The 2018 stock assessment of pāua (Haliotis iris) for PAU 5D

We conducted a Bayesian length-based stock assessment for pāua (Haliotis iris) in pāua quota management area PAU 5D. The assessment model used the same population dynamics model as previous assessments, but the data models that linked the population dynamics (process) model with different data types were significantly updated. Unlike previous assessments, the present model used only model-derived inputs and did not fit directly to data. It, therefore, represents a Bayesian synthesis of available information rather than an integrated model that fits to data directly. This development is most significant for the growth process as represented in the model, which previously relied on fitting directly to available data from particular quota management areas. In this model, growth information was given in the form of a rather vague prior, and the model used this information with other inputs to estimate stock-level growth. This approach led to slower estimated growth across all models that were considered to be robust (by the Fisheries New Zealand Shellfish Working Group), which in turn resulted in higher estimated spawning stock biomass.

Other changes in the current stock assessment included a new Dirichlet-Multinomial/Multivariate-Normal formulation for catch sampling length frequency (CSLF) data, and estimation of process error for both CSLF and catch-per-unit-effort (CPUE) inputs.

Relative weighting between these inputs was achieved via explicit constraints on information loss in terms of Kullback-Leibler divergence (KLD) for the two main input sources (CPUE and CSLF). The KLD was then used to calculate posterior information loss in the model for both input types, and to adjust weights in favour of one or the other input.

Two sets of relative weights and two sets of priors for natural mortality M were selected as the main sensitivity runs alongside a base case that gave slightly more weight to CPUE data. Both the base case and the two main sensitivity runs suggested that the stock status was near or at 40% of the unfished spawning stock. For all models, however, the relative available biomass was relatively low (near 25%). Projections at current catch levels suggest that rebuilding towards higher levels of available biomass will be likely to be relatively slow despite current voluntary shelving of 35% of the allowable commercial catch.