Harvest control rules for data limited stocks using length-based reference points and survey biomass indices

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ContentslistsavailableatScienceDirect

Fisheries

Research

jo u r n al h om ep ag e :w w w . e l s e v i e r . c o m / l o c a t e / f i s h r e s

Harvest

control

rules

for

data

limited

stocks

using

length-based

reference

points

and

survey

biomass

indices

Ernesto

Jardim

a,b,∗

_,

_Manuela

_Azevedo

a,1

_,

_Nuno

_M.

_Brites

a,c,1,2 a_IPMA,_Instituto_Português_do_Mar_e_da_Atmosfera,_Av._Brasília,_1449-006_Lisboa,_Portugal

b_European_Commission,_Joint_Research_Centre,_Institute_for_the_Protection_and_Security_of_the_Citizen,_Maritime_Affairs_Unit,_TP_051,₂₁₀₂₇_Ispra,_VA,_Italy c_Departamento_de_Matemática,_Centro_de_Investigaç_ão_em_Matemática_e_Aplicaç_ões,_Instituto_de_Investigaç_ão_e_Formaç_ão_Avanç_ada,_Universidade_de Évora,RuaRomãoRamalho,59,7000-671Évora,Portugal

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received22April2014 Receivedinrevisedform 18November2014 Accepted20November2014 HandlingEditorA.E.Punt Availableonline24December2014 Keywords:

Datalimitedstocks Risk

Surveyindices Lengthfrequencies Harvestcontrolrules LifeHistory

a

b

s

t

r

a

c

t

Therearealargenumberofcommerciallyexploitedstockslackingquantitativeassessmentsandreliable estimatesofstockstatus.ProvidingMSY-basedadviceforthesedata-limitedstocksremainsachallenge forﬁsheriesscience.Formanydata-limitedstocks,catchlengthcompositionand/orsurveybiomass indicesorcatch-per-uniteffort(cpue)areavailable.Informationonlifehistorytraitsmayalsobeavailable orborrowedfromsimilarspecies/stocks.Inthisworkwepresentthreeharvestcontrolrules(HCRs), drivenbyindicatorsderivedfromkeymonitoringdata.Theseweretestedthroughsimulationusingtwo exploitationscenarios(developmentandover-exploitation)appliedto50stocks(pelagic,demersal,deep seaspeciesandNephrops).WeexaminetheperformanceoftheHCRstodelivercatch-basedadvicethat isriskadverseanddrivesstockstoMSY.TheHCRwithabiomassindex-adjustedstatusquocatch,usedto providecatch-basedadviceforseveralEuropeandata-limitedstocks,showedthepoorestperformance, keepingthebiomassatloworverylowlevels.TheHCRsthatadjustthestatusquocatchbasedonthe variabilityofthebiomassindextimeserieswasabletodrivemostofthestockstoMSY,showinglow tomoderatebiologicalrisk.Therecoveryofbiomassrequiredasymmetricconﬁdenceintervalsforthe biomassindexandlargerdecreasesinstatusquocatchthanincreases.TheHCRbasedonlengthreference pointsasproxiesfortheFSQ/FMSYratiowasabletoreversethedecreasingtrendinbiomassbutwith

levelsofcatchbelowMSY.ThisHCRdidnotpreventsomeofthestocksdecliningwhensubjectto over-exploitation.Fordata-limitedstocks,theempiricalHCRstestedinthisworkcanprovidethebasisfor catchadvice.Nevertheless,applicationstoreallifecasesrequiresimulationtestingtobecarriedoutto tunetheHCRs.Ourapproachtosimulationtestingcanbeusedforsuchanalysis.

1. Introduction

The majority of worldwide commercially exploited ﬁsh and

shellﬁshstocksdonothaveaformalstockassessment,dueto

insuf-ﬁcientdatatoestimatestocksizesandﬁshingmortality(Rosenberg

etal.,2014).IntheNortheastAtlantic,morethanhalfofthe200

stocksforwhichICESprovidesadvicelackaquantitative

assess-ment and estimatesof stock status (ICES,2013a). Thesestocks

∗ Correspondingauthorat:EuropeanCommission,JointResearchCentre,Institute fortheProtectionandSecurityoftheCitizen,MaritimeAffairsUnit,TP051,21027 Ispra,VA,Italy.Tel.:+390332785311.

E-mailaddresses:ernesto.jardim@jrc.ec.europa.eu(E.Jardim),

mazevedo@ipma.pt(M.Azevedo),brites@uevora.pt(N.M.Brites). 1 _Tel.:₊₃₅₁₂₁₃₀₂₇_000.

2 _Tel.:₊₃₅₁₂₆₆₇₄₅_370.

areclassiﬁedbyICESasdata-limitedstocks(ICES,2012a).Inthe

absenceofestimatesofstockstatus,providingquantitative

MSY-basedadviceremainsachallengeforﬁsheriesscience,whilefor

managementbodiesitcontinuestobeakeytopicforincreasing

thesustainableharvestingofmarineresources(Anon.,2013,2008,

2007,2006).

Thelastﬁveyearshaveseenanincreaseinthedevelopment

andtestingofassessmentmethodstoestimatesustainableyields

andharvestlevelsfordata-limitedstocks(Rosenbergetal.,2014;

MartellandFroese,2013;WetzelandPunt,2011;MacCall,2009).

