1 Introduction / notes

A comparison report for reference grid OMs with length composition weighting of 1/20 (factor level L)

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
1 1 A – L 1 A – L
2 2 A – L 2 A – L
4 1 B – L 1 B – L
5 2 B – L 2 B – L
7 1 A -+ L 1 A -+ L
8 2 A -+ L 2 A -+ L
10 1 B -+ L 1 B -+ L
11 2 B -+ L 2 B -+ L
13 1 A +- L 1 A +- L
14 2 A +- L 2 A +- L
16 1 B +- L 1 B +- L
17 2 B +- L 2 B +- L
19 1 A ++ L 1 A ++ L
20 2 A ++ L 2 A ++ L
22 1 B ++ L 1 B ++ L
23 2 B ++ L 2 B ++ L

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
1 1 A – L 88120 743478 0.338 0.957 0.324
2 2 A – L 26209 413649 0.301 1.133 0.341
4 1 B – L 89581 820123 0.381 0.82 0.312
5 2 B – L 25060 337265 0.351 1.254 0.44
7 1 A -+ L 73629 682449 0.262 1.872 0.491
8 2 A -+ L 28103 471476 0.302 1.324 0.4
10 1 B -+ L 77432 795790 0.291 1.296 0.377
11 2 B -+ L 21168 391419 0.29 1.046 0.303
13 1 A +- L 53940 519520 0.271 0.908 0.246
14 2 A +- L 21753 338007 0.325 1.062 0.345
16 1 B +- L 65679 664354 0.297 1.146 0.34
17 2 B +- L 25603 363662 0.353 1.233 0.435
19 1 A ++ L 79292 743653 0.269 1.922 0.517
20 2 A ++ L 34455 544959 0.325 1.128 0.366
22 1 B ++ L 77928 811893 0.292 1.224 0.357
23 2 B ++ L 28436 429418 0.343 1.261 0.433

4.2 Western stock

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

OM Code MSY BMSY BMSY_B0 B_BMSY Dep
1 1 A – L 1078 13361 0.292 0.503 0.147
2 2 A – L 983 17497 0.358 0.477 0.171
4 1 B – L 1262 10622 0.265 0.394 0.104
5 2 B – L 1297 23655 0.363 0.385 0.14
7 1 A -+ L 1150 13640 0.296 0.493 0.146
8 2 A -+ L 978 17963 0.36 0.488 0.176
10 1 B -+ L 1375 11639 0.27 0.366 0.099
11 2 B -+ L 954 16173 0.349 0.489 0.171
13 1 A +- L 985 14733 0.3 1.459 0.438
14 2 A +- L 997 23501 0.368 0.762 0.28
16 1 B +- L 1132 10232 0.265 1.128 0.299
17 2 B +- L 1146 24325 0.365 0.655 0.239
19 1 A ++ L 1381 16585 0.293 1.14 0.334
20 2 A ++ L 783 15660 0.362 1.019 0.369
22 1 B ++ L 1175 10995 0.269 1.376 0.37
23 2 B ++ L 1067 22576 0.363 0.67 0.243

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
1 1 A – L 163 503 1089 1268 562 177 2446 31 316 129 0 16 52 47 6255 6800
2 2 A – L 208 486 1278 1252 430 146 2512 81 317 127 0 0 50 -4 6308 6883
4 1 B – L 77 491 1174 1142 553 174 2435 31 310 128 2 13 51 34 6079 6615
5 2 B – L 90 493 1306 1218 355 128 2660 68 315 126 6 0 46 26 6277 6838
7 1 A -+ L 128 488 1080 1198 493 174 2439 38 320 129 0 14 55 -13 5987 6542
8 2 A -+ L 162 490 1202 1254 446 150 2512 79 319 127 0 0 53 -10 6206 6783
10 1 B -+ L 62 468 1122 1156 500 175 2425 32 314 128 3 11 54 -15 5892 6434
11 2 B -+ L 150 463 1195 1292 405 139 2538 49 310 129 6 0 63 18 6201 6757
13 1 A +- L -7 426 1129 1214 390 128 2393 24 311 129 0 15 39 11 5683 6201
14 2 A +- L 123 483 1206 1224 410 137 2593 66 306 128 0 0 43 13 6190 6734
16 1 B +- L 46 512 1332 1116 510 154 2378 34 306 129 0 15 46 29 6077 6607
17 2 B +- L 71 487 1306 1222 340 119 2624 69 312 127 1 0 44 22 6191 6744
19 1 A ++ L 63 517 1304 1160 415 151 2378 44 314 129 0 18 46 -17 5971 6521
20 2 A ++ L 113 457 1282 1252 446 138 2432 73 314 127 0 0 52 8 6127 6694
22 1 B ++ L 19 513 1285 1133 414 146 2373 43 311 129 0 13 46 -17 5865 6408
23 2 B ++ L 36 477 1256 1216 404 138 2518 60 307 128 2 0 44 8 6052 6593

