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ICES NEA M ACKEREL REPORT 2 0 0 8

ICES ADVISORY COMMITTEE

ICES CM 2 0 0 8 / ACOM:5 4

Report of t he Working Group on NEA Mack- erel Long- Term Managem ent Scient ific

Evaluat ions (NEAMACKLTM)

12 - 13 April 2007

Am st erdam , The Net herlands

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International Council for the Exploration of the Sea Conseil International pour l Exploration de la Mer

H. C. Andersens Boulevard 44 46 DK-1553 Copenhagen V

Denmark

Telephone (+45) 33 38 67 00 Telefax (+45) 33 93 42 15

www.ices.dk [email protected]

Recommended format for purposes of citation:

ICES.2008. Report of the Working Group on NEA Mackerel Long-Term Management Scientific Evaluations (NEAMACKLTM), 12 - 13 April 2007, Amsterdam, The Nether- lands. 233 pp.

For permission to reproduce material from this publication, please apply to the Gen- eral Secretary.

The document is a report of an Expert Group under the auspices of the International Council for the Exploration of the Sea and does not necessarily represent the views of the Council.

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ICES NEA Mackerel REPORT 2008 i

Co n t e n t s

1 Introduction ... 1

1.1 Development Participants... 1

1.2 Background... 1

2 Methods ... 3

2.1 Model Conditioning ... 3

2.1.1 Simulation Set-up and Initialization... 3

2.1.2 Recruitment... 3

2.1.3 Weight- and Maturity-at-age ... 5

2.1.4 Selection... 5

2.1.5 Observation model... 5

2.1.6 The Implementation Model ... 6

2.2 Simulation tools... 6

2.2.1 FLR ... 6

2.2.2 HCM... 7

2.2.3 F-PRESS (Fisheries Projection and Evalu ation by Stochastic Simulation) ... 8

2.3 Harvest Control Rules ... 9

2.3.1 F-rule proposed by the EU Commission... 9

2.3.2 Fixed TAC rule ... 9

2.3.3 Fixed Harvest Rate (HR) rule ... 10

2.4 Model validation ... 10

2.5 Management scenarios ... 10

2.6 Performance Statistics... 11

2.7 Reference points ... 12

3 Results ... 13

3.1 Model validation ... 13

3.2 Interpretation of acceptable risk ... 14

3.3 F-rule... 17

3.4 Harvest rate rule... 24

3.5 Target TAC rule ... 31

4 Discussion ... 35

4.1 SSB year used to set the TAC ... 35

4.2 Period of HCR setting... 36

4.3 Trigger biomass ... 36

4.4 Constraining TAC variability ... 37

4.5 Missing catches... 37

5 Conclusions... 38

5.1 F-rule as proposed by the EU Commission ... 38

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ii ICES NEA Mackerel REPORT 2008

5.2 Harvest Rate rule... 38

5.3 Fixed TAC rule... 38

5.4 Summary Conclusions ... 39

6 Literature cited... 40

Annex 1: EU Request... 68

Annex 2: Exploration of exploitation with different measurement methods... 69

Annex 3:HCM: Simulations of the harvest rule for mackerel proposed by the EU commision and some alternative rules. ... 80

Annex 4: FPress Simulations ... 115

Annex 5: Outline of program and Subroutines... 169

Annex 6: Mackerel Stock Recruit models... 181

Annex 8: EU rule ... 199

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ICES NEA Mackerel REPORT 2008 1

1 In t r o d u ct i o n

1 .1 Devel o p m en t Par t i ci p an t s Beatriz A. Roel

Chair, Cefas, Lowestoft, UK Andrew Campbell Marine Institute, Galway, Ireland Ciaran Kelly

Marine Institute, Galway, Ireland John Simmonds FRS, Scotland, UK

Dankert Skagen IMR, Bergen, Norway

1 .2 Back g r o u n d

At the start of 2007, the EU requ ested ICES to evalu ate m u lti-annu al p lans for N orth East Atlantic m ackerel (N EA m ackerel) in the form of the cu rrent coastal states agreem ent (w hich is ap p lied annu ally). This requ est also su ggested that ICES shou ld exam ine other ap p roaches on its ow n initiative (see Annex 1). ICES d ecid ed to d e- velop the evalu ations of p otential m anagem ent p lans throu gh consu ltation w ith stakehold ers and m anagers in line w ith the recom m end ations of SGMAS (ICES, 2007a) and invited a group of scientists to carry out the work.

At a first m eeting w ith som e stakehold ers in Ap ril 2007¹, the ind u stry stakehold ers p resent exp ressed the view that catch stability, the m aintenance of larger size fish in the stock, and the avoid ance of stock collap se w ere objectives they w ou ld like inclu d ed in any p lan. The scientists ou tlined the know led ge base and stock d ynam ics for N EA m ackerel. It w as conclu d ed from this m eeting that H arvest Control Ru les (H CR) that w ere m ore d iverse than the ones p rop osed by EU for evalu ation, shou ld be explored.

Follow ing this m eeting sim u lations w ere u nd ertaken to exp lore the trad e-offs u nd er three strategies. A target total allow able catch (TAC) strategy (Section 2.3.2) and 2 harvest rate strategies, one w here the TAC is a fraction of the estim ated cu rrent spawning-stock biom ass (SSB) and a second , F-ru le, w here the TAC is d erived by p rojecting the stock forw ard s and ap p lying an F in line w ith the cu rrent coastal states agreement (Sections 2.3.1 and 2.3.3). In all three cases the TAC, the harvest rate, or the F w ere fixed w hen the assessed stock w as above the trigger p oint, and red u ced p ro- p ortionally w hen the stock w as below the trigger p oint. Figu re 1.2.1 illu strates the H CR u sed to evalu ate the ABC ru le for the EU w here [A] corresp ond s to the target F and [C] to the trigger SSB. An equivalent diagram applies to the harvest rate strategy.

