Assumptions influencing the estimation of natural mortality in a tag-integrated statistical model for western and central Pacific Ocean skipjack

The status of skipjack tuna (Katsuwonus pelamis) in the western and central Pacific Ocean is regularly assessed using the integrated catch-at-age model MULTIFAN-CL. The model utilizes catch, fishery-dependent standardized CPUE indices, unstandardized effort, mark-recapture, and length-composition data. We tested the sensitivity of natural mortality estimation to functional forms of M at age, assumptions of tag reporting rate parameters, and modeling decisions that influence the fit to the length composition and tag data. We estimated M at age internal to the tag-integrated spatially-explicit model using a range of parameterizations. Likelihood component profiles for mean natural mortality values, nodes in a cubic spline of M at age, and reporting rate parameters were conducted to determine which data were contributing to the estimation of these parameters. The functional form of M at age did not have a large influence on performance indicators (Frecent/FMSY and SBrecent/SBF=0), but cubic splines proved a parameter efficient method of estimation. Assumed functional forms of selectivity and the fixed growth curve influenced estimates of M at age and had moderate impacts on performance indicators, though the weighting of the length composition data was less influential. Some reporting rate parameters were estimated on the upper bound for all models; changes to assumptions of these parameters impacted performance indicators slightly more than length composition changes, but did not strongly influence M-at-age estimates. Assumptions that affected the amount of tagging data included in the model, such as the mixing period, had a large impact on the performance indicators and shape of M at age, but only moderate changes to mean M estimates. Likelihood profiling showed that both tagging data and length composition data strongly influenced estimates of M at age in this catch-at-length tag-integrated model, but there is conflict among the data sources and tagging programs. Standard errors of M at age were small for most ages, particularly those with numerous tag recaptures, and mean M estimates across tested sensitivity models were mostly consistent. There is some concern that estimates may be biased due to incomplete mixing of tags and other assumption violations, but simulation studies are needed to determine the severity. Research is also recommended on methods to resolve data conflict that may be causing reporting rates estimated on upper bounds and to determine appropriate mixing periods of tagging data.