Toothfish stock assessment results are strongly influenced by tag-release and tag-recapture data, and rely on the assumption that tagged and untagged fish have constant probabilities of recapture regardless of the spatial distribution of releases or subsequent fishing effort for recaptures. Conceptually this assumption implies either that tagged and untagged fish mix equally in the population, or that fishing effort for recaptures is distributed in proportion to the underlying abundance. Neither of these conditions are likely to occur in practice, and violation of this assumption may lead to bias. In this paper we investigate such potential biases in the assessment of Antarctic toothfish in the Ross Sea fishery using simulated outputs from spatially explicit operating models.
Two spatially explicit operating models were developed: each was comprised of 189 discrete cells, with a cell size of about 25,000 km2. The first model was restricted to those locations of the Ross Sea region that have been fished (restricted model), and the second model extended to encompass all areas (unrestricted model). Simulated observations were generated from these models, and used as inputs into a simplified non-spatial stock model based on the 2011 Ross Sea toothfish stock assessment.
Results suggested that the assessment model was biased low by 17% or 43% assuming movements defined by the restricted and unrestricted models respectively. The bias was thought to reflect the underlying distributions of tag-releases and subsequent fishing effort, and the limited mixing of fish between areas — more than half of tags have been released (and subsequently recaptured) from SSRUs 88.1H and 88.1I, while a large proportion of the fish are in remaining SSRUs where fewer tags were released and with lower fishing effort. This effect is accentuated in the unrestricted model, where about half of the fish are distributed in areas that had not been subject to fishing effort.
We note that the extent of bias will depend on both the proportion of fish in unfished areas and movement rates between fished and unfished areas, but that misspecification of other parameters in the assessment models (for example tag mortality rates and tag detection rates) or alternate spatial hypotheses may also introduce biases that we have not considered in this paper. While additional analyses need to be undertaken to confirm or improve the spatial models used here and alternative movement hypotheses should be tested, we consider that these simulation experiments provide a useful tool to evaluate potential bias and uncertainty in our understanding of the assessment in the Ross Sea toothfish stock and potentially similar tag-based assessments elsewhere in the CCAMLR Area. They are also useful in investigate the likely consequences of management strategies for stock assessments, including changes in fishing effort or tagging distributions. They can also be used to investigate the potential effects of alternative biological hypotheses for less well defined parameters, for example maturity and natural mortality rates.