Figu re 1.2.2 illu strates the H CR u sed for a target TAC strategy. A third p arameter

1 Participants at the meeting: Michala Ovens (ICES Secretariat),Invild H arkes (Secretary, Pelagic RAC), Christian Olesen (Denm ark, Pelagic RAC), Sean O Donoghu e (Ireland , Killybegs Fisherm en s Organisation), Eric Roeleveld (The N etherland s, Ind u stry), Iain McSw een, Scottish Ind u stry, Gerard van Balsfoort, Du tch Ind u stry, Martin Pastoors (Chair of ACFM), Mark Dickey-Collas (IMARES), Leif N øttestad (IMR, N orw ay), Ciaran Kelly (Marine Lab, Ireland ), John Sim m ond s (FRS, UK Scotland ), Dim itri Vasilyev (Ru ssia), Beatriz Roel, Chair (CEFAS, UK Eng- land).

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2 ICES NEA Mackerel REPORT 2008

([B], for the EU proposed rule) determines the extent the TAC is allowed to vary from one year to the next.

SSB F

[A]

[C]

SSB

TAC

Figure 1.2.1. Harvest control rules (HCR). F-rule and resulting TAC.

0 SSB

TAC

Figure 1.2.2. Harvest control rules (HCR). Fixed TAC strategy.

The strategies described above were tested for annual and 3-year TAC regimes.

At a second m eeting in Sep tem ber stakehold ers asked for an ad d itional evalu ation of the risks in all H CRs w hen a 15% TAC change lim itation w as ap p lied irresp ective of the stock cond ition (i.e. w hether the stock w as above or below B^trig). Sim u lation testing of this op tion w as p erform ed in the case of the constant TAC and the harvest rate rules.

This d ocu m ent d escribes the technical basis and the resu lts from the sim u lations in ord er that they m ay be evalu ated by ACOM, and p rovid e an answ er to the EU requ est (see Section 3.3 and 4.2). It shou ld be recognized that these sim u lations, w hile they m ay form the basis for a p u tative m anagem ent p lan, d o not in them selves con- stitu te su ch p lan. If a m anagem ent p lan is to be d evelop ed , it w ill requ ire a clarifica- tion of objectives, and a fu ll consid eration of review p eriod , p erform ance m onitoring, and actions to be taken in exceptional circumstances. This will require further interac- tion with stakeholders.

B

trig

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2 Met h o d s

2 .1 Mo d el Co n d i t i o n i n g

2 .1 .1 Si m u l at i o n Set - u p an d In i t i al i z at i o n

The qu antitative evalu ation of the p rop osed H CR are all based on the assessm ent d ataset for N EA Atlantic m ackerel (ICES 2007b). The sim u lation p eriod is 21 years (i.e. u p to and inclu d ing 2027). 1000 iterations are ru n and statistics calcu lated for the sim u lation p eriod 2017 2027. This p eriod w as selected to red u ce the influ ence of the initial stock condition on the results of the HCRs.

In H CM and F-PRESS, the initial p op u lation vector is taken from the short-term p re- d iction inp u t table in the WGMH SA rep ort for 2007. For ages 2 and above these fig- u res are d erived from the final ICA assessm ent. For ages 0 and 1 valu es are d erived from the geom etric m ean of the recru itm ent tim e-series u p to 2003 (for age 0) and the geom etric m ean brou ght forw ard one year by the total m ortality-at-age 0 (age 1). Un- certainty in initial stock size reflecting a CV of 29% on the SSB, was implemented as a log-norm ally d istribu ted age-sp ecific CV (taken from ICA) w ith a log-norm ally d istribu ted year error scaled to give an overall CV of 29% on the SSB. Stock and catch w eights, m atu rities, natu ral m ortality, the F-at-age vector, and the p rop ortions of m ortality p rior to sp aw ning are also as p er the ICA assessm ent. See Annex 4 (F- PRESS results) for the actual values used.

FLR w as cond itioned on the d ata and then p op u lations w ere created u sing ICA w ith sp ecific settings. H ow ever, as this w as d one before the 2007 assessm ent, the sim u lations w ere cond itioned on d ata and an assessm ent that in all resp ects w ere sim ilar to the 2006 assessm ent (ICES 2006), excep t for the selection p attern on old est age (and p lu s grou p ) w hich w as changed from 1.2 to 1.34 to red u ce bias in the sim u lations.

This change in selection is sim ilar to the change su bsequ ently selected in the 2007 assessment (ICES, 2007b).

2 .1 .2 Recr u i t m en t

The p ossibility of im p lem enting a single m od el w as exam ined bu t it w as fou nd that the resu lts w ere very sensitive to the choice of m od el, w hich w as not w ell fou nd ed . This w as d u e to the sm all historical range of SSB. Therefore, a p robabilistic hybrid m od el w as u sed to generate recru itm ent as a fu nction of SSB (Michielsens and McAllister, 2004). To estim ate the p robability of d ifferent fu nctional form s of the S/R relationship a Bayesian analysis w as u sed to evalu ate the com bined u ncertainty in p aram eter estim ates and p robability of the d ifferent fu nctional m od els and d istribu- tions (see Annex 6: Mackerel stock recru it m od els for a fu ll d escrip tion of the m eth- od ology u sed ). A collection of 1000 sets of stock recru itm ent m od el p aram eters w as p rovid ed . Each set sp ecifies a stock recru it relation (Ricker or hockey stick), p aram e- ters a and b of the relation, the d istribu tion (norm al or log-norm al) w ith a variance p aram eter and tru ncation lim its. These sets w ere u sed in sequ ence, one for each of the 1000 iterations in each ru n. Plots com p aring observed and sim u lated recru itm ent for each of the simulation frameworks used can be found in Annexes 2 4.

The historical tim e-series w as tested for au tocorrelation in d eviations betw een years.

This w as fou nd to be slightly negative <0.075 and w ell below significant. Inclu sion of a negative correlation w ou ld have slightly red u ced estim ated risks, bu t becau se the level is w ell below significant it w as d ecid ed not to inclu d e it and not consid ered fu r- ther.

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The resu lting d istribu tion of sim u lated recru itm ent for d ifferent SSB levels is illu s- trated in Figu re 2.1.2a. A com p arison of the cu m u lative d istribu tions of observed and sim u lated recru itm ent valu es for the observed SSB is given in Figu re 2.1.2b. The m atch is a good com p rom ise, better than the one achieved by any single m od el (see Annex 6, Figu res 6 and 7). The m ean sim u lated recru itm ent is less than 3% greater than the observed valu e and the d istribu tion of d eviations is a good m atch to the observed d eviations as d escribed either throu gh a com p arison of cu m u lative d istribu- tions (Figure 2.1.2b) or a Q Q plot (Figure 2.1.2c).