Thecategoryofdata-limitedstocks,inthesenseofstocks

with-outananalyticalassessment,includesstockswithaconsiderable

amountofinformation,althoughnotalwaysavailableorcompiled.

Forexample,lifehistoryparametersexistformoststocksexploited

commercially(seeﬁshbase.org),lengthfrequenciesoflandingsare

cheaptocollect,and scientiﬁc surveyscatchmore speciesthan

thoseforwhichabundanceindicesaretraditionallyderived.Insuch

http://dx.doi.org/10.1016/j.ﬁshres.2014.11.013

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casestheproblemtendstoberelatedtothedifﬁcultytoevaluate

thequalityofthedata,and/orthecostsofprocessingthe

informa-tion,and/ortheshorttimeseriesavailable.InEuropeanwaters,all

stockscaughtbyEuropeanﬂeetsarecoveredbytheEuropeanData

CollectionFramework(CouncilRegulation(EC)No199/2008)and,

hence,suchinformationexists.Moreover,datasetsaregrowing

everyyear,whichwillcontributetomovingstocksupwardsinthe

levelofinformationavailable.

GeromontandButterworth(2014)usedsimulationtestingto

checktherobustnesstouncertainties aboutresourcedynamics,

ofsimpleempiricalTAC-basedharvestcontrolrules(HCRs).These

authorsconsideredtwodata-poorscenariosfordataavailability:

a data-limited scenarioin which the stock had historical catch

data and information onthe mean length of the catch, and a

data-moderatescenariowherea directindexofabundancewas

also available for thestock. The empirical management

proce-duresinvestigatedbyGeromontandButterworth(2014)setfuture

TACsbyadjustingthepreviousyear’sTACupwardsordownwards,

dependingonwhethertherecentmeanlengthisaboveorbelow

atargetmeanlength.Inthecaseofthedata-moderatestocks,the

TACadjustmentwasbasedontherecentslopeoftheabundance

series(cpue)andonthedifferencebetweentherecentcpueanda

targetlevel.

Since 2012, ICES hasapplied a framework to provide catch

advicefortheEuropeandata-limitedstocks(ICES,2013a)within

aprecautionaryapproach.Forstockswherehistoricalcatchdata

andsurveysorotherrelativeabundanceindicesareavailable,catch

adviceisbasedontheapplicationofanHCRusingbiomassor

abun-danceindexadjustedstatusquocatches(ICES,2012b).Withinthis

HCR,itisquitecommontoadoptacomparisonoftheaveragesof

thetwomostrecentindexvalueswiththethreeprecedingones,

althoughthenumberofyearstobeusedtocomputethese

aver-agesmayvaryamongstocks,inordertoaccountforinter-annual

variabilityofsurveysorcpueseries.Simulationtestinghasshown

thatthisHCRdoesnotensureconservativecatchadvicewhena

stockisover-exploited,whileit’sperformancedeteriorateswhen

awell-managedstockbecomesover-exploited(ICES,2013b).

The work presented here has three main objectives: (i) to

developandtestgenericHCRsforstocksforwhichtheamountand

qualityofdataisinsufﬁcienttoperformquantitativeassessments;

(ii)tounderstandthemechanismsthatdrivetheperformanceof

theseHCRs;and(iii)tosuggestasimulationprocedurebasedon

ManagementStrategiesEvaluation(MSE;Butterworthetal.,1997;

Cooke,1999;ButterworthandPunt,1999;Kelletal.,2005;Punt andDonovan,2007)tobeusedfordatalimitedstocks.

ThesimulationprocedureandtheHCRsproposedhereprovide

aframeworkfordesigningandtestingmanagementplansfordata

limitedstocks.However,whendealingwithareal-lifeapplication,

itis importanttotune thecandidate HCRstothespeciﬁcstock

andﬁshery(notattemptedhere)andtestitsimplementationwith

simulations.

2. Methods

Twoalternativestotheharvestcontrolrulesetby(ICES,2012a)

weredeveloped.Oneusessurveyinformationandthestatistical

characteristicsofthebiomassindex,whiletheotherusescatch

lengthcompositionsandlifehistoryparameters.TheseHCRswere

developedtakingintoaccountcommonindicatorsderivedfrom

ﬁsheriesmonitoringprogrammesandinthemselvesdeﬁne

differ-entlevelsof datalimitation.Survey informationisindependent

oftheﬁsheryandconstitutesa directobservationofthetrends

inbiomass.It’sanexpensivetypeofinformation,butalsoagood

sourceaboutthetrendsinbiomass,ifthesurveyisperformed

fol-lowingthegoodpracticesofdatacollectionandtheindexderived

with sound statistical methods. On the other hand, the length

distributionsofthecatchis ﬁshery-dependentinformation. Itis

cheapertocollectthansurveyinformation,andoncealinkis

estab-lishedbetweenanexploitedstock’sexpectedlengthcomposition

and itsspawningpotentialratio(Hordyket al.,2014)it

consti-tutesanindirectobservationofthestockstatus.Duetotheirdata

requirements,theseHCRscanbeappliedtoawiderangeofstocks

withdistinctlevelsofdatalimitations,standingbetween

catch-onlytypeapproaches(MartellandFroese,2013)andfullanalytical

approaches.

