An example of a workflow to build an Operating Model based on life history, project it forward for a \(F/F_{\mathrm{MSY}}\) trajectory, recover process-error residuals, then fit JABBA with and without depletion-dependent PE, then evaluate ability to i) classify stock status relative to target and limit biomass and exploitation rate reference points; ii) identify trends, and iii) prediction rebuilding horizons.

Setup

Set quick=FALSE to match the slide figures (100 iterations, full \(F\) grid).

1. Life-history OM

lhPar() / lhEql() give an FLBRP. Convert to an FLStock and project with ffwd() and recruitment deviations.

#> An object of class "FLPar"
#>        quant
#> refpt   harvest  ssb      eb       yield   
#>   msy   4.38e-01 1.69e+02 2.54e+02 8.05e+01
#>   crash 3.24e+00 4.45e-06 1.26e-05 1.69e-05
#> units:  NA

2. Constant \(F/F_{\mathrm{MSY}}\): PE scale vs \(F\)

Project a grid of constant \(F\) multipliers. Process error is the log residual after catch (location="after"). SD of that series is the PE scale at each \(F\).

Figure 1. Process-error scale (SD of log surplus-production residuals) against constant \(F/F_{\mathrm{MSY}}\).

PE scale increases with \(F\): i.e. the surplus-production residual is larger when the stock is fished harder.

3. Increasing vs declining \(F\)

Trajectories that ramp up from \(0.01F_{\mathrm{MSY}}\) to \(2F_{\mathrm{MSY}}\); and declines from \(2F_{\mathrm{MSY}}\) to \(0.01F_{\mathrm{MSY}}\); noise is based on same recruitment residuals.

Figure 2. Operating-model trajectories under increasing and declining \(F/F_{\mathrm{MSY}}\).

Year-wise SD of log PE (after a burn-in):

Figure 3. SD of log process error after burn-in, for increasing and declining \(F\).

4. Four-panel PE diagnostics

Compares PE and \(B/B_{\mathrm{MSY}}\) for an example iteration

Figure 4. Four-panel process-error diagnostics for a single increasing-\(F\) realisation: time, status versus \(B/B_{\mathrm{MSY}}\), ACF, and histogram.

The status panel is the empirical counterpart of JABBA’s proc.dyn curve: note PE SD is larger at low \(B/B_{\mathrm{MSY}}\).

5. Life-history sensitivity

Grid for \(k\), \(M\), \(\sigma_R\)

6. Fit JABBA to example iteration

Take one realisation (it) of the increasing-\(F\) stock, use catch and the biomass index from FLStock and fit JABBA is fitted to the exploitable-biomass index. \(F_{\mathrm{MSY}}\), \(B_{\mathrm{MSY}}\) and \(B_0\) from FLBRP. quick=TRUE uses JABBA’s short MCMC. plotJabbaTs() draws the posterior median with 95% credible-interval ribbons. OM overlays (dashed) are spawning biomass and exploitable biomass, each relative to its own \(B_{\mathrm{MSY}}\) from FLBRP (refpts SSB and refptsEB()).

Figure 5. Process-error diagnostics for the JABBA fit with constant process-error variance.

Figure 6. JABBA posterior medians and 95% credible intervals (constant PE).

Figure 7. JABBA \(B/B_{\mathrm{MSY}}\) (median and 95% CI) with spawning biomass and exploitable biomass (dashed) relative to its own \(B_{\mathrm{MSY}}\).

Optional: same iteration with proc.dyn=TRUE.

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Figure 8. Process-error diagnostics for the JABBA fit with depletion-dependent PE (proc.dyn).

Figure 9. JABBA posterior medians and 95% credible intervals (depletion-dependent PE).

Figure 10. Depletion-dependent JABBA \(B/B_{\mathrm{MSY}}\) with OM spawning biomass and exploitable biomass (dashed).

Figure 11. Constant versus depletion-dependent JABBA \(B/B_{\mathrm{MSY}}\) (median and 95% CI) and OM spawning and exploitable biomass (dashed).

Figure 12. Same \(B/B_{\mathrm{MSY}}\) comparison as the previous figure, restricted to the recent period (year \(> 100\)).

Figure 13. Constant versus depletion-dependent JABBA \(B/B_{\mathrm{MSY}}\), \(F/F_{\mathrm{MSY}}\) and process error, with 95% CIs and OM biomass overlays.