0 1 2 3 4 5

02468101214

Simulated values

SSB

Recruits

0 2 4 6 8 10

0.00.20.40.60.81.0

Observed / Simulated values

Recruitment

Cumulative Probability

2 4 6 8

2468

Q Q plot

Simulated

Observed

Figure 2.1.2.Comparison of observed (red) and simulated (black) recruitment for a) SSB from 100000 to 5M tonnes SSB, b) cumulative probability distributions of observed and simulated values for observed SSB, and c) Q Q plot of observed and simulated values for observed SSB.

Simulated values derived from 1000 models w ith hockey stick and Ricker functional forms and Normal or Log-normal stochastic deviation.

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2 .1 .3 Wei g h t - an d Mat u r i t y- at - ag e

These are fixed valu es, taken from Table 10.2.1 (inp u t from short-term p red iction) in the WGMH SA rep ort for 2007. Variability in m ean w eights-at-age in the catch observed in the d ataset w as inclu d ed in the sim u lations by ad d ing a 2% error to the implementation error (see Annex 4 for a detailed explanation).

There is som e evid ence of sp atial variability in m atu rity-at-age (ICES 2007b) w hich gives rise to <1% variability in p rop ortion m atu re in the p op u lation (by biom ass).

H ow ever, this m ay u nd erestim ate the tru e variability. There is very little inform ation on variability of maturity-at-age by year. Most pelagic stocks show limited variability in m atu ration-at-size, and thu s variability in w eight-at-age is a good su rrogate for variability in m atu rity and has been show n to be sm all (see above). So it is exp ected that true variability in maturity will be similar to the variation in mean weight and be of the order of a few per cent.

Variability in maturity-and w eight-at-age in the stock w ou ld ad d to the variability in relation to the egg survey SSB. With variability in the egg survey estimated as a CV of 22.4%, ad d ing variability at theu p p er end of the p otential range at arou nd 5% w ou ld increase the CV of 22.4% to 24.9%. This change in variability is negligible and has been ignored.

2 .1 .4 Sel ect i o n

Selectivity-at-age w as based on the 2007 WGMH SA rep ort. In F-PRESS, stochastic F- at-age was derived by combining the ICA errors for the F in the terminal year and the selection-at-age vector (Annex 4). In H CM, the im p lem ented selection resu lts from inclu d ing an im p lem entation error w hen d eriving the actu al rem ovals from the stock (see corresponding section in Annex 3).

2 .1 .5 Ob ser vat i o n m o d el

The simulation frameworks differ in the way the observed population is generated.

In the case of FLR the uncertainty in the assessed population was generated by fitting the ICA assessm ent to the sim u lated observations of catch and egg su rvey SSB. The u ncertainty estim ates u sed in the other sim u lation tools w ere generated from the fit assu m ing that the m agnitu d e and au tocorrelation of the observation errors w ere in- d ep end ent of the H CR im p lem ented . The m agnitu d e of the observation error d e- p end s on the relative p osition of assessm ent year and Egg su rvey. The valu e for the CV of SSB to be u sed in H CM and F-PRESS w as 29%, w hich corresp ond s to the m id- dle year of the 3-year Egg survey cycle (Kienzle and Simmonds, 2005, Annex 7).

Using FLR, an au toregressive coefficient of 0.84 w as d erived for a lag of one year (Sim m ond s, Exp loration of som e issu es w ith ICA.WD). A sim p le au toregressive m od el w ith this valu e of gave a higher au tocorrelation at 3-year lag, w hile an alternative of 0.75 retu rns a com p rom ise fit at one and at three years. The d ifference between these two approaches is negligible.

With H CM, error is introd u ced to the stock nu m bers-at-age w ith 2 log-norm al d istribu ted rand om m u ltip liers: one is a year factor (w hich m ay inclu d e bias) and the other is an age factor. A one-year au toregressive m od el w as ap p lied to the com bined errors above (Annex 3). Alpha value was 0.84. The year factor standard deviation was chosen at 0.27, p rovid ing a CV of ap p roxim ately 29% for the resu lting d istribu tion of SSBs in the intermediate year.

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In the F-PRESS m od el, the error in the observation (assessm ent) m od el is assu m ed to exhibit au tocorrelation w ith = 0.75. In ord er to sim p lify m atters, the error term has been generated in ad vance of the sim u lation, w hich rand om ly selects from the generated error tim e-series for each iteration. The form of the annu al error is d escribed in Annex 4.

2 .1 .6 Th e Im p l em en t at i o n Mo d el

These w ere d erived by an algorithm sim ilar to that in the observation m od el, bu t applied to the catch-at-age, and autocorrelation was not included. A 5% implementation bias based on historical rep orted overshoot of the TAC (ICES WG Rep orts 1995 to date) was used in the simulations as base case. Additional levels of 0%, 15%, and 25%

w ere also tested in F-PRESS (Annex 4). Effects of im p lem entation error (5%, 15%, 25%, and 50%) on the m ean realized fishing m ortality w ere exp lored in H CM for the F-rule (Annex 3).

2 .2 Si m u l at i o n t o o l s

Simulations were carried out using three different tools:

FLR (http://flr-project.org/doku.php?id=doc:biblio:evaluation );

F-PRESS (http://www.marine.ie/NR/rdonlyres/8442D077 7E7B-4679-AF0F- CAD7A1B9B2C9/0/FPRESSCodlingKelly2006MIFisheriesInvestigationSerie sNo171.pdf);

H CM (H arvest Control ru le evalu ation for Mackerel) (Skagen 2008, Annex 5).

A brief description of each tool follows.

2 .2 .1 FLR

A sim u lated p op u lation m easu rem ent and H CR loop w as set u p in R u sing FLR. The loop consists of the cu rrent m anagem ent cycle that for N EA m ackerel is a three-year cycle: assessm ent d ata year, interm ed iate year, and TAC year. The assessm ent is tuned using a triennial survey in from 1992 to 2007 and every subsequent third year.