The simulation procedure uses life history parameters and

information about the ﬁshery’s selectivity to create a

simula-tionenvironment fortestingHCRs.Althoughsomeassumptions

arerequired,thesesimulationscanprovideinsight intothe

rel-ative effect of different HCRsand theirrobustness to common

uncertainties, like those about stock recruitment relationships,

implementationerror,etc.

2.1. SimulationsandMSE

Thestocksusedinthecurrentstudyweresimulatedbasedon

lifehistorytraitsthatlooselyrepresentthebiologyofthespecies

(Table1),coveringawiderangeoflifehistorycharacteristics.There

were50stocks:3pelagicstocks(2species:HerringandSandeel),

36demersalstocks(17species:Cod,Haddock,Whiting,Pollack,

Megrim, Anglerﬁsh,Plaice, Sole,Striped redmulet,Lemon sole,

Brill,Dab,Redﬁsh,Goldenredﬁsh,Greenlandhalibut,Turbotand

Witch),6deepseastocks(4species:Ling,Blueling,Greater

sil-versmeltandRoundnosegrenadier)andNephropsintheshellﬁsh

grouping(Table1).ThelifehistoryM/Kratioofthesimulatedstocks

rangedfrom1.09to4.20,withtheexceptionofthedeepseastock

‘rng-comb’thatpresentedahighM/Kratioof8.98(Table1and

Fig.1).

An age-structuredpopulationdynamics model with

recruit-mentgovernedbytheBeverton–Holtstock-recruitfunctionwith

steepness,h,of0.75(tosimulatestockswithmedium

productiv-ity)andvirginbiomass,Bv,of1000twasadopted.Thehvaluewas

adaptedfromMyersetal.(1999),whoindicatedamedianof0.71.

NaturalmortalityforeachstockwascomputedfollowingGislason

etal.(2010)andwasassumedtobetime-invariant.Fishgrowth

wasmodeledwiththevonBertalanffyfunction,withparameter’s

givenbyICES(2012b).Fleetselectivitywasmodeledwithadouble

normaldistribution(Hilbornetal.,2003)withthemodeequalto

thetheageof50%maturity,whilesurveyselectivitywasmodeled

withanasymptoticallyﬂattopcurvewithmaximumretentionat

age10.Fig.2showsanexampleforastockwithageof50%

matu-rityof5.4years.Bothselectivityfunctionsweresetconstantover

time.

Simulationswereperformedfortwodistincttrendsinﬁshing

mortalitytotesttheHCR’sperformancein‘development’and

‘over-exploitation’ ﬁshery scenarios. For the‘development’ phase the

stocksweresubject,duringyears−14to0,toalinearincreasing

ﬁshingmortalityfromF=0to2FMSY.The‘over-exploitation’phase

wasobtainedbykeepingﬁshingmortalityat2FMSY for25years

(years:−24to0),althoughonlythelast15(years:−14to0)were

usedforthesimulationstudy.Inbothcases,theHCRswereapplied

for25years(years:1–25).

Uncertaintywasintroducedin:

• theoperatingmodelconditioning,throughcatch-at-ageandthe

stock-recruitmentrelationship;

• theobservationerrormodel,throughtheobservationoftheindex

ortheratioM/K;

• theimplementationerrormodel,throughtherealizedcatches,

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Table1

Lifehistoryparametersusedtosimulatestocks.aandb:length-weightrelationshipparameters;a50:ageof50%retention;a0,K,L∞:vonBertalanffygrowthfunction parameters;FMSY:ﬁshingmortalitythatproducesMSYcatchesandM:naturalmortality.

Stockcode Group a b a50 a0 K L∞ FMSY M

ang-78ab Demersal 0.00001 3.000 5.680 −0.100 0.121 162.000 0.095 0.217 ang-ivvi Demersal 0.00001 3.000 4.320 −0.100 0.160 150.000 0.121 0.261 arg-comb-exVa Deep 0.01000 3.000 3.569 −0.100 0.220 42.400 0.219 0.348 arg-comb-Va Deep 0.01000 3.000 4.586 −0.100 0.170 47.900 0.165 0.324 bli-comb Deep 0.00116 3.273 5.379 −0.100 0.130 140.000 0.089 0.302 bll-2232 Demersal 0.02470 2.930 2.837 −0.100 0.270 50.100 0.263 0.502 cod-coas Demersal 0.01000 3.000 5.035 −0.100 0.140 130.000 0.097 0.351 cod-ewgr Demersal 0.00750 3.040 5.924 −0.100 0.117 150.000 0.068 0.485 cod-farb Demersal 0.00001 3.000 4.594 −0.100 0.156 110.000 0.124 0.280 cod-iceg Demersal 0.01000 3.000 4.692 −0.100 0.150 128.000 0.115 0.303 cod-rock Demersal 0.00001 3.000 3.483 −0.100 0.200 132.000 0.151 0.312 cod-wgr-in Demersal 0.01025 2.979 6.491 −0.100 0.107 150.000 0.065 0.376 dab-2232 Demersal 0.00001 3.000 1.980 −0.100 0.400 32.000 0.497 0.792 dab-nsea Demersal 0.00500 3.140 1.954 −0.100 0.400 36.000 0.455 0.777 GHL-DIS Demersal 0.00333 3.249 9.757 −0.100 0.073 120.000 0.043 0.308 had-iris Demersal 0.00001 3.000 4.697 −0.100 0.160 68.000 0.142 0.330 her-31 Pelagic 0.00360 3.039 2.322 −0.100 0.360 21.000 0.468 0.573 her-nirs Pelagic 0.00360 3.039 2.510 −0.100 0.320 31.000 0.334 0.655 lem-nsea Demersal 0.07560 3.142 2.608 −0.100 0.300 40.000 0.295 0.512

