine the population size of fish stocks. Although stock assessment models are complex, they still make simplifying assumptions. Generally, they treat each species separately, include little, if any, spatial structure, and may not adequately quantify uncertainty. These assumptions can introduce bias and can lead to incorrect inferences. This thesis is about more realistic models and their inference. This realism may be incorporated by explicitly modelling complex processes, or by admitting our uncertainty and modelling it correctly.  We develop an agent-based model that can describe fish populations as a collection of individuals which differ in their growth, maturation, migration, and mortality. The aim of this model is to better capture the richness in natural processes that determine fish abundance and subsequent population response to anthropogenic removals. However, this detail comes at considerable computational cost. A single model run can take many hours, making inference using standard methods impractical. We apply this model to New Zealand snapper (Pagurus auratus) in northern New Zealand.  Next, we developed an age-structured state-space model. We suggest that this sophisticated model has the potential to better represent uncertainty in stock assessment. However, it pushes the boundaries of the current practical limits of computing and we admit that its practical application remains limited until the MCMC mixing issues that we encountered can be resolved.   The processes that underpin agent-based models are complex and we may need to seek new sources of data to inform these types of models. To make a start here we derive a state-space model to estimate the path taken by individual fish from the day they are tagged to the day of their recapture. The model uses environmental information collected using pop-up satellite archival tags. We use tag recorded depth and oceanographic temperature to estimate the location at any given time. We apply this model to Antarctic toothfish (Dissostichus mawsoni) in the Ross Sea.  Finally, to reduce the computational burden of agent-based models we use Bayesian emulation. This approach replaces the simulation model with an approximating algorithm called an emulator. The emulator is calibrated using relatively few runs of the original model. A good emulator provides a close approximation to the original model and has significant speed gains. Thus, inferences become tractable.  We have made the first steps towards developing a tractable approach to fisheries modelling in complex settings through the creation of realistic models, and their emulation. With further development, Bayesian emulation could result in the increased ability to consider and evaluate innovative methods in fisheries modelling. Future avenues for application and exploration range from spatial and multi species models, to ecosystem-based models and beyond.