The sim u lation fram ew ork attem p ts to inclu d e a m ore realistic evalu ation loop in- volving a sim u lated su rvey, d ata collection from the fishery, assessm ent, and short- term forecast. The sim u lated p op u lation ind ex is based on an Egg su rvey every 3 years w ith a CV of 22.4%, w hich is the average of the su rvey CVs. Sim u lated catch m easu rem ent is annu al w ith the correlated errors d ocu m ented in the error section above. The assessm ent p ackage ICA and short-term forecasts w ere im p lem ented u s- ing FLICA and FLSTF.ad . The p op u lation m od el is necessarily sim p ler than the ones u sed in the other fram ew orks and consists of a single hockey stick stock recru it relationship p aram eterized on the 2006 ICES assessm ent. FLR sim u lations take m u ch longer to carry ou t than those rep orted in other sections and m ore restricted exp loration w as p ossible. In ad d ition to fu ll analysis, tw o m anagem ent variants w ere tested : one w ith the short-term forecast om itted and TAC set on the basis of the term inal year assessment, and the second omitting subsequent assessments and using only the su rvey every three years. This sim u lation is not u sed to test the fu ll extent of yield , interannu al variability, and risk. It has been u sed to p rovid e inform ation on the sta- tistical p rop erties of the observation m od el u sed in the other fram ew orks. Fu rther, it has been u sed to com p are the F-ru le and the harvest rate ru le u nd er m ore realistic

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error conditions. The flow diagram illustrating the main elements in the framework is given in Figure 2.2.1.

Stock in intermediate year Egg Survey every 3 yrs With error

Stock in data year Catch data with error

ICA Assessment

1)Short Term Projection using TAC rule

No error Stock in TAC year

Stochastic Recruitment Model

3)TAC using Survey SSB Harvest Rate Rule

2)TAC using Survey SSB Harvest Rate Rule

Figure 2.2.1. Standard management cycle implemented in FLR shown for 3 methods: 1) Short-term forecast (STF), 2) Assessment-based harvest rate (AHR), and 3) Survey-based harvest rate SHR.

2 .2 .2 HCM

The program is run as a bootstrap, with the following stochastic elements:

Initial numbers Recruitments Observation noise Implementation noise

P opula tion mode l

O bs e rva tion mode l

De cis ion rule Imple me nta tion

Actua l re mova l by the fis he ry True s tock

Appa re nt s tock

TAC

Mode l s e que nce Da ta flow

Figure 2.2.2. Outline of the HCM program.

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A m ore d etailed d escrip tion of the m od el can be fou nd in Annex 5 H CS and H CM:

Ou tline of p rogram and su brou tines .

2 .2 .3 F- PRESS (Fi sh er i es Pr o j ect i o n an d Eval u at i o n b y St o ch ast i c Si m u l at i o n ) The d esign ofthe F-PRESS m od el is based on the w ork of WGMG (ICES, 2004) and SGMAS (ICES, 2005a) w hich id entified an ap p rop riate fram ew ork for the evalu ation of m anagem ent strategies by sim u lation. The m od el is d esigned as a stochastic sim u- lation tool for evalu ating fisheries m anagem ent strategies and d evelop ing m anage- m ent ad vice. The fram ew ork is p rogram m ed in the op en sou rce R langu age (R Development Core Team, 2003).

F-PRESS is d esigned as a p op u lation p rojection m od el w ith the follow ing characteris- tics and limitations:

Stochastic, Single species, Non-spatial,

Age-structured population, Exponential mortality, F or TAC controlled fishery, Various recruitment models, and Various harvest control strategies.

The cod ing stru ctu re u sed for F-PRESS (op en sou rce, m od u lar p rogram m ing) m eans that the m od el can be read ily ad ap ted to incorp orate sp ecific recru itm ent m od els or harvest control rules.

The F-PRESS op erating m od el u ses the stand ard single-sp ecies age-stru ctu red p op u- lation with an exponential mortality model (as used in most virtual population analy- ses). It d oes not inclu d e any sp atial elem ents or allow for m ixed sp ecies interactions.

N oise and bias can be ad d ed to the p op u lation vectors (initial nu m bers, w eights, m a- tu rities, fishing and natu ral m ortalities). These stochastic elem ents are im p lem ented as m u ltip liers for bias and rand om d raw s from a norm al d istribu tion for noise. Im- p lem entation errors are incorp orated in a sim ilar fashion via a CV and bias on F or TAC.

In ad d ition to the op erating m od el, F-PRESS inclu d es an observation (assessm ent) m od el w here the stock assessm ent p rocess can be sim u lated and a m anagem ent and decision-m aking m od el w ill ap p ly the p rescribed harvest control ru le. Both of these m od el elem ents can inclu d e stochastic behaviou r via a p rescribed noise and bias. In this w ay, it is p ossible to p aram eterize the effects of u ncertainty in the stock assess- m ent p rocess and p henom ena su ch as TAC non-com p liance and d ata errors. The m od el (d eliberately) avoid s a com p lex assessm ent feed back m od el so that all bias and noise introduced in the assessment process can be qualitatively controlled.

F-PRESS inputs are the stock and fishery parameter data with appropriate CV values.

These valu es are often d erived from recent stock assessm ents and stu d ies of p aram e- ter accu racy. The m od el ou tp u t is configu rable and is saved as FLR FLQu ant objects.

In this w ay, the fu nctionality offered by the FLR library (Kell et al., 2007) can be u sed to exp lore the m od el ou tp u t. Inclu d ed in the F-PRESS m od el are a nu m ber of fu nc- tions for graphing and analysing model output.

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START

END INPUT:

Initial data and parameters

FUNCTION (Level B):

Observation / assessment (possible bias and random error are applied to observed F)

FUNCTION (Level B):

Management

(HCR based on changing TAC relative to a target F) 1 INPUT:

TAC

1 OUTPUT:

Fishery data

FUNCTION (Level B):

Population dynamics (exponential mortality, TAC fishery, stochastic recruitment)

2 INPUT:

Fishery data

2 OUTPUT:

Randomised / biased observed F

3 INPUT:

Observed F

3 OUTPUT:

HCR TAC multiplier FUNCTION (Top Level):

Multiple-year stock projection Run order:

- 1 Population dynamics - 2 Observation / assessment - 3 Management.

Repeat loop for n years.

OUTPUT:

Results of single complete

projection

Figure 2.1.3 Flow diagram of the structure of the F-PRESS programme.

F-PRESS was implemented to test forms of the fixed TAC strategy only. The intention of doing this in parallel with FLR and HCM was to verify the results between simulation platforms.