lin-combinSubareasI-II Deep 0.00390 3.074 5.446 −0.100 0.128 150.000 0.097 0.227

lin-combotherareas Deep 0.00390 3.074 5.225 −0.100 0.136 119.000 0.102 0.309

meg-4a6a Demersal 0.00001 3.000 6.455 −0.100 0.120 54.000 0.116 0.299 mut-comb Demersal 0.00440 3.351 4.204 −0.100 0.183 53.340 0.124 0.620 nep-25 Shellfish 0.00001 3.000 4.683 −0.100 0.160 70.000 0.141 0.328 nep-2627 Shellfish 0.00001 3.000 4.931 −0.100 0.150 80.000 0.128 0.301 nep-2829 Shellfish 0.00001 3.000 3.726 −0.100 0.200 70.000 0.176 0.373 nep-30 Shellfish 0.00001 3.000 4.761 −0.100 0.160 60.000 0.145 0.345 nep-31 Shellfish 0.00001 3.000 4.899 −0.100 0.150 85.000 0.126 0.298 ple-2232 Demersal 0.01000 3.000 4.287 −0.100 0.180 52.000 0.169 0.391 ple-7b-c Demersal 0.00001 3.000 6.978 −0.100 0.110 59.400 0.103 0.275 ple-89a Demersal 0.00001 3.000 1.572 −0.100 0.470 54.576 0.605 0.702 ple-celt Demersal 0.00001 3.000 6.983 −0.100 0.110 59.000 0.104 0.280 ple-eche Demersal 0.00001 3.000 3.542 −0.100 0.211 68.500 0.178 0.397 ple-iris Demersal 0.00001 3.000 4.360 −0.100 0.165 100.000 0.134 0.302 pol-89a Demersal 0.00001 3.000 3.844 −0.100 0.190 85.600 0.159 0.342 pol-nsea Demersal 0.00001 3.000 3.928 −0.100 0.186 85.600 0.156 0.342 rng-comb Deep 0.21360 2.987 23.962 −0.100 0.035 28.700 0.015 0.314 san-ns4 Pelagic 0.00001 3.000 1.891 −0.100 0.436 22.000 0.670 0.916 smn-arct Demersal 0.00001 3.000 2.945 −0.100 0.261 49.000 0.248 0.502 smn-con Demersal 0.00001 3.000 2.945 −0.100 0.261 49.000 0.253 0.284 smn-dp Demersal 0.00001 3.000 15.483 −0.100 0.051 49.000 0.051 0.196 smr-5614 Demersal 0.00001 3.000 12.886 −0.100 0.060 59.000 0.062 0.183 sol-7b-c Demersal 0.00001 3.000 6.003 −0.100 0.130 49.800 0.120 0.327 sol-8c9a Demersal 0.00001 3.000 6.978 −0.100 0.110 59.400 0.103 0.275 tur-nsea Demersal 0.00001 3.132 2.576 −0.100 0.290 61.200 0.257 0.385 whg-7e-k Demersal 0.00001 3.000 3.441 −0.100 0.218 65.000 0.188 0.401 whg-89a Demersal 0.00001 3.000 3.928 −0.100 0.190 70.000 0.167 0.363 whg-rock Demersal 0.00001 3.000 1.241 −0.420 0.483 45.000 0.864 0.676 whg-scow Demersal 0.00001 3.000 7.019 −0.100 0.110 56.300 0.105 0.282 wit-nsea Demersal 0.00170 3.390 2.970 −0.100 0.260 47.000 0.220 0.505

Forallcasesindependentlog-normalerrorswithaCVof20%

wereusedand250simulationsranforeachcase(combinationof

stock,scenarioandHCR).

2.2. Harvestcontrolrules

TheHarvestControlRulestestedinthispapertaketheform:

Cy+1=Cy−1·˛

whereCarecatchesinweightandyindexesyears.

Differentformsfor˛,thecatchmultiplier,leadtoalternative

HCRs.Threerulesweretested,onebasedonshorttermtrendsin

surveys(usedfrequentlybyICEStoprovidecatchadvicefor

data-limitedstocks);analternativethatusestheconﬁdenceintervalof

themeanabundanceofthesurvey,totakeintoaccountlongterm

information;andathirdthatuseslength-basedreferencepoints.

Therulebasedonshorttermchangesinabundance,hereafter

referredtoasHCR1,comparesthetwomostrecentindexvalues

withthethreeprecedingvaluesandtakesthefollowingform:

˛=

y−1 i=y−2Ii/2

_y−3 i=y−5Ii/3 ,

where I refers tothe stock biomass or abundanceindex and i

indexesyears.

