SEDAR48BlackGrouperLengthandWeight 1

BlackGrouperLengthandWeightRelationshipsforSEDAR48

JoeO’HopFloridaFishandWildlifeConservationCommission

FishandWildlifeResearchInstituteSt.Petersburg,Florida

Introduction Fisheriesresearchprojects,surveys,andmonitoringprogramsintheSouthAtlanticandGulfofMexicoregionsroutinelycollectlengthandweightdataaspartofprovidingbasicinformationonspeciesencountered.Thetypesofmeasurementsemployedvaryamongtheprograms(e.g.,Table1),andpotentiallycanprovideinformationonconversionsbetweenmeasurementtypeswhenmultiplelengthorweighttypesarecollectedfromindividualfish.Conversionequationsaresometimesnecessarytostandardizetheobservedinformationacrosssurveysandpreparedataforstockassessments(e.g.,Lombardi-Carlson,2014).Methods

LengthandweightdataforSEDAR19(O’HopandBeaver2009)wereobtainedfromvarioussources(CrabtreeandBullock1998;NMFSTripInterviewProgram(TIP),NMFSSoutheastRegionHeadboatSurvey(SRHS),NMFSMarineRecreationalInformationProgram[formerlyknownastheMarineRecreationalFisheryStatisticsSurvey(MRFSS)]NMFSObserverPrograms(SharkBottomLonglineObserverProgram(SBLOP)andGulfReefFishObserverProgram(GOP)),opportunisticsamplesfromNMFSoffshorefisheryindependentsurveys,statefisheriesprograms(NorthCarolinaDivisionofMarineFisheries(NCDMF),FloridaFishandWildlifeConservationCommission(FWC)FisheriesDependent(FDM)andFisheriesIndependentMonitoring(FIM)programsandarchiveddata).Eachoftheseprogramsmayalsocollectbiologicalsamples(typicallyotoliths)whicharesubmittedtoregionallaboratories(NMFSPanamaCity,NMFBeaufort,FWCFishandWildlifeResearchInstitute)forprocessing.TheFDMBiostatisticalprogrammaycollectadditionalsamples(e.g.,otolithsforageing,finclipsforgeneticsamples,muscletissueformercurydeterminations)frommeasuredspecimenswhichmayhaveoriginatedthroughsamplingforotherprograms(e.g.,TIP,SRHS).

ForSEDAR48,lengthandweightdatausedtodevelopthemeristicrelationshipsforSEDAR19

(Table2)werere-analyzedandadditionalsampledatawerecompiledfromavailablesources(TIP,SRHS,MRFSS/MRIP,NCDMF,FDMBiostat,FIM,etc.).BecauseofsomeoverlapbetweenthedatausedinSEDAR19andtheothersources,datawerecross-checkedusingthesamplingidentifiersofthevariousprogramstopreventduplication.Inaddition,becauseoftheoverlapofdatasources,lengthandweightfieldswerere-matchedtothemeasurementsusedinSEDAR19toincorporateanyrevisionsthatmayhaveoccurredsincethosedatawerecompiledin2008.

Simplelinearregressions(SASInstitute,2016)wereusedtoanalyzethelength-length

relationshipsand,afterloge-transformation,thelength-weightrelationships.Measurements(Table3)wereexaminedusingtworoundsofoutlierdetection,andstandardizedresidualswerecomputedduringeachroundfollowingmethodsoutlinedinO’HopandBeaver(2009).Inthefirstroundofoutlierdetections,measurementswithstandardizedresidualsof8orlarger(possiblydatarecordingorentryerrors)wereremovedfromdatasets.Theremainingdatawerere-analyzed,andmeasurementswithstandardizedresidualsof4orlargerwereconsideredoutliersandremovedfromtheanalysis,priorto

SEDAR48BlackGrouperLengthandWeight 2

estimatingregressioncoefficients(Table4)andplottingmodelfitsandresiduals(Figs1and2).OutliersidentifiedintheseanalyseswereinvestigatedandsomerevisionsweremadetocorrectdataentryerrorsintheTIPandFDMBiostatisticaldatabases.

Simplelinearregressiontechniquesareusedinthisreporttodeveloptheconversionequations.