2 .3 Har vest Co n t r o l Ru l es

2 .3 .1 F- r u l e p r o p o sed b y t h e EU Co m m i ssi o n

This rule sets the TAC according to an F-value that is derived as follows:

If SSB > B^trig(p aram eter B), F= F^targ(p aram eter A), bu t TAC in year y shall atm ost d e- viate by C% from the TAC in year y-1.

If SSB < B^trig, the F is set at F= F^targ*SSB/ B^trig, and the constraint on TAC change d oes not apply.

Points of interpretation.

1 ) The action below B^trigis a sim p lification of the requ est, w hich requ ired rebuilding to above B^trigwithin an unspecified time.

2 ) The SSB that is u sed for d ecision w as the SSB p rojected throu gh the intermediate year and into the TAC year.

2 .3 .2 Fi x ed TAC r u l e

This is a rule where the TAC is set as a function of the SSB in the year before the TAC year. The ru le has 3 p aram eters, C^target, Btrig, and C^constraint. It has the follow ing form , where SSB always is the estimated SSB in the year before the TAC year:

If SSB > B^trig, TAC = C^target

If SSB < B^trig, TAC = C^target*SSB/ B^trig

If

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abs{(TAC(y-1)-TAC(y))/TAC(y-1)} > Cconstraint

and (optionally) SSB > B^trig

TAC(y)= TAC(y-1)*(1+C^constraint) if TAC(y)>TAC(y-1) TAC(y)= TAC(y-1)*(1-C^constraint) if TAC(y)<TAC(y-1)

The rule was applied either each year or every three years. In the latter case, the same TAC w as ap p lied u nchanged for the w hole three-year p eriod (H CM), bu t the ap- p roach w ith F-PRESS w as to allow a m axim u m of 15% change in each year. The ru le w as tested w ith and w ithou t the op tion to ap p ly the TAC constraint only at SSB >

B^trig.

2 .3 .3 Fi x ed Har vest Rat e (HR) r u l e

This is another ru le w here the TAC is set as a fu nction of the SSB and the TAC in the year before the TAC year. Basically, the TAC is set as a fraction (the H R) of the observed SSB. The ru le has 3 p aram eters, H R^target, B^trig, and Cconstraint. It has the follow ing form, where SSB always is the estimated SSB in the year before the TAC year:

If SSB > B^trig, TAC = HR^target*SSB

If SSB < B^trig, TAC = HR^target*SSB*SSB/B^trig

If

abs{(TAC(y-1)-TAC(y))/TAC(y-1)} > Cconstraint

and (optionally) SSB > B^trig then

TAC(y)= TAC(y-1)*(1+C^constraint) if TAC(y)>TAC(y-1) TAC(y)= TAC(y-1)*(1-C^constraint) if TAC(y)<TAC(y-1)

2 .4 Mo d el val i d at i o n

The m ain id ea of testing H CR w ith d ifferent fram ew orks w as to d em onstrate that the resu lts are reliable and that there are no p rogram m ing m istakes. Also, it m ay be u se- fu l for the ind ivid u al labs involved in this exercise to valid ate the softw are they have d evelop ed . H ow ever, there are alternative form u lations for m od elling som e asp ects of the d ynam ics w ith d ifferent tools. The ap p roach taken w as to m inim ize the d ifferences w here p ossible and com p are m od els w ith the sam e settings to valid ate the cod- ing and evaluate the impact of any differences.

2 .5 Man ag em en t scen ar i o s

The H CRs d escribed in the p reviou s section w ere exp lored u nd er the follow ing conditions:

A one- or three-year m anagem ent cycle on d ecision-m aking and implementation of the TAC;

B^trig between 2.0 Mt and 3.5 Mt;

Year-on-year constraint on change in TAC inclu d ed or exclu d ed . In cases w here 15% year-on-year restrictions w ere allow ed these w ere

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im p lem ented for all years irresp ective of the SSB in relation to the trigger biom ass. For the three-year regim e, tw o ap p roaches w ere taken: A) The TAC w as fixed d u ring the p eriod (H CM) and the constraint w as only ap p lied at the beginning. B) The 15% constraint w as im p lem ented over the p eriod u ntil the requ ired red u ction or increm ent w as achieved (u p to a m axim u m of 45% over 3 years, i.e. 20% red u ction im p lies an initial 15%

constraint followed by 5% 1 year later (F-PRESS and FLR)).

A su m m ary of the cond itioning op tions consid ered in each sim u lation tool is p ro- vided in the following table:

Table 2.2.1 Conditioning options applied under each HCR strategy simulated by tool type.

Sim Tool HCR Strategy Population

model SSB measure from Constraint above

Trigger Period of rule Correl Errors SSB trig TAC Bias Iteratio ns

F-PRESS Target TAC Assessment none or 15% 1 & 3 yes 2000-3500 5, 15, 25%

400-750 in steps steps 500 1000

of 50 Recruitment:

HCM Target TAC Ricker/hockey Assessment range 0, 5, 15, 25; 1 & 3 yes 2000-3500 5, 15, 25%

400-750 in steps stick with gradual change steps 500

of 50 normal/log-normal or abrupt. 1000

F-based errors Assessment 1

0.14 - 0.22 in Initial N Short-term forecast steps of 0.02 from 2007 Survey

Harvest rate assessm. Assessment 1 & 3

0.14 - 0.22 in steps of 0.02

FLR F-based Conditioned Short-term forecast none or 15% 1 & 3 full feed-back 2300 or 5% 100

on the data Assessment 3000

R hockey-stick Survey

2 .6 Per f o r m an ce St at i st i cs

In the initial p hase, it isassu m ed that the first TAC d ecision is m ad e som e tim e d u r- ing the initial year, so that the first d ecid ed TAC ap p lies to the year after (cou nted as year 1). In year 0, w hich corresp ond s to 2007, a fixed catch of 499 kt is assu m ed . The su m m ary statistics are p resented for years 10 to 20 (2017 2027), so that the effect of the assumptions in the initial phase is small.

The output statistics presented apply to years 10 20 in the simulations:

Yr/Yr lim it; yes m eans a m axim u m of 15% change annu ally (im p lies a maxim u m 45% change over 3 years w here H CR(yr) =3), no m eans no lim it on the TAC change.