Therulebasedonsurveyconﬁdenceintervals,namedHCR2,sets

˛as: ˛=

⎧

⎪

⎨

⎪

⎩

˛l ifIy−1<I+zlow√_nI I 1 if_I₊_z_low_√I nI ≤Iy−1≤I+zupp I √_n I ˛u ifIy−1>I+zupp√_nI I,

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Fig.1.LifehistoryinvariantM/Kforthestocksusedinthisstudy.

Fig.2.Maturity,ﬂeetselectivityandsurveyselectivitymodelsbyageusedinthis study.Fleetselectivitywasmodeledwithadoublenormaldistributionwiththe modeequaltotheageof50%maturity.Surveyselectivitywasmodeledasan asymp-toticallyﬂatcurvewithmaximumretentionatage10.Bothwereheldconstantover time.Exampleshownforastockwithageof50%maturityof5.4years.

withIthemeanindexabundance,Itheindex’sstandard

devi-ation,nIthelengthoftheindextime-series,andzxthez-statistic

fromthestandardnormaldistributionforwhichP[Z≤zx]=x.zlow

andzuppdeﬁnetheconﬁdenceintervallimits,whichdon’thaveto

besymmetric,and˛land˛uthecatchmultiplierswhentheindexis

outsidethelowerorupperconﬁdenceinterval,respectively.Note

thatinthisrulethelengthoftheindexincreaseswithtime,asnew

databecomesavailable,whichintheorymeansthattheprecision

oftheindexmean,I,willincreasewithnewdata.

HCR2wasparametrizedusinganasymmetricconﬁdence

inter-val,withzlow=z0.33=−0.44andzupp=z0.974=1.96,andasymmetric

changes in TAC, with ˛l=0.75 and ˛u=1.05. For comparison

purposes HCR2was alsoran with symmetric conﬁdence

inter-vals, referred to as ‘HCR2.sym’, where zlow=z0.025=−1.96 and

zupp=z0.975=1.96, and symmetric changes in TAC,˛l=0.75 and

˛u=1.25.

Therulebasedonlength-basedreferencepoints,namedHCR3,

hasthefollowingformfor˛:

˛=_LLSQ

F=M

whereFistheﬁshingmortalityrate,Mthenaturalmortalityrate,

Lreferstoindividuallength,andLSQthestatusquo(current)mean

lengthinthecatch,whichisgivenby:

LSQ=

A a=1Ca,yLa

A

a=1Ca,y

withaindexingages.LF=Mreferstothemeanlengthinthecatch

thatsetsﬁshingmortalityatthesamelevelasnaturalmortality

(BevertonandHolt,1957),givenby:

LF=M=0.75Lc+0.25L∞ (1)

withLc,themeanlengthatﬁrstcapture,deﬁnedby:

Lc=Lac =L∞(1−e−K(ac−a0))

whereL_∞,Kanda0arethevonBertalanffygrowthmodel

parame-ters,andactheageofﬁrstcapture,whichwassetattheageof25%

maturity.

The length-based reference points LSQ and LF=M were used,

respectively, as proxies of current ﬁshing mortality, FSQ,

and the ﬁshing mortality at MSY, FMSY (ICES, 2012c). Thus,

LSQ/LF=M≈FSQ/FMSY,andratiosdifferentfrom1shoulddrivethe

ﬁshery toMSY.Appendix Apresents ageneralized formof this

proxywhereFcanbesettoanyproportionofM.

TheapplicationoftheHCRswithinthemanagementprocedure

wasperformedignoringtheparametersusedinthesimulation,to

maximizetheindependenceofthedecisionmakingprocesswith

respecttothesimulations.Inparticular,thelengthbasedHCRused

thecommonlifehistoryinvariant,K=2M/3,althoughthe

popula-tionsweresimulatedwiththeirownestimatesoftheseparameters.

Thisapproachtriestoreplicatethemostfrequentoptionstakenby

assessmentworkinggroups,whileatthesametimeadding

obser-vationerrortotheindicatorusedforHCR3.

ComputationswerecarriedoutwithR(http://r-project.org)and

FLR(http://ﬂr-project.org;Kelletal.,2007).Thecodeanddatacan

bemadeavailableuponrequesttotheﬁrstauthor.

3. Results

Fig.3showsthemedianSSBtrajectoriesforeachstockover40

yearsbyHCRandexploitationscenarios(developmentand

over-exploitation, named ‘dev’and ‘hi’, respectively). Biologicalrisk,

computedastheratioofSSBovervirginbiomassinyears16-20,

wascategorizedbyiterationas‘low’whenSSB>0.30Bv,‘medium’

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Fig.3.Medianspawningstockbiomass(ssb)trajectoriesbystock,scenarioandharvestcontrolrule(HCR).Scenariosarelabeled‘dev’fordevelopment,or‘hi’for over-exploited.

percentageofsimulations(i.eof50stocksby5yearsby250

iter-ations)ineach category reﬂectsthebiological riskby HCR and

exploitationscenario(Table2).Toevaluatetheperformanceofthe

HCRsinrelationtoyield,thedistributionoftheratiocatch/MSYfor

theyear20,byscenarioandHCRwascomputed(Fig.4).

