Local sensitivity of per-recruit fishing mortality reference points

Figures & data

Figure 1. Illustration of a precautionary approach fisheries harvest decision rule that involves stock status zones defined by RPs and a harvest rate limit RP. Fisheries may harvest less than the limit.

Figure 2. Selectivity function $s\left(t\right)$ of age t for the illustrative example.

Figure 3. Illustration of a YPR curve and two fishing mortality RPs, $F_{max}$ and $F_{0.1}$.

Figure 4. Illustration of a spawner potential ratio curve, $\mathrm{SPR}\left(f\right)/\mathrm{SPR}\left(0\right)$, and three fishing mortality RPs, $F_{20\mathrm{\%}},F_{35\mathrm{\%}}$ and $F_{40\mathrm{\%}}$.

Figure 5. Solid black curves are values of F RPs for perturbed values of the Von Bertalanffy growth parameter k. Solid grey curves are the local slopes. Reference lines (grey dashed) indicate a local slope of zero and the corresponding value for k.

Figure 6. YPR divided by the maximum over f (scaled YPR) for different values of the VonB k parameter. The inset figure shows the maximum YPR (over f) versus k.

Figure 7. Selectivity function $s\left(t\right)$ of age t that is a composite function of a selectivity function $\tilde{s}\left(l\right)$ of length l and a length function $l\left(t\right)$ of age with growth rate parameter k. $s\left(t\right)=\tilde{s}\left\{l\right(t\left)\right\}$.

Figure 8. Solid black curves are values of F RPs for perturbed values of the Von Bertalanffy growth parameter k but a fixed k=0.2 in the length-based selectivity function. Dashed black curves are values of F RPs with perturbed k's in the selectivity function. Grey curves are F RPs scaled by the average selectivity at ages 0–20.

Figure 9. Gamma selectivity functions, $s\left(t\right)$ and $s_{\omega }\left(t\right)=s(t+1)$. Vertical lines indicate the age at maximum selection.

Figure 10. Yield and spawner per recruit curves and four fishing mortality RPs, $F_{max},F_{0.1},F_{20\mathrm{\%}}$, and $F_{40\mathrm{\%}}$ for $s\left(t\right)$ in Figure 9.

Figure 11. Solid black curves are values of F RPs for perturbed values of the selectivity function, $s_{\omega }\left(t\right)=s(t+\omega )$ in Figure 9. Solid grey curves are the local slopes. Reference lines (grey dashed) indicate the local slope at $\omega =0$.

Figure 12. Gamma selectivity functions, $s\left(t\right)$ and $s_{\omega }\left(t\right)=s(t+1)$. Vertical lines indicate the age at maximum selection.

Figure 13. Yield and spawner per recruit curves and four fishing mortality RPs, $F_{max},F_{0.1},F_{20\mathrm{\%}}$, and $F_{40\mathrm{\%}}$ for $s\left(t\right)$ in Figure 12.

Figure 14. Solid black curves are values of F RPs for perturbed values of the selectivity function, $s_{\omega }\left(t\right)=s(t+\omega )$ in Figure 11. Solid grey curves are the local slopes. Reference lines (grey dashed) indicate the local slope at $\omega =0$.