MSY Reference Points

The calculation of maximum sustainable yield (MSY) and related reference points are also impacted by inter-annual variability in life-history and fishing parameters (i.e., selectivity pattern). For example, if there is large inter-annual variability in natural mortality or growth, MSY and $\text{SB}_{\text{MSY}}$ may vary significantly between years.

We calculate MSY and related metrics (e.g., $B_{\text{MSY}}$) for each time-step in the model based on the life-history and fishing parameters in that year. The MSY reference points are used in both the simulated Data object, and to evaluate the performance of the management procedures.

For the simulated Data object, we calculate MSY reference points following a similar procedure to that described above for $B_0$. We use $A_{50}$ as an approximation of generation time, and average the annual MSY values over $A_{50}$ years around the last historical year. For example, if OM@nyears = 50 and $A_{50}=5$, $SB_{\text{MSY}}$ is calculated as:

$$ SB_{\text{MSY}} = \sum_{y=48}^{52}{SB_y^{\text{MSY}}} $$ where $SB_y^{\text{MSY}}$ is the spawning biomass corresponding with maximum sustainable yield in year $y$. The logic behind this is, if estimates of MSY, $\text{SB}_\text{MSY}$, etc are available, they are likely calculated based on current life-history information, which would be estimated from data spanning several age classes.

The MSY reference points in the Data object are not updated in the future projection years. The MSY reference points and MSY values by year are returned in MSE@Misc$MSYRefs.

Note

The MSY metrics are always calculated by year. The slot MSE@SB_SBMSY returns the spawning biomass in the projections divided by $SB_\text{MSY}$ in each year of the projections. For alternative methods to calculate $\text{SB}/\text{SB}_{\text{MSY}}$, such as relative to the constant $\text{SB}_\text{MSY}$ described above, use MSE@SSB or MSE@B and the data stored in MSE@RefPoint.