Amongtheassumptionsfortheseanalysesarethattherearefunctionalrelationshipsbetweenthevariablesmeasuredandthatmeasurementerrorisrandomforeachofthevariables.Regressionassumesthatindependentvariablesaremeasuredwithouterror,andalltheerrorisassignedtothemeasured“dependent”variable.Thissimplifyingassumptionismadetodeveloptheconversionequations.Becauseoftimepressuresandotherenvironmentalfactorsinthefield,therecanbeerrorsinmeasurementtechnique,theactualmeasurement,andrecordingandentryofdata(e.g.,Bunchetal.2013).Withtheexistingsurveydataavailable,itisnotpossibletoexaminetheerrorassociatedwithmakinganindividualmeasurement,butitispossibletoestimatethedegreeofrelationshipbetweenthemeasurementtypesandproducesuitableconversionsbetweenthem.ResultsandDiscussion

Whileanalysesoflength-lengthandlength-weightrelationshipsforspeciesareroutine,itisgoodpracticetoexaminedataforoutliersandpotentialbiasesinmeasurement.Theoutliersidentifiedfromtheseanalysesusuallyaccountedfor1.6%orfeweroftherecordsavailableforanalyses(Table3)withtheexceptionthatalargerpercentage(7.5%)ofrecordswereexcludedfortheforklength(FL)versuswholeweightregression.Relativelyfew(0-5)oftheoutliershadstandardizedresiduals>=8.Plotsoftheregressionfitsandrawresiduals(Figs.1,2)weretypicalforlength-lengthandlog-transformedlength-weightregressions.UponexaminationoftheFLversuswholeweightregression(Fig.3a),therewereunusualrunsofweightsforspecimensunder400mminFL(Fig.3a,“redbox”).These“runs”werefromspecimens(95%ofthempriorto1991)measuredfromtheMRFSS/MRIPsurvey,andmayhaveresultedfromthechoiceofscalesusedtomeasuretheweightofthespecimens(i.e.,weightrangeforthescalewasmoresuitableforheavierspecimens).AlthoughsimilaroutlieranalyseswereperformedduringSEDAR19,thesepatternswentunnoticedwhentheregressionsforSEDAR19wereestimated(Table2).ThewholeweightversusFLregressionfromSEDAR19waslikethenewregressionbeforetheMRFSS/MRIPspecimensbelow400mmwereremoved.Becauseoftheleverageexertedbysomeoftherecordedweightsofthesesmallerspecimens,theregressionover-statedtheweightofspecimensunder700mmandunderstatedtheweightoflargerspecimenscomparedwiththefitafterthesemeasurementswereremoved(Fig.3c).Manyoftheexcludedspecimenswerewithinthe99%predictionintervaloftheFL-wholewt.regression(Fig.3c,inset).

TheSEDAR48relationships(Table4)differlittlefromthoserecommendedforSEDAR19except

forthewholeweightversusFLregression.BecausetheregressionsforSEDAR48containthesamemeasurementsaswereavailableinSEDAR19(andtosomeextenttheresearchofCrabtreeandBullock1998)andwereaugmentedwithmeasurementsmadesubsequently,theresultsareunsurprising.

AcknowledgementsNumerousfieldbiologistsfromstatesinsoutheasternFloridaandtheNationalMarineFisheriesService(NMFS,includingtheircontractors)contributedtheessentialrawinformationsummarizedinthisreport.Thiseffortanddedicationtocollectingbasicbiologicaldataonspecimensoftengoesunrecognized.Thanksalsogoestothesupervisorsofthesefieldprogramsanddatabasesupportinmakingthesedataavailable.IthanktheNMFSSoutheastFisheriesScienceCenter,particularlyLarryBeerkircher(Miami

SEDAR48BlackGrouperLengthandWeight 3

Laboratory)fortheTripInterviewProgramdataandKennethBrennanandKellyFitzpatrick(BeaufortLaboratory)fortheSoutheastRegionHeadboatSurveydata,BeverlyBarnettandDr.LindaLombardioftheNMFSPanamaCityLab,andDr.JenniferPottsoftheBeaufortLaboratory,andtheNMFSstaffinSilverSpring,MD,oftheMarineRecreationalFisheriesStatisticsSurvey(pre-2004)andMarineRecreationalInformationProgram(2004andlater)formaintainingandmakingavailablethenationalmarinerecreationalsurveydata.KelleyKowal,JuliaReeves,BridgetCermak,SteveBrown,ChrisBradshaw,andDr.RichardCodyoftheFWRIFisheriesDependentMonitoringProgramprovidedvaluableassistanceinchasingdowninformationrecordedindatabasesandondatasheetsandverifyingorrevisingdatabaseentrieswhennecessary.AnneMarkwith(NorthCarolinaDivisionofMarineFisheries)providedfieldinformationandlengthsforspecimenscollectedbytheirbiologists.SpecialthankstoDr.RoyCrabtreeandLewisBullockformakingtheirresearchdataavailablefortheseanalyses.LiteraturecitedBunch,A.J.,C.J.Walters,andL.G.Coggins,Jr.2013.Measurementerrorinfishlengths:evaluationandmanagementimplications.Fisheries38:320-326.Crabtree,R.E.andL.H.Bullock.1998.Age,growth,andreproductionofblackgrouper,Mycteropercabonaci,inFloridawaters.FisheryBulletin96:735-753.http://fishbull.noaa.gov/964/crabtree1.pdfGarcia-Cagide,A.andT.Garcia.1996.ReproducciondeMycteropercabonaciyMycteropercavenenosa(Pisces:Serranidae)enlaplataformacubana.Rev.Bio.Trop.44:771-780.

