1 Introduction / notes

A comparison report for reference grid OMs with length composition weighting of 1 (factor level H)

2 OM design

2.1 Factor 1: Regime shift

1: West: h=0.6 to h=0.9 1975+, East: h=0.98 for 1987- to h=0.98 1988+
2: West: B-H h=0.6 all years, East: B-H h=0.7 all years
3: West: post 75+ changes to pre ’75 after 10 yrs, East: 88+ to ’50-87 after 10 years

2.2 Factor 2: Natural Mortality / Maturity

A: Younger spawning, High M
B: Older spawning, Low M

2.3 Factor 3: Scale

–: mean SSB 15kt West, 200kt East
-+: mean SSB 15kt West, 400kt East
+-: mean SSB 50kt West, 200kt East
++: mean SSB 50kt West, 400kt East

2.4 Factor 4: Length composition weighting

L: Low length composition weight of 1/20
H: High length composition weight of 1

3 OMs presented in this report

Table 1. The subset of wider operating models included in this comparison report.

Code. Regime shift Maturity / M Scale Length Comp wt
25 1 A – H 1 A – H
26 2 A – H 2 A – H
28 1 B – H 1 B – H
29 2 B – H 2 B – H
31 1 A -+ H 1 A -+ H
32 2 A -+ H 2 A -+ H
34 1 B -+ H 1 B -+ H
35 2 B -+ H 2 B -+ H
37 1 A +- H 1 A +- H
38 2 A +- H 2 A +- H
40 1 B +- H 1 B +- H
41 2 B +- H 2 B +- H
43 1 A ++ H 1 A ++ H
44 2 A ++ H 2 A ++ H
46 1 B ++ H 1 B ++ H
47 2 B ++ H 2 B ++ H

4 Reference points

4.1 Eastern stock

Table 2. Reference points for the Eastern stock using 2019 stock-recruitment (R0 and steepness). Tabulated biomass numbers (BMSY, BMSY_B0) refer to spawning biomass. These biomass numbers and MSY numbers are expressed in thousands of tonnes. Depletion is spawning biomass in 2019 relative to the ‘dynamic B0’ (the spawning biomass under zero fishing accounting for shifts in recruitment).

OM Code MSY BMSY BMSY_B0 B_BMSY Dep
25 1 A – H 83356 632557 0.286 1.652 0.473
26 2 A – H 26730 335683 0.315 1.107 0.349
28 1 B – H 86915 744581 0.324 1.147 0.372
29 2 B – H 27955 361548 0.345 1.366 0.471
31 1 A -+ H 95642 724173 0.284 1.895 0.538
32 2 A -+ H 38651 487271 0.322 1.624 0.523
34 1 B -+ H 102524 879020 0.32 1.342 0.429
35 2 B -+ H 48733 554564 0.365 1.307 0.477
37 1 A +- H 86622 650855 0.287 1.732 0.497
38 2 A +- H 26894 373874 0.301 1.353 0.407
40 1 B +- H 89792 766918 0.325 1.207 0.392
41 2 B +- H 24866 334116 0.313 1.183 0.37
43 1 A ++ H 105112 795656 0.284 1.944 0.552
44 2 A ++ H 32452 452184 0.301 1.623 0.489
46 1 B ++ H 110045 948126 0.322 1.388 0.447
47 2 B ++ H 33027 414663 0.349 1.588 0.554

4.2 Western stock

Table 3. As Table 2 but for the Western stock.

OM Code MSY BMSY BMSY_B0 B_BMSY Dep
25 1 A – H 900 9965 0.301 0.817 0.246
26 2 A – H 1598 28253 0.362 0.73 0.264
28 1 B – H 1308 9620 0.28 0.506 0.142
29 2 B – H 1371 20873 0.362 0.37 0.134
31 1 A -+ H 902 10167 0.305 0.81 0.247
32 2 A -+ H 1153 21640 0.361 0.49 0.177
34 1 B -+ H 1270 9688 0.282 0.517 0.146
35 2 B -+ H 1581 24154 0.354 0.413 0.146
37 1 A +- H 1272 14626 0.294 1.523 0.448
38 2 A +- H 1996 34938 0.363 1.425 0.517
40 1 B +- H 1201 10589 0.276 1.302 0.359
41 2 B +- H 2329 37259 0.35 1.084 0.379
43 1 A ++ H 1264 14398 0.296 1.524 0.451
44 2 A ++ H 2006 34713 0.363 1.434 0.521
46 1 B ++ H 1193 10824 0.279 1.27 0.354
47 2 B ++ H 2256 36693 0.364 1.214 0.442

5 Comparison of global likelihoods

Table 4. These are weighted negative log-likelihoods. Color coding is by column. Rows with all black values depict models that did not converge.

