Estimation of population dynamics for the Indian Ocean albacore tuna using state-space production models - ML and Bayesian approaches

Population dynamics for the Indian Ocean albacore tuna was inferred using state-space ageaggregated
surplus production models. For the estimation, both the maximum likelihood (ML)
method with a Laplace approximation and Bayesian methods with several MCMC sampling
approaches were employed. A total of 12 scenarios were assumed for the state-space models as
combinations of [two different surplus production functions: Fox and Pella-Tomlinson]*[two
different assumptions for initial depletion: start at 1950 with the assumption of B1950=K and
start at 1979 with B1979 = D1979*K < K] *[Assumed extents of sampling CV for CPUE=0, 10% and
20%, in addition to an unknown additional model error]. Furthermore, non-state-space models
were run for comparison purposes. In both the ML and Bayesian estimation methods, key
parameters in the production function were not well estimated under the Pella-Tomlinson model
because of unidentifiability between shape and intrinsic growth rate. As a result, mainly to
highlight the impact of presence/absence of process errors (for the comparison of the results in
this paper to the ASPIC paper) and to draw attention to the influence of the assumed CV in the
CPUE in the estimation process, the results of the Fox production model are shown. These results
showed that when estimating the initial depletion level in 1979, the presence/absence of process
errors displayed a difference in the population trajectory. Furthermore, the assumed extent of
the CV of the CPUE influenced trajectory to some extent, which implied a risk in subjectivity for
such assumptions. Regarding the stock status, the results also suggested that the albacore tuna
population had not been overfished and had not been subjected to overfishing. One of the main
intentions behind the submission of this paper, with a focus on state-space production models,
is to compare full assessment results which might be agreed upon in the Working Party with
those driven by these simplified models, as is done in this paper. Such simplified models can be
used for underlying stock assessment models within model-based management procedures, and
therefore it is worth confirming whether there is a consistency between these approaches.