Hubbs,C.L.andK.F.Lagler.1964.FishesoftheGreatLakesRegion.Univ.MichiganPress,AnnArbor,MI.213p.

Lombardi-Carlson,L.2014.AnageandgrowthdescriptionofRedGrouper(Epinephelusmorio)fromthenortheasternGulfofMexico:1978-2013forSEDAR42.SEDAR42-DW-10.SouthAtlanticFisheryManagementCouncil.NorthCharleston,SC.http://sedarweb.org/sedar-42-data-workshop

O’Hop,J.andR.Beaver.2009.Age,growth,andmaturityofBlackGrouper(Mycteropercabonaci)–CrabtreeandBullock(1998)revisited.SEDAR19-DW-09.SouthAtlanticFisheryManagementCouncil.NorthCharleston,SC.http://sedarweb.org/sedar-19-data-workshop

Saari,C.andL.Beerkircher.2014.User’sGuidefortheTIPTripInterviewProgram.Version6.NOAAFisheries.SoutheastFisheriesScienceCenter,FisheriesStatisticsDivision.75VirginiaBeachDrive.Miami,FL33149.https://www.sefsc.noaa.gov/docs/TIP_UsersGuide_Ver6.pdf

SASInstitute,Inc.2016.SAS/STAT14.2.User’sGuide.Cary,NC.

SEDAR.2010.GulfofMexicoandSouthAtlanticBlackGrouper.SEDAR19StockAssessmentReport.SouthAtlanticFisheryManagementCouncil.Charleston,SC.http://sedarweb.org/sedar-19-final-stock-assessment-report-south-atlantic-and-gulf-mexico-black-grouper

SEDAR.2016.SEDARDataBestPractices:LivingDocument–September2016.SEDAR.NorthCharleston,SC.http://sedarweb.org/sedar-data-best-practices

Zar,J.H.1996.BiostatisticalAnalysis.Thirdedition.Prentice-Hall,EnglewoodCliffs,NewJersey.

SEDAR48BlackGrouperLengthandWeight 4

Table1.AcomparisonofmeasurementtypesandtypicalunitsusedbyselectedSouthAtlanticandGulfofMexicofisherymonitoringprogramsandpreviousBlackGrouperresearchprojects.

Program/Project

StandardLength(SL)

ForkLength1(FL)

“Natural”TotalLength2(TLnatural)

“Maximum”Totallength(TLmax)3

Wholeweight(TW)

Guttedweight(GW)

CrabtreeandBullock1998 mm mm -------4 mm4 lbsorkg lbsorkg

TIPinches,cm,ormm

inches,cm,ormm -------5

inches,cm,or,mm5

lbs,kg,org6

lbs,kg,org6

SRHS ------- mm mm ------- grams -------MRFSS/MRIP ------- mm ------- ------- kg -------FDMBiostat mm mm mm mm kg kgFIM mm mm ------- mm kgorg -------1Infishwithoutforkedtails,thismeasurementisthestraight-linedistancefromthetipofthesnouttotherearcenteredgeofthetail.Itisalsoreferredtoasthe“mid-linelength”.2Thismeasurementismadewiththetailinits“natural”orflatorientation.3ThismeasurementfollowsthemethoddescribedinHubbsandLagler(1964)wherethemeasurementismadebycompressingthetipsofthetailtoits“maximum”length4ThisprojectmeasuredthetailfollowingthemethoddescribedinHubbsandLagler(1964).5TherecommendedmeasurementmethoddescribedintheTIPmanual(v.6)followsthemethoddescribedinHubbsandLagler(1964).RecentlytheTIPdatabasehasaddedcodestodistinguishbetweena“natural”TLand“maximum”TLmeasurements.Recommendedprecisionofmeasurementswasto1mmforlengths,and1gramor0.01poundsforweights.6TheTIPdatabasecurrentlystoresawholeweightoraguttedweight,butnotboth.

