Western Horse Mackerel

Although Stock Synthesis can estimate parameters such as the steepness (\(h\)) of the stock and recruitment relationship and natural mortality (\(M\)) there is often insufficient infomation in the data to do so. Therefore these values are commonly fixed, even though they can have a large impact on estimates of stock status relative to reference points. Therefore the asessment for Western Horse Mackerel was rerun for a range of values for \(h\) and \(M\). This allows i) likelihood profiles to be plotted as the shape and curvature of the likelihood surface allows the stability of the estimates to be evaluated, and sensitivity analysis to be run.

Figure 1 plots the profile for \(h\) and Figure 2 for \(M\), these both show that higher values are more likely than low values and that for \(h\) the most likely value is between 0.6 and 0.7 which is lower than the value of 0.99 used in the assessment. For \(M\) the most likely value is 0.175 which is slighly higher than the value of 0.15 used by the WG.

The impact on the absolute trend in biomass and \(F\) are shown in Figures 3 and 4, varying steepness has little effect, presumably as the stock has not decline below 20% of virgin biomass in the past which is required to provide infomation on steepness. The chioce of \(M\) does, however, have a large impact on absaolute trends, this is because as \(M\) inceases both biomass has to increase to explain the catches, while \(F\) decreases as although biomass incrases catches remain the same.

The biggest difference is seen in reference points andthe stock status relative to reference points.

Figures 5 and 6 compare the \(MSY\) reference points and \(K\) to the ICES \(PA\) and \(MSY\) reference points for the different values of \(h\) and \(M\). As steepness inceases \(B_{MSY}\) and \(K\) decrease, while \(F_{MSY}\) increases, For M although \(F_{MSY}\) increases \(B_{MSY}\) and \(K\) decline then increase. The ICES reference points obtained fron eqsim are biased, and in the case of higher \(M\) eqsim did not converge.

The biggest difference were seen for the trends relative to the \(MSY\) benchmarks, Figure 7 and 8, current status, i.e. is the stock over fished on being over fished, depends on the choice of \(h\) and \(M\).

The SS3 values are not necessarily correct, as more work is required to validate the assessment. However, if the exercise is regarded as a simulation evaluation and the SS results as an Operating Model that is consistent with the data then there are large biases in the ICES reference points, e.g. \(F_{MSY}\) is underestimated and biomass reference points overestimated. This is likely to have a large impact on management advice.

If eqsim used in an MSE it is part of the MP, it should not be used to set up the OM. Otherwise it is not being simulation tested, however, it is too slow to be used as part of an MP.

Figure 1. Likelihood by steepness.

Figure 2. Likelihood by \(M\).

Figure 3. Time series for steepness scenarios.

Figure 4. Time series for \(M\) scenarios.

Figure 5. SS3 benchmarks with 95% CIs and ICES reference points for steepnesss scenarios.

Figure 6. SS3 benchmarks with 95% CIs and ICES reference points for \(M\) scenarios.

Figure 7. Time series for steepness scenarios relative to \(MSY\) benchmarks/

Figure 8. Time series for \(M\) scenarios relative to \(MSY\) benchmarks.