SSBtrig is the trigger point below which the HCR changes.

HCR(yr) is the period of the HCR. This refers to the management cycle.

Catch is rep orted as average and p ercentiles in kt. This is calcu lated as a median for HCM.

IAV is Interannu al variability, calcu lated as the m ean absolu te change in TAC from year to year, relative to the p reviou s year s TAC. This is calculated as a mean and expressed in percent.

F is reported as average and percentiles.

2017 2027 is the average SSB over this period.

2027 is the average SSB in this year (the terminal year of the simulations).

TAC variation; Evts is the average number of times the TAC is changed.

TAC variation; Evts+ is the average number of times the TAC is increased.

TAC variation; Evts is the average nu m ber of tim es the TAC is d ecreased . TAC variation; Avg Inc is the average increase in the TAC in kt (w hen the TAC is increased).

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TAC variation; Avg Dec is the average decrease in the TAC in kt (when the TAC is decreased).

Risk is the average nu m ber of tim es w here SSB is below the reference level expressed as a percentage.

Percentage catch is the fraction by nu m ber-at-age and above (these are p roxies for the p rop ortion of the p op u lation in com m ercial grad es G4 and G6).

Risk of d ep letion: Fraction of iterations w here at som e tim e the d ecid ed TAC cou ld not be taken w ith a fishing m ortality of 3.0 (rep orted for H CM only).

Lim Once: Probability that the SSB w ill be below the lim it at least once in the time period year 10-20. Added to some runs with HCM.

2 .7 Ref er en ce p o i n t s

The grou p exam ined the ju stification of existing reference p oints and recognized that the existing biom ass reference p oint (B^pa) w as based on assessm ents p erform ed p rior to recent m ajor revisions of the p ercep tion of the stock. Exam ination of the existing reference p oints in the light of the m ost recent benchm ark assessm ent ind icated a m i- nor revision. H ow ever, based on criteria for revision of reference p oints, the grou p agreed that a minor revision was not appropriate.

To be in accordance with the basis for the advise, the risk associated with the harvest ru les in selected cases is p resented as the p robability that SSB w ill be below the lowest observed level of 1.67 ~ i.7 Mt.

The p resent fishing m ortality lim it reference p oint is based on a p reviou s estim ate of F^loss. A d eterm inistic F^loss= F^lim= 0.42 w as estim ated by the grou p based on 1972 2003 d ata. This estim ate w as based on a segm ented regression fit to stock and recru itm ent d ata and Sp aw ning Biom ass p er Recru it calcu lations. The estim ate w as sensitive to the 2002 data pair and that is reflected in the estimates obtained by bootstrapping.

The estimate of F^pa is currently derived from F^lim taking into account the error in the F estim ate, w hich is estim ated p oorly (p articu larly the m ost recent F). Work carried ou t in 2005 and rep orted at the WGMH SA that year (ICES 2005b) looked at the p recision of the assessm ents u nd er a variety of assu m p tions. Estim ates of the variability in F in the term inal year exp ressed as stand ard d eviation of ln(F^assess/F^true) resu lted in a stan- d ard d eviation of 0.36, (Sim m ond s, 2007). Taking that into accou nt w ou ld resu lt in F^pa= 0.23, im p lying a su bstantial revision to the existing F^pa. There are ind ications p rovid ed below in Section 3.2 that this valu e is consistent w ith the p recau tionary ap- p roach. It is su ggested that the WGWIDE exam ines existing F reference p oints in the light of these findings.

THERE IS NO BIOLOGICAL BASIS FOR DEFINING B^LIM.

B^PA BE SET AT 2.3^{MILLION T}.

Flim is 0.26, the fishing mortality estimated to lead to potential stock collapse.

Fpa be set at 0.17. This F is considered to provide approximately 95% probability of avoiding Flim, taking into account the uncertainty in the assessments.

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3 Resu l t s

3 .1 Mo d el val i d at i o n

The results for the unconstrained fixed TAC rule from the HCM and F-PRESS models are com p ared (Figu re 3.1.1) for 3-and 1-year TAC p eriod s, show ing that the d ifferences between frameworks are negligible.

Figu re 3.1.2 com p ares associated risks for the u nconstrained target TAC ru le. Sm all d ifferences in cond itioning betw een m od els reflect in d ifferences in risk of the ord er of 2 3% on average when options resulting in risks of <50% were considered.

Figure 3.1.1. Fixed TAC strategy. Comparison of performance between F-PRESS and HCM.

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Figure 3.1.2. Fixed TAC strategy. F-PRESS vs. HCM associated risk to SSB = 2.3 million tonnes for the HCR evaluated.

Perform ance statistics corresp ond ing to the three H CRs evalu ated are p resented in Tables 3.1 to 3.8 for a range of targets and trigger SSB 2.3 and 3 m illion tonnes. For the fixed TAC rule, results from F-PRESS and HCM are presented in Tables 3.5 to 3.8.

These resu lts are strictly com p arable and w ere intend ed for valid ation of the sim u lation tools used.

3 .2 In t er p r et at i o n o f accep t ab l e r i sk

The EU requ est requ ires strategies that conform to the p recau tionary ap p roach and have a low risk of stock d ep letion along w ith criteria on m axim izing and stabilizing yield . In selecting strategies, w e need to id entify those that w ou ld conform to these p recau tionary requ irem ents. ICES norm ally ad vises that the p recau tionary ap p roach im p lies avoid ance of the p oint at w hich recru itm ent is im p aired (B^lim) w ith a high p robability (95%). For N EA m ackerel, B^limis not d efined and only B^pais available as an SSB reference p oint. Avoid ing B^paw ith a 95% p robability w ou ld ensu re a low risk of d ep letion and w ou ld be p recau tionary bu t w ou ld also be m ore restrictive than ICES has p reviou sly ad vised for other stocks. The N EA m ackerel stock has not exhib- ited red u ced recru itm ent for SSBs d ow n to 1.67 Mt; how ever, recru itm ent below this level is u nknow n. It cou ld be consid ered p recau tionary to avoid this biom ass w ith a high p robability, thu s avoid ing d ep letion w ith a high p robability. The relationship betw een the p robability of SSB being below 1.67 Mt, the p robability of SSB being below B^pa,and equ ilibriu m biom ass can be established by taking into accou nt the d istribu tion of an assessm ent error w ith a CV of 29%. Som e selected valu es of p robability are given in the table below.

