Statistical catch-at-age analysis vs. ADAPT-VPA: the case of Gulf of Maine cod

In 2003, given an estimate of a spawning-stock biomass (B-sp) of 27% of the maximum sustainable yield (MSY) level (B-MSY(sp)) based on an adaptive framework-virtual population analysis (ADAPT-VPA) assessment using data only after 1981, the Gulf of Maine cod (Gadus morhua) stock was deemed "overfished" under the US Magnuson-Stevens Act. However, an alternative statistical catch-at-age assessment (SCAA) at the time, using survey data from 1964, indicated B-sp above B-MSY(bp). This is investigated, together with other (sometimes conflicting) suggestions made during a number of recent assessment reviews of this stock. The primary reason for the different result is that the ADAPT-VPA assessment imposed asymptotically flat selectivity-at-age when there was strong statistical evidence for dome-shaped selectivity. Once adjusted for this, either assessment method robustly estimates B-sp relatively close to B-MSY(sp) rather than below the "overfished" threshold of 0.5 B-MSY(sp). SCAA allows the longer series of survey data available to be incorporated, providing a better basis to estimate MSY-related targets and doubling the related precision in some cases. As such targets are important when implementing the Magnuson-Stevens Act, SCAA seems preferable to ADAPT-VPA for assessing this stock. Some broader inferences to be drawn from this comparative process include the need for: (i) careful treatment of the plus-group, especially if selectivity may be dome-shaped; (ii) flexible parameterizations of selectivity-at-age in SCAA to avoid false perceptions of the precision of results; and (iii) care in the use of the Beverton-Holt stock-recruitment function, as it gives inappropriately low estimates of B-MSY(sp) if there is an overall negative trend in the estimates of recruitment plotted against B-sp.