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
1 1 A – L 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6800
2 2 A – L 45 -17 189 -16 -132 -31 66 50 1 -2 0 -16 -2 -51 53 6883
4 1 B – L -86 -12 85 -126 -9 -3 -11 0 -6 -1 2 -3 -1 -13 -176 6615
5 2 B – L -73 -10 217 -50 -207 -49 214 37 -1 -3 6 -16 -6 -21 22 6838
7 1 A -+ L -35 -15 -9 -70 -69 -3 -7 7 4 0 0 -2 3 -60 -268 6542
8 2 A -+ L -1 -13 113 -14 -116 -27 66 48 3 -2 0 -16 1 -57 -49 6783
10 1 B -+ L -101 -35 33 -112 -62 -2 -21 1 -2 -1 3 -5 2 -62 -363 6434
11 2 B -+ L -13 -40 106 24 -157 -38 92 18 -6 0 6 -16 11 -29 -54 6757
13 1 A +- L -170 -77 40 -54 -172 -49 -53 -7 -5 0 0 -1 -13 -36 -572 6201
14 2 A +- L -40 -20 117 -44 -152 -40 147 35 -10 -1 0 -16 -9 -34 -65 6734
16 1 B +- L -117 9 243 -152 -52 -23 -68 3 -10 0 0 -1 -6 -18 -178 6607
17 2 B +- L -92 -16 217 -46 -222 -58 178 38 -4 -2 1 -16 -8 -25 -64 6744
19 1 A ++ L -100 14 215 -108 -147 -26 -68 13 -2 0 0 2 -6 -64 -284 6521
20 2 A ++ L -50 -46 193 -16 -116 -39 -14 42 -2 -2 0 -16 0 -39 -128 6694
22 1 B ++ L -144 10 196 -135 -148 -31 -73 12 -5 0 0 -3 -6 -64 -390 6408
23 2 B ++ L -127 -26 167 -52 -158 -39 72 29 -9 -1 2 -16 -8 -39 -203 6593

Table 6. Weightings of likelihood components.

OM Code Cat CR Surv Comp SOOm SOOg Tag Rec Mov Sel SRA R0diff MI SPr
1 1 A – L 0.02 1 2 0.05 1 1 5 1 1 1 1 1 1 1
2 2 A – L 0.02 1 2 0.05 1 1 5 1 1 1 1 1 1 1
4 1 B – L 0.02 1 2 0.05 1 1 5 1 1 1 1 1 1 1
5 2 B – L 0.02 1 2 0.05 1 1 5 1 1 1 1 1 1 1
7 1 A -+ L 0.02 1 2 0.05 1 1 5 1 1 1 1 1 1 1
8 2 A -+ L 0.02 1 2 0.05 1 1 5 1 1 1 1 1 1 1
10 1 B -+ L 0.02 1 2 0.05 1 1 5 1 1 1 1 1 1 1
11 2 B -+ L 0.02 1 2 0.05 1 1 5 1 1 1 1 1 1 1
13 1 A +- L 0.02 1 2 0.05 1 1 5 1 1 1 1 1 1 1
14 2 A +- L 0.02 1 2 0.05 1 1 5 1 1 1 1 1 1 1
16 1 B +- L 0.02 1 2 0.05 1 1 5 1 1 1 1 1 1 1
17 2 B +- L 0.02 1 2 0.05 1 1 5 1 1 1 1 1 1 1
19 1 A ++ L 0.02 1 2 0.05 1 1 5 1 1 1 1 1 1 1
20 2 A ++ L 0.02 1 2 0.05 1 1 5 1 1 1 1 1 1 1
22 1 B ++ L 0.02 1 2 0.05 1 1 5 1 1 1 1 1 1 1
23 2 B ++ L 0.02 1 2 0.05 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 - 1.46 0.49 - 1.05 0.82 - 1.92 1.06 - 1.27
2016 SSB (kt) 4.2 - 21.5 7.6 - 15.9 359 - 1429.3 463.6 - 819.4
SSB trajectory 2007-2016 (% per year) 5.59 - 15.49 10.79 - 14.47 7.94 - 25.6 10.72 - 20.27

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

Figure 12. All SSB trajectories by area.