OM Code Cat CR Surv Comp SOOm SOOg Tag Rec Mov Sel SRA R0diff MI SPr TOT_nP TOT
25 1 A – H 254 534 1317 20735 570 187 2536 31 311 129 0 16 51 -3 26130 26668
26 2 A – H 479 488 1766 21187 331 141 2751 47 317 127 0 0 45 31 27175 27712
28 1 B – H 141 524 1357 20704 542 181 2574 30 315 129 2 14 49 -2 26021 26559
29 2 B – H 286 473 1779 20926 460 153 3016 56 316 126 14 0 54 8 27101 27667
31 1 A -+ H 244 523 1274 20719 559 193 2531 31 317 130 0 16 57 -4 26039 26589
32 2 A -+ H 304 450 1444 21054 470 173 2902 63 322 127 0 0 53 46 26841 27406
34 1 B -+ H 142 522 1334 20662 539 185 2553 29 315 129 3 13 54 -5 25934 26477
35 2 B -+ H 428 455 1665 20987 393 153 2772 57 329 126 22 0 52 372 27225 27812
37 1 A +- H 128 579 1568 20701 480 161 2481 34 306 130 0 19 39 -5 26094 26622
38 2 A +- H 452 524 2301 20783 271 124 2603 45 308 128 0 0 43 12 27071 27596
40 1 B +- H 114 545 1552 20659 478 161 2501 30 308 130 0 16 41 -3 26007 26531
41 2 B +- H 553 489 2045 20774 263 118 2857 37 315 126 3 0 40 1 27100 27620
43 1 A ++ H 134 564 1530 20646 484 171 2492 33 308 130 0 19 43 -6 26016 26550
44 2 A ++ H 429 509 2166 20812 281 129 2592 46 309 128 0 0 46 6 26923 27453
46 1 B ++ H 88 544 1515 20631 485 170 2496 30 309 129 0 16 45 -6 25923 26451
47 2 B ++ H 376 486 2259 20789 283 127 2728 35 311 126 9 0 44 15 27064 27590

Cat = catch data by fleet, quarter and area. CR = the fishery dependent catch rate (CPUE) indices, Surv = fishery-independent survey indices, Comp = length composition data, SOOm = stock of origin microchemistry data, SOOg = stock of origin genetics, Tag = Electronic tagging data, Rec = prior on recruitment deviations, Mov = prior on movement parameters, Sel = prior on size selectivity parameters, SRA = penalty incurred when catches exceed F=1 catches in the stock reduction analysis phase (1864-1964), MI = a prior on similarity to the ‘Master Index’ that predicts F by year, area, season and fleet, R0diff = a prior on the difference in R0 estimated in two-phase recruitment models (recruitment level 1 and 3), SPr = seasonal distribution prior, TOT_nP = total global objective function without priors, TOT = total global objective function.

Table 5. These are weighted negative log-likelihoods expressed as differences from the base-case weighting. Color coding is by column. Rows with all black values depict models that did not converge.

OM Code Cat CR Surv Comp SOOm SOOg Tag Rec Mov Sel SRA R0diff MI SPr TOT_nP TOT
25 1 A – H 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 26668
26 2 A – H 225 -46 449 452 -239 -46 215 16 6 -2 0 -16 -6 34 1045 27712
28 1 B – H -113 -10 40 -31 -28 -6 38 -1 4 0 2 -2 -2 1 -109 26559
29 2 B – H 32 -61 462 191 -110 -34 480 25 5 -3 14 -16 3 11 971 27667
31 1 A -+ H -10 -11 -43 -16 -11 6 -5 0 6 1 0 0 6 -1 -91 26589
32 2 A -+ H 50 -84 127 319 -100 -14 366 32 11 -2 0 -16 2 49 711 27406
34 1 B -+ H -112 -12 17 -73 -31 -2 17 -2 4 0 3 -3 3 -2 -196 26477
35 2 B -+ H 174 -79 348 252 -177 -34 236 26 18 -3 22 -16 1 375 1095 27812
37 1 A +- H -126 45 251 -34 -90 -26 -55 3 -5 1 0 3 -12 -2 -36 26622
38 2 A +- H 198 -10 984 48 -299 -63 67 14 -3 -1 0 -16 -8 15 941 27596
40 1 B +- H -140 11 235 -76 -92 -26 -35 -1 -3 1 0 0 -10 0 -123 26531
41 2 B +- H 299 -45 728 39 -307 -69 321 6 4 -3 3 -16 -11 4 970 27620
43 1 A ++ H -120 30 213 -89 -86 -16 -44 2 -3 1 0 3 -8 -3 -114 26550
44 2 A ++ H 175 -25 849 77 -289 -58 56 15 -2 -1 0 -16 -5 9 793 27453
46 1 B ++ H -166 10 198 -104 -85 -17 -40 -1 -2 0 0 0 -6 -3 -207 26451
47 2 B ++ H 122 -48 942 54 -287 -60 192 4 0 -3 9 -16 -7 18 934 27590

Table 6. Weightings of likelihood components.