%PROBABILITY SSB <B^PA=2.3M^T 5% 15% 20% 50%

% Probability SSB <1.67 Mt 1.6 4.5 6.0 17.2

Equilibrium SSB 4.40 3.29 3.04 2.30

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The above text table show s that to avoid 1.67 Mt w ith a 95% p robability requ ires an equilibriu m biom ass of arou nd 3.1 Mt and a p robability of avoid ing B^paclose to 15%.

Figu re 3.2.1 show s the relationship betw een m ean SSB, catch, and realized F at d ifferent p robabilities and show s that long-term m ean Fs below the p u tative F^paof 0.23 are compatible with avoidance of B^paat this level of probability.

It is su ggested that strategies that have p robabilities of SSB < B^palow er that 15%

w ou ld be regard ed as p recau tionary and shou ld p rovid e a high p robability of avoiding stock depletion.

Another op tion is to consid er the p robability that SSB 1.67 Mt at least once in the 10 year period under consideration. The value 1.67 Mt is he lowest SSB in the time series in the estimate by the 2007 WGMHSA.

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Figure 3.2.1 Relationship between mean SSB, mean Catch, and mean realized F for strategies with different probabilities (as indicated w ith colors) of falling below 1.67Mt at least once during the time period from year 10 to year 20. Strategies w ith low probability of SSB <1.67 Mt)lead to real- ized F less than 0.23 .

0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25 0.275 0.3 2500

2750 3000 3250 3500 3750 4000 4250 4500 4750

SSB and Realized F

<1 1-5 5-10

>10

Realized F

SSB

0.05 0.1 0.15 0.2 0.25 0.3

400 425 450 475 500 525 550 575 600 625 650 675

Catch and Realized F

<1 1-5 5-10

>10

Realized F

Catch

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3 .3 F- r u l e

Results of simulations with the F-rule as proposed by the EU Commission.

H CM w as u sed to screen over ranges of valu es for the p aram eters Target F (A), Trig- ger SSB (C), and Percentage constraint on TAC variation (B). The constraint on TAC variation was only applied when it led to an SSB above the trigger biomass.

The resu lts are p resented as m eans over the years 10 20 and over 1000 iterations for each com bination of the p aram eters. These resu lts are p resented in Table 3.9. The results are illustrated graphically in Figures 3.3.1 3.3.3. The main trends in these results can be summarized as follows:

The risk to B^paincreases w ith increasing Target F, and is red u ced w ith increasing Trigger SSB. A stronger constraint red u ces the risk. The realized catch increases w ith increasing Target F, and w ith increasing Trigger SSB. A stronger constraint on the TAC variation d ecreases the catch. The interannu al variation increases w ith increasing Trigger SSB and w ith increasing Target F. A stronger constraint on the IAV variation reduces the interannual variation.

H ence, to obtain m axim u m m ean catch, a high target F, a high trigger biom ass, and a w eak constraint on TAC variation w ill be requ ired . This w ill lead to a high risk and a high interannu al variation of the TACs. The m axim u m stability is achieved w ith a low trigger SSB, a low Target F, and a strong constraint on TAC variation. This w ill also lead to a low risk, but the catches will be low.

Figure 3.3.1. Realized catch with F-rule.

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Figure 3.3.2. Risk with F-rule.

0.12 0.18 0.24 0.3

2000 2500 3000 3500

Inter-Annual Variability 5% change constraint

<10%

10-20%

20-30%

>30%

Target F

Trigger SSB

0.12 0.18 0.24 0.3

2000 2500 3000 3500

<1 0 % 1 0 -2 0 % 2 0 -3 0 %

>3 0 %

Target F

Trigger SSB

0.12 0.18 0.24 0.3

2000 2500 3000 3500

<10%

10-20%

20-30%

>30%

Target F

Trigger SSB

0.12 0.18 0.24 0.3

2000 2500 3000 3500

<10%

10-20%

20-30%

>30%

Target F

Trigger SSB

Figure 3.3.3. Interannual TAC variability.

0.12 0.18 0.24 0.3

2000 2500 3000 3500

Risk to SSB<2300 5% change constraint

<1 1-5 5-10

>10

Target F

Trigger SSB

0.12 0.18 0.24 0.3

2000 2500 3000 3500

Risk to SSB<2300

15% change constraint

<1 1 -5 5 -1 0

>10

Target F

Trigger SSB

0.12 0.18 0.24 0.3

2000 2500 3000 3500

<1 1-5 5-10

>10

Target F

Trigger SSB

0.12 0.18 0.24 0.3

2000 2500 3000 3500

<1 1-5 5-10

>10

Target F

Trigger SSB

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To show the trad e-off betw een stable catches and su stained yield , the su bset of the parameter options that was associated with a risk to B^pa in the range 10 15% was consid ered fu rther (Figu res 3.3.4 to 3.3.6). This p roced u re selects op tions w ith high catches that conform to the p recau tionary ap p roach. Op tions w ith low er risks are associated w ith low er catches. With this level of risk, catches are in the range of 580 640 thou sand tonnes and the IAV betw een 10% and 30%. The target F is in the range of 0.24 0.30. The figure should allow managers to select the parameter option according to their p referred trad e-off betw een stability and catch, w ith this level of risk.

Som e exam p les of p aram eter choices are given in the text table below . One ou t- stand ing resu lt is that to have a catch near the m axim u m , the IAV has to be qu ite high, w ell above 15%. More stability requ ires su bstantial red u ction in catch, w hich in general also will imply a lower risk.

A com p lete list of the H CR p aram eters exp lored and associated p erform ance statistics is shown in Table 8.9.

570 580 590 600 610 620 630 640

0 15 30 45

Catch and IAV for different levels of constraint Cases with 10 - 15% risk to Bpa

5%

10%

'15%

20%

Catch

IAV %

Figure 3.3.4. Mean catch and interannual variability for all F-rule options that lead to a risk to Bpa

betw een 10% and 15%. The colours indicate the level of the constraint on TAC variation in the F- rule.

