Outline

Fit a sigmoidal Beverton and Holt stock recruitment relationship to North Sea plaice
Project for 2000 onwards, for high F and different depensation parameters, i.e. 0.5, 1, 2
Compare equilibrium curves, i.e. \(MSY\) targets and limit reference points

Summary

If there is an Allee effect then for the same high F, the stock will be more depleted (Figure 1).
The effect on biomass benchmarks and \(B_0\) can be seen from examination of the equilibrium Yield v SSB curves in Figure 2
- The Allee effect results in a decline in \(MSY\), \(B_{MSY}\), and \(K\)
The effect on \(F\) benchmarks can be seen from Figure 3, the Allee effect results in
- a slight increase in \(F_{MSY}\), i.e. the maximum catch is seen at a higher value of \(F\)
- \(F_{crash}\), i.e. the level of \(F\) that will cause stock collapse being greatly reduced and the slope of the righthand limb of the Yield v F curve is very steep. + Therefore, to allow for processess included in the assessment model and to avoid the associated risks, e.g. multi-species interactions (Rindorf, et al., 2017), Allee effects (Perälä et al., 2021), and climate change (XXX), it is best to aim for pretty good yield, i.e. keep biomass on the right-hand side of the production function so \(B_{MSY}\) should be reported, and the trigger should be close to the \(B_{target}\) and not at the \(5_{th}\) percentile of \(B_{MSY}\).
To ensure robustness and to avoid cyclically effects and to ensure stability HCR should be evaluated using feedback control which includes the stock assessment.

Figure 1. Beverton and Holt for c=1.0

Figure 2. Beverton and Holt for c=0.5

Figure 3. Beverton and Holt for c=2.0

Figure 4. Beverton and Holt for c=3.0

Figure 5. Project stock for different stock recruitment relationships under high F.

Figure 6. Equilibrium curves for Yield v SSB.

Figure 7. Equilibrium curves for Yield v F.