OM Code Cat CR Surv Comp SOOm SOOg Tag Rec Mov Sel SRA R0diff MI SPr
25 1 A – H 0.02 1 2 1 1 1 5 1 1 1 1 1 1 1
26 2 A – H 0.02 1 2 1 1 1 5 1 1 1 1 1 1 1
28 1 B – H 0.02 1 2 1 1 1 5 1 1 1 1 1 1 1
29 2 B – H 0.02 1 2 1 1 1 5 1 1 1 1 1 1 1
31 1 A -+ H 0.02 1 2 1 1 1 5 1 1 1 1 1 1 1
32 2 A -+ H 0.02 1 2 1 1 1 5 1 1 1 1 1 1 1
34 1 B -+ H 0.02 1 2 1 1 1 5 1 1 1 1 1 1 1
35 2 B -+ H 0.02 1 2 1 1 1 5 1 1 1 1 1 1 1
37 1 A +- H 0.02 1 2 1 1 1 5 1 1 1 1 1 1 1
38 2 A +- H 0.02 1 2 1 1 1 5 1 1 1 1 1 1 1
40 1 B +- H 0.02 1 2 1 1 1 5 1 1 1 1 1 1 1
41 2 B +- H 0.02 1 2 1 1 1 5 1 1 1 1 1 1 1
43 1 A ++ H 0.02 1 2 1 1 1 5 1 1 1 1 1 1 1
44 2 A ++ H 0.02 1 2 1 1 1 5 1 1 1 1 1 1 1
46 1 B ++ H 0.02 1 2 1 1 1 5 1 1 1 1 1 1 1
47 2 B ++ H 0.02 1 2 1 1 1 5 1 1 1 1 1 1 1

6 Comparison with 2017 Stock Assessments

Figure 1. Regional spawning stock comparisons (by area, divisible by 45deg W) with 2017 stock assessment. Note that annual estimates from the operating model are calculated from average of the seasonal predictions.

7 Spawning Stock Biomass

Figure 2. Stock-specific spawning biomass in kilo tonnes (top row) and relative to 1952 (bottom row)

8 Spawning stock biomass by stock and area

Figure 3. Comparison of stock (top row) and area (bottom row) specific spawning biomass in kilo tonnes.

9 SSB relative to dynamic BMSY

Figure 4. Comparison of stock status estimates (SSB relative to dynamic SSBMSY)

10 Stock mixing

Figure 5a. Biomass fractions by stock (top row) and area (bottom row).

Figure 5b. Fraction of stock biomass in the opposite ocean area (average over last 5 years)(e.g. a value of 0.05 in the top left plot indicates that 5% of the western stock biomass was located in the east Atlantic area over the last 5 years of the historical model fitting)

Figure 5c.The mean fraction of stock SSB found in the spawning area and spawning season. CAUTION: these fractions can be hard to interpret. For example, lets consider a case where 100% of eastern fish entered the Mediterranean to spawn and then left after a month. In this case the average fraction would be 1/3 (the spawning season is 3 months long in the model). This may explain why it is not straighforward to link model estimated recruitment to these mean fractions whose principal purpose is to model availability of vulnerably biomass to fishing.

Figure 5d. Fraction of stock biomass in the natal spawning area: Med for the Eastern stock and GOM for the Western stock (average over last 5 years)

Figure 5e. The mean fraction of stock biomass (by age class) that is found in the so called ‘SATL’ (South Atlantic Area) which includes the East Atlantic waters of southern Spain, Portugal, Gibraltar and Morocco. The model uses these fractions to model availability to fishing so fractions may be estimated to be high if areas are a focal point for feeding or a migration route.

11 Fits to stock-specific larval indices

Figure 6. Fits to stock specific larval indices

12 Fits to seasonal / spatial priors

Figure 7. Fit to seasonal-spatial priors (red points are the specified prior medians).

13 Fits to aggregate annual catches

Figure 8. Fits to total annual catches (red points are observed catches).

14 Fits to composition data

Figure 9. Fits to catch at length composition data.

15 Final age structure

Figure 10a. Final age structure of each stock.

Figure 10b. Biomass-age structure of each stock in the final year of conditioning.

16 Summary of aggregated OM estimates

Table 7. Summary of estimate of status, scale and recent trajectory over all operating models

West range West interquartile East range East interquartile
SSB2016 relative to dyn SSBMSY 0.37 - 1.52 0.52 - 1.33 1.11 - 1.94 1.29 - 1.63
2016 SSB (kt) 4.9 - 49.8 8.2 - 26.8 371.6 - 1546.8 620.4 - 1140.4
SSB trajectory 2007-2016 (% per year) 3.02 - 15.48 5.88 - 11.43 6.05 - 24.41 9.12 - 19.86

Figure 11. Summary of estimate of status, scale and recent trajectory over all operating models

Figure 12. All SSB trajectories by area.