SEDAR48BlackGrouperLengthandWeight 5

Table2.Length-length,wholeweighttoguttedweight,andlength-weightregressionsdevelopedforSEDAR19[seeSEDAR(2010)Table2.14.7].

Length-LengthandWholeWeight-GuttedWeight

Source Y a b X n MinX MaxX

SEDAR19

SL(mm) -23.85 0.8827 FL1(mm) 1320 238 1495TLnatural2(mm) 21.29 1.1595 SL(mm) 74 435 1135TLnatural(mm) -2.84 1.0193 FL(mm) 137 387 1336TLmax

3(mm) 26.96 1.1630 SL(mm) 1338 51.2 1325

TLmax(mm) -1.44 1.0276 FL(mm) 1339 238 1495TLmax(mm) 4.30 1.0097 TLnatural(mm) 78 528 1252TW4(kg) -----5 1.061 GW4(kg) 636 0.44kg 58.64kgTW(kg) 1.006 1.055 GW(kg) 636 0.44kg 58.64kg

CrabtreeandBullock1998 TW(kg) 0.0815 1.056 GW(kg) 638 0.47kg 61.59kg

Length-Weight

Source Ln(Y) Ln(a) b Ln(X) n Min Max

SEDAR19

TW4(kg) -18.5545 3.0843 FL1(mm) 2552 206mm 1495mmTW(kg) -19.2684 3.1863 TLmax

3(mm) 904 77.5mm 1525mmGW4(kg) -18.8956 3.1306 FL(mm) 2420 314mm 1495mmGW(kg) -19.0487 3.1438 TLmax(mm) 1075 334mm 1525mm

1FL–Forklength(mm;inthisspecies,thestraight-linedistancefromthetipofthesnouttotherear-centeredgeofthetail,alsocalleda“mid-line”length).2TLnatural-Tailflat(mm),initsnaturalstate3TLmax-Tailcompressedtoitsmaximumlength(mm)4TW=wholeweight(kg),GW=guttedweight(kg)5nointerceptmodel

Table3.Availablerecordsandnumbersofoutliersexcludedforvariouslength-lengthandlength-weightregressionsforSEDAR48andSEDAR19.dependentvariable units

independentvariable units

availablerecords*

outliersexcluded

recordsexcluded(%)

SEDAR19regressions

SL mm FL mm 1573 17 1.1% 1320TLnatural mm FL mm 516 3 0.6% 137TLnatural mm TLmax mm 167 0 0.0% 78TLmax mm SL mm 1548 16 1.0% 1338TLmax mm FL mm 1683 12 0.7% 1339TW kg FL mm 3220 242** 8.1% 2552TW kg TLnatural mm 1055 15 1.4% ------TW kg TLmax mm 982 6 0.6% 904

GW kg FL mm 3404 29 0.9% 2420GW kg TLnatural mm 130 2 1.6% ------GW kg TLmax mm 1596 15 0.9% 1075*beforeexclusionofoutliers**MRFSS/MRIPFLmeasurementslessthan400mmexcluded(n=226)becauseofmeasurement/scaleissues.

SEDAR48BlackGrouperLengthandWeight 6

Table4.Length-length(mm)andLength-weightrelationshipsdevelopedforBlackGrouper(Mycteropercabonaci).LinearregressionsareintheformY=a+bX.SL:standardlength(mm);FL:forklength(mm);TL:totallength(mm);TW:totalweight(kg),GW:guttedweight(kg).