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570 580 590 600 610 620 630 640

0 15 30 45

5%

10%

'15%

20%

Catch

IAV %

570 580 590 600 610 620 630 640

0 15 30 45

5%

10%

'15%

20%

Catch

IAV %

0.2 0.22 0.24 0.26 0.28 0.3

2000 2500 3000 3500

Realized catch 10% change constraint

575-599 600-624 625-650%

Target F

Trigger SSB

0.2 0.22 0.24 0.26 0.28 0.3

2000 2500 3000 3500

Realized catch 20% change constraint

5 7 5 -5 9 9 6 0 0 -6 2 4 6 2 5 -6 5 0 %

Target F

Trigger SSB

Figure 3.3.5. Mean catch as a function of Trigger SSB, Target F, and the level of constraints for the range of F-rule options that lead to a risk to Bpa betw een 10% and 15%. The colours indicate the level of the mean catch.

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0.2 0.22 0.24 0.26 0.28 0.3

2000 2500 3000 3500

10-14 15-19 20-29

>30

Target F

Trigger SSB

0.2 0.22 0.24 0.26 0.28 0.3

2000 2500 3000 3500

10-14 15-19 20-29

>30

Target F

Trigger SSB

0.2 0.22 0.24 0.26 0.28 0.3

2000 2500 3000 3500

10-14 15-19 20-29

>30

Target F

Trigger SSB

0.2 0.22 0.24 0.26 0.28 0.3

2000 2500 3000 3500

10-14 15-19 20-29

>30

Target F

Trigger SSB

Figure 3.3.6.Interannual variability as a function of Trigger SSB, Target F, and the level of con- straints for the range of F-rule options that lead to a risk to B^pa between 10% and 15%. The colours indicate the level of actual interannual variation (IAV).

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Table 3.3.1. F-rule.Set of HCR parameters that result in highest average catch, low est IAV and highest catch with a moderate IAV. The associated risk to Bpa is always below 15%.

P^ERC (B)

T^ARG F (A)

T^RIG. SSB(C)

C MEAN

C10 C50 C90 F^MEAN F10 F50 F90 SSB MEAN

IAV 4+ 7+

Minimum IAV

5 0.28 2300 583 406 579 755 0.19 0.10 0.19 0.26 3313 10.3 85 44

High catch with IAV<15%

5 0.30 2400 593 413 593 755 0.20 0.11 0.20 0.28 3202 12.1 84 42

High catch with IAV<20%

15 0.24 2300 631 493 626 788 0.21 0.16 0.21 0.27 3046 18.4 84 41

Max.

catch

20 0.24 2400 639 495 634 787 0.22 0.17 0.22 0.28 2969 22.7 83 40

The IAV is a measure of the mean relative change in TAC. The actual development of the catches is m ore variable, d ep end ing on variations in the natu ral cond itions. To illu strate the link betw een IAV and p ossible trajectories of the catch, the evolu tion of the first 20 ou t of 1000 iterations is show n in Figu re 3.3.7 for each of the exam p les show n in the Table above. Typ ically, scenarios w ith a low IAV have a grad u al increase in the TAC u ntil it has reached a stage w here a d rastic red u ction is need ed (and allow ed ). This is a resu lt of a relatively high target F that is cou nteracted by the constraint, bu t tend s to force the TACs u p w ard s. The asym m etry in the p erform ance, i. e. a grad u al increase and an abru p t d ecrease lead s to a m od erate risk d esp ite the high target F.

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0 5 10 15 20

0 300 600 900 1200 1500

F-rule: TAC trajectories

Target F=0.28; Trigger SSB = 2300, Constraint 5%

Year

TAC

0 5 10 15 20

0 300 600 900 1200 1500

Year

TAC

0 5 10 15 20

0 300 600 900 1200 1500

Year

TAC

0 5 10 15 20

0 300 600 900 1200 1500

Year

TAC

Figure 3.3.7. TAC trajectories corresponding to four sets of parameters A, B, and C in the F-rule.

The first 20 of 1000 realizations of the rule are shown in each panel.

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3 .4 Har vest r at e r u l e

This ru le w as exp lored by both H CM and FLR. The ru le w as ap p lied either each year or every three years. For the 3-year TACs, H CM im p lem ented the constraint in the first year and then the TAC rem ained u nchanged for the w hole three-year p eriod , w hile FLR allow ed a 15% change every year. The ru le w as tested w ith and w ithou t the option to apply the TAC constraint only at SSB > SSB^trigger.

The exp loration w ith H CM su ggested that harvest rates (H R) associated w ith risk to B^pabetw een 10 and 15% are generally betw een 0.30 0.20 if the TAC is revised every year and 0.10 0.24 if it is revised only every three years (Figu res corresp ond ing to these resu lts are show n in Annex 3). A strong constraint requ ires a low er H R, and corresp ond ingly low er catches to keep the risk low , in p articu lar if the constraint ap- p lies at all levels of SSB. The catches associated w ith a low risk are low er w ith a 3- year ru le than w ith a one-year ru le. There is a trad e-off betw een stability and average catch across all op tions; if m ore year-to year variation is accep table, the average catch can be higher.

Figu res 3.4.1 to 3.4.6 illu strate the p erform ance of harvest rate ru les for a range of trigger SSB, TAC constraints, and harvest rates. Also shown are results for:

1- and 3-year TAC periods,

TAC constraint applied only when SSB > B^trig and TAC constraint applied at all levels of SSB.

When the constraint is ap p lied only w hen SSB>SSB^trigger, the realized catch is generally higher than w hen the constraint is ap p lied at all levels of SSB (Figu res 3.4.1 and 3.4.4). Sim ilarly, the associated risk is higher w hen the constraint is ap p lied alw ays (Figs. 3.4.2 and 3.4.5). These effects are m ore p ronou nced w hen the constraint is strong and for 3-year TACs. With a 15% constraint and risk to B^pabetw een 10 15%, the average catch is in the ord er of 620 640 thou sand tonnes for an annu al ru le and betw een 590 and 560 thou sand tonnes for a tri-annu al ru le. The trade-offs betw een catch and stability in a H R-ru le are illu strated in Figu re 3.4.7 for selected scenarios.

The selection resu lts in a risk to B^pabetw een 10% and 15%. The p erform ance statistics associated with the full range of HCR parameters explored are shown in Annex 8.

The exp loration w ith FLR w as u sed to com p are p erform ance w ith the F-ru le. Resu lts are discussed in Section 4.1.