TheresultsshowthatHCR1isnotabletorecoverthebiomassin

bothscenarios(Fig.3).Theruleresultedinahighbiologicalriskfor

themajorityofthestocks(79%ofthesimulationsinthe‘hi’scenario

and69%inthe‘dev’scenario;Table2).HCRs2and3showedbetter

performanceintermsofSSBrecoveryandbiologicalriskforboth

exploitationscenarios.HCR2showsonly11%ofthesimulationsin

the‘hi’scenarioand5%inthe‘dev’scenariowithhighrisk,while

HCR3shows16%ofthesimulationsinthe‘hi’scenarioand27%in

the‘dev’scenariowithhighrisk.

Fig.4.DistributionofthecatchoverMSYratioinyear20,byscenarioandharvestcontrolrule(HCR).Thedistributionsarecomputedfromthesimulations(250)performed foreachstock(50).Scenariosarelabeled‘dev’fordevelopment,or‘hi’forover-exploited.

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Table2

Biologicalrisk,betweenyear16and20,byscenarioandharvestcontrolrule(HCR), computedastheproportionofsimulations(i.e.proportionof50stocksby5years by250iterations)ineachcategoryofbiomasstovirginbiomass(Bv)ratio.The categoriesare:high:<10%Bv,med:10–30%Bv,low:>30%Bv.

Scenario Biologicalrisk HCR1 HCR2 HCR3

dev low 0.01 0.48 0.49 dev med 0.31 0.47 0.24 dev high 0.69 0.05 0.27 hi low 0.00 0.18 0.61 hi med 0.21 0.71 0.23 hi high 0.79 0.11 0.16 Table3

Probabilityofstocksbreakingtheinter-annualcatchconstraint(IACC)of25%, betweenyear16and20,byscenarioandharvestcontrolrule(HCR),computedas theproportionofsimulations(i.e.proportionof50stocksby5yearsby250 itera-tions)above,beloworwithinthe25%catchrangeinrelationtothepreviousyear’s catch. scenario IACC HCR1 HCR2 HCR3 dev below 0.39 0.36 0.38 dev within 0.24 0.24 0.32 dev above 0.37 0.40 0.30 hi below 0.41 0.37 0.36 hi within 0.23 0.23 0.32 hi above 0.36 0.40 0.32

Fig.4showsthatallHCRsdrivemostﬁsheriestolevelsofcatches

belowMSY,althoughinthecaseofHCR1itisduetolowlevels

ofbiomass,whileforHCR2andHCR3thiseffectisrelatedtolow

levelsofﬁshingmortality,whichreﬂectsthemoreprecautionary

approachoftheserules.HCR2seemstobehavebetter,showinga

lowernumberofverysmallcatch/MSYratios.

Table3 presentstheprobability ofviolating aninter-annual

catchconstraint of 25% for years 16-20. AllHCRs have similar

results, although HCR3 shows slightly better results regarding

inter-annualcatchstability.NotethatinthecaseofHCR2these

resultsreﬂecttheuncertaintyincatchesintroducedthroughthe

implementationerror,giventhefactthatthisrulehasthecatch

limitsembeddedinitsparameters.Additionally,theHCRsoperate

withatwoyearlagononesingleyearcatch(Cy+1=Cy−1·˛);

replac-ingCy−1byanaveragecatchoverarecentperiodmaysmooththe

catchvariability.

To furtherinvestigatethereasons for thepoorperformance

foundinsomecases,weselectedtwostocksofherring(inBothnian

Bay,area31,coded‘her-31’;andintheIrishSea,coded‘her-nirs’)

withsimilarlifehistoryparametersbutwhichperformed

differ-ently.Fig.5showsSSB,catchinweightandthecatchmultipliers

(˛).In thecaseofHCR1themultiplierincreasesassoon asthe

biomassincreases,whichresultsinanincreaseincatcheskeeping

thebiomassatlowlevels.Thisruleclearlystabilizesthebiomass

atlevelssimilartothemostrecentobservedones.HCR2identiﬁes

correctlythatbothstocksareover-exploited,butcatchesarenot

reducedquicklyenoughinitiallytorecoverthebiomassofher-31.

Thisrulehasaﬁxedcatchreductionof 25%.Theopposite

hap-pensforher-nirsandbiomassincreasesaswellasthemultiplier,

yieldinganincreaseincatches.HCR3shows˛above1forher-31,

whichresultsfromwronglyidentifyingthestockasbeing

under-exploited.Thissituationis duetoalowerL_∞ (21cmfor her-31

comparedto31cmforher-nirs),andalowerlengthof50%mature,

whichisindirectlydeﬁningtheageofﬁrstcapture,ac.Botheffects

resultinalowerLF=Mforher-31which,inthisparticularcase,sets

theratiowiththestatusquolengthabove1.

Fig.6showsacomparisonbetweentheparametrizationusedfor

HCR2inthisstudyandafullysymmetricparametrization(named

‘HCR2.sym’),witha0.05%conﬁdenceintervalandthe˛multipliers

of0.75and1.25,appliedtothestockofplaiceinIberianwaters.SSB,

catchandthe˛multiplierareshown.Themostimportant

differ-encebetweenthetwoisthestabilizationofSSBafterrecoveringin

thecaseofasymmetry,whilethesymmetricHCRdrivesSSBbackto

lowlevels.Thiseffectresultsfromthehighervaluesof_˛,thatthis

Fig.5.Trendsinspawningstockbiomass(ssb),catchandcatchmultiplier(˛intheformulations),whichdeﬁnesthemultipliertothecatchinyeary−1thatderivesthe catchadviceforyeary+1,forthestocksofherringintheBothnianBay,area31(‘her-31’),andintheIrishSea(‘her-nirs’).Resultsareforthe‘dev’scenario.

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Fig.6.Trendsinspawningstockbiomass(ssb),catchandcatchmultiplier(˛inthe formulations),whichdefinesthemultipliertothecatchinyeary−1thatderives thecatchadviceforyeary+1,forthestockofplaiceinIberianwatersby sce-nario.‘HCR2.sym’reflectsadifferentparametrizationofHCR2,withasymmetric confidenceintervalof5%andmultipliersof0.75and1.25.

parametrizationholds,whichprovideshighercatchesbutalsorisks

forSSB.Theexampleshowsthatthereisawiderangeofoptions

forparameterizingthisHCR,which,inareallifesituation,should

bedoneusingMSEanalysis.

4. Discussion

Inthisstudyweinvestigatedtheperformanceofthreesimple

HCRs,inviewoftheirpotentialapplicationtodata-limitedstocks,

withdifferentdatasituationsregardingtheamountandqualityof

information.HCR1andHCR2canbeusedtoprovidecatchadvice

ifsurveydataexists,whileHCR3canbeusedinmoreseveredata

limitedcaseswhereonlycatchlengthcompositionsareavailable.

Ifbothinformationsourcesexist,combinationsoftheseHCRscan

beexplored.

TheHCRstestedwerenotabletosteersimultaneouslyallstocks

tooptimalexploitation,withSSBsandﬁshingmortalitiesaround

valuesthatprovideMSY.Suchresultsareexpected,consideringit

isunlikelythatasingleparametrizationcancopewiththe

diver-sityinpopulationlifehistories.Inreal-lifesituations,theseHCRs

shouldbetunedtothespeciﬁcitiesofthestockandﬁsheriessubject

tomanagement.Nevertheless,HCR2withthecurrent

parametriza-tionwasmuchmoreefﬁcientthanHCR1inapproachingMSYlevels,

failinginonecaseonly.HCR3wasabletodriveSSBtosafelevelsin

mostcasesbutlefttheﬁsherieswithlowcatches,mostlikelydue

toapoorapproximationtoFMSYbyLF=M.AsinthecaseofHCR2,

itwasmoreefﬁcientthanHCR1atkeepingthestockswithinsafe

levels.Klaeretal.(2012)exploredtheperformanceofrulessimilar

toHCR3andalsofoundawiderangeofresults,withcaseswhere

theSSBwasdriventoveryhighlevelsinrelationtovirginbiomass

andotherswherethisratiowasverylow.Theauthorsjustifythese

resultswiththedisparitybetweenthenaturalmortalityassumed

bytheassessmentmethodandtherealnaturalmortality.Inour

studywedidn’texplorethiseffect.

NotethatHCR3usesindirectinformationaboutthestatusofthe

stockandlifehistoryparameterstocomputeproxiestoFMSY.Itisa

rulethatcanbeappliedtostocksthathavemoreseveredata

lim-itationsthanHCR1andHCR2,butshowsperformancelimitations,

althoughwiththeadvantageofsteeringthestocktosafebiological

levelsinsteadofstabilizingSSBattheirrecentlevels,likeHCR1.As

inanyotherHCR,add-hocadjustmentscanbeincludedtoimprove

itsperformance,e.g.intheformofadditionaltuningparameters.

Theapproachtosimulationtestingusedcanprovidethe

nec-essaryframeworktotunedatalimited HCRs.Depending onthe

informationavailable,theoperatingmodelwillbeabetterorworse

representation of the real system. Nevertheless, our approach

allows studying the robustness of the HCR to a set of

com-monuncertaintyfactors,suchasstock-recruitmentrelationships,

growth,ﬂeetselectivity,implementationerror,etc.

Analysing theresults obtainedin more detail, one can

con-cludethatHCR1,whichwasdesignedtoprovidestatusquocatch

adviceadjustedbythebiomassindexratio,showedthepoorest

performance,decreasingorkeepingSSBatlowlevelsandcatches

mostlybelowtheMSYtarget.Thisruleadjuststhecatchbasedon

short-termchangesinbiomass,whichprovesefﬁcientat

stabiliz-ingthecatchesandthebiomassesatrecentlevels,butisunable

toimplementthenecessarycatchreductionthatwouldsteerSSB

tosustainablelevels.Improvedperformanceoftherulemaybe

achievedbyreplacingthedenominatorbyabiomassindextarget,

orincludingapenalizingtermaccountingfortheover-exploitation

ofthestock.Thesetweaksrequireassumptionstobemadeabout

therelationshipbetweentheindexandthestateofthestock.Such

assumptionsmaybepossible,ifthesurveytimeseriescoversa

knownperiodofmoderateexploitation,butwillbeoflimited

inter-estifthesurveytimeseriesisshortoronlycoversaperiodwhen

thestockwasalreadyover-exploited.

HCR2,thatadjuststhestatusquocatchbasedonthevariabilityof

thebiomassindextimeseries,showedthebestoverallperformance

inbothscenarios.However,toobtainsuchresults,itwasnecessary

toapplyanasymmetricconﬁdenceintervalcombinedwithlarger

decreasesinstatusquocatch(0.75)thanincreases(1.05).Theneed

toparametrizethisHCR maybealimitationtoitsapplicability.

Theruleofthumbisthatifthestockislikelytobeover-exploited,

thenanasymmetricalparametrizationwillbemore

precaution-arythanonethatissymmetrical.Thelevelofasymmetrythatwill

increasethechancesofsteeringtheﬁsherytoMSYmustbefound

throughsimulationtesting,althoughtheparametrizationprovided

hereappearedtobeprecautionary.

HCR3uses themeanlengthinthecatch(LSQ)asa proxyfor

currentﬁshingmortalityandthemeanlengthwhenﬁshing

mor-talityequalsnaturalmortality(LF=M)asaproxyforFMSY.Therule

isdesignedtoadjustthestatusquocatchdownwardsorupwards

whenthemeanlengthinthecatchisbeloworabovethetarget

(LF=M),respectively.Thesimulationsshowedthatforthemajority

ofthestocks,HCR3resultedinareductionofFtobelowFMSY,which

hadtheeffectofdrivingcatchesofthesestocksbelowMSY(Fig.4).

Inthesecases,LF=MwasapoorapproximationtoFMSY,resulting

in acatchmultiplier(˛)wellbelow one.A commonfeatureof

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exploitation(lengthatﬁrstcapture,Lc)startswellbelowthelength

ofﬁrstmaturity(L50%).Infact,forthestocksfailingwithHCR3,the

ratioLc/L50%wasbelow0.25.Moreover,SSBrecoverywasweaker

orstockdepletionmoresevere,forstockswithlatematurity,i.e

whenthelengthatﬁrstmaturityisclosertomaximumlength.

Fur-thersimulationtestingisrequiredtoinvestigatemodiﬁcationsof

HCR3thatalignthetargetmeanlengthinthedenominator,which

dependsonLcandL∞,withtheexploitationandlife-history

char-acteristicsofthestocks,inordertoreducetheadvisedcatchand

promotetherebuildingofthestock.Onepossibilityworth

explor-ingistoaddacorrectionfactortoLF=MlinkedtotheLc,L50%andL∞

forthegivenstocktoimprovetheyield/risktrade-off.Inspiteof

thelowcatches,HCR3wasabletoreverse,relativelyquickly,the

decreasingtrendinSSBinthe‘dev’scenarioandtoincreasethelow

SSBlevelsinthe‘hi’scenario,resultinginlowbiologicalrisks.

Finally,theapproachpresentedheredoesnotreplaceanalytical

assessments.Theinformationprovidedbythesemethodsismore

limitedthantheinformationgivenbyananalyticalmethod.Itis

importanttoavoidthe“data-poortrap”,whereduetothefactthat

catchadviceisbeinggivenforthesestocks,thecollectionofdata

isseenasunnecessary(Bentley,2014).Movingthestocksupon

the“datalevel”isanimportantobjectivethatshouldbekeptin

managementpolicies.

Acknowledgements

Theauthorswouldliketothankthethoroughreviewsoftwo

anonymousreviewers.Part ofthisworkwascarriedoutwithin

GesPeProject(PlanosdeGestaoPesqueira,PROMAR

31-03-01-FEP-0017,EUco-ﬁnanced).

AppendixA. GeneralizingthelengthbasedHCR

NotethataninterestingdevelopmentaboutHCR3canbemade.

FromBevertonandHolt(1957)themeanlengthﬁshintheannual

catchisdeﬁnedby ¯Ly=L∞

1− (F+M)(1−e−(F+M+K)) (F+M+K)(1−e−(F+M)₎e−K(ac−a0)

.

Considering =a−ac the ﬁshable life-span, then setting

→+∞intheequationaboveresultsin

¯Ly=L∞

1−(F+M)e−K(ac−a0)

F+M+K

. (A.1)

From Ly=L∞(1−e−K(a−a0)₎ _and _taking _into _account _that

a=ac⇒Ly=Lc,weobtain

Lc=L∞(1−e−K(ac−a0)₎,

whichcanbewrittenas

e−K(ac−a0)= L∞−Lc

L∞ . (A.2)

WecannowsubstituteEq.(A.2)intoEq.(A.1)toobtain

¯Ly=KL∞_F+₊FL_Mc₊+_KMLc.

SettingF=M,with>0andK=Mresultsin

LF=M,K=M=L∞+₊Lc(₊₁+1). (A.3)

Whichisageneralizedformthatallowssettingtheproxyfor

FMSY atanylevelofnaturalmortalityandnotonlyF=M.Eq.(1)

holdsifweset=1and=2/3inEq.(A.3).

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