*Avg.X,MSE,Σx2,Σxy,Σy2-Meanofindependentvariable(X),meansquareerrorandcorrectedsumsofsquares(CSS)fortheindependentvariable(X),correctedsumofcross-productsforXY,andCSSforthedependentvariable(Y);usedforgeneratingpredictionintervalsandforanalysisofcovariance(Zar1996),andMSEalsousedforbiascorrectionsforthemeansoflog-transformeddata[e.g.,Haddon(2001)].Usually,lengthsweremeasuredtothenearestmillimeter,andweighttothenearest0.02kg.However,somedatamayhavebeentakenusinglengthmeasurementstothenearest0.5cmorinfractionsofinchesandweightmeasurementstothenearest0.1or0.01pound.Estimatesderivedfromtheaboveequationsshouldberoundedtothenearest0.5centimeterandnearest0.02kg.Thenumberofdecimalsshowninthetableweremeantsolelytoreduceroundingerrorsforcalculationofpredictionintervalsandforgeneratingsumsofsquaresandcross-productsneededforanalysisofcovariance.1FL–Forklength(mm;inthisspecies,thestraight-linedistancefromthetipofthesnouttotherear-centeredgeofthetail,alsocalleda“mid-line”length).2TLnatural-Tailflat(mm),initsnaturalstate3TLmax-Tailcompressedtoitsmaximumlength(mm)4TW=wholeweight(kg),GW=guttedweight(kg)5convertedfromcommonlogarithmsandweightingramstonaturallogarithmsandweightinkg

LENGTH-LENGTH

Source Y(mm) a b X(mm) nMinX(mm)

MaxX

(mm)Avg.X*(mm) MSE* r2 Σx2* Σxy* Σy2*

SEDAR48

SL -24.681 0.883 FL1 1556 238 1495 776.44 46.880 0.99 88234626.27 77920795.14 68885409.52TLnatural

2 8.429 1.011 FL 513 387 1347 725.86 81.574 0.99 7329205.89 7409609.11 7532578.56TLnatural -2.886 0.993 TLmax 167 534 1270 725.11 37.916 0.99 1946234.06 1931882.26 1923892.36TLmax

3 26.860 1.164 SL 1532 51.2 1260 663.74 81.923 0.99 71735840.75 83503806.48 97327599.60TLmax -2.080 1.029 FL 1671 238 1495 777.00 22.834 0.99 91866919.09 94487308.81 97220551.61

SL -23.712 0.883 FL 1134 0.99 CrabtreeandBullock1998

TLmax 26.186 1.164 SL 1141 0.99 TLmax -1.317 1.028 FL 1150 0.99

Garcia-CagideyGarcia1996 TL 17.8 1.10 SL 209

LENGTH-WEIGHT

SourceLn

(Y[kg]) Ln(a) bLn

(X[mm]) nMin[mm]

Max[mm]

Avg.Ln(X[mm]) MSE r2 Σx2 Σxy Σy2

SEDAR48

TW4 -19.2391 3.1896 FL 2978 238 1495 6.493 0.01925 0.97 171.0718 545.6546 1797.7224TW -18.5636 3.0722 TLnatural 1040 260 1600 6.536 0.01566 0.97 66.8133 205.2621 646.85420TW -19.1945 3.1742 TLmax 976 63 1518 6.521 0.01023 0.99 114.1667 362.3831 1160.2217GW4 -18.8323 3.1217 FL 3375 327 1495 6.755 0.00782 0.99 240.0079 749.2236 2365.2037GW -19.0112 3.1528 TLnatural 128 602 1184 6.575 0.00697 0.96 1.96605 6.198593 20.421136GW -18.8867 3.1195 TLmax 1581 332 1518 6.707 0.00864 0.99 136.4381 425.6203 1341.3646

CrabtreeandBullock1998 TW -19.4735 3.218 TLmax 772 177 1518 0.99

SEDAR48BlackGrouperLengthandWeight 7

Figure1.Predictedfitsandrawresiduals(inmm)forlength-lengthregressions.

a. SLvs.FLpredictedfit b. SLvs.FLresidualplot

c. TLnaturalvs.FLpredictedfit d. TLnaturalvs.FLresidualplot

e. TLmaxvs.FLpredictedfit f. TLmaxvs.FLresidualplot

SEDAR48BlackGrouperLengthandWeight 8

Figure1.(continued)Predictedfitsandrawresiduals(inmm)forlength-lengthregressions.

g. TLmaxvs.SLpredictedfit h. TLmaxvs.SLresidualplot

i. TLnaturalvs.TLmaxpredictedfit j. TLnaturalvs.TLmaxresidualplot

SEDAR48BlackGrouperLengthandWeight 9

Figure2.Predictedfitsandrawresiduals(inlogekg)forloge-transformedlength-weightregressions.

a. Loge(Wholewt.)vs.Loge(FL)predictedfit b. Loge(Wholewt.)vs.Loge(FL)residualplot

c. Loge(Wholewt.)vs.Loge(TLnatural)

predictedfitd. Loge(Wholewt.)vs.Loge(TLnatural)residual

plot

e. Loge(Wholewt.)vs.Loge(TLmax)

predictedfitf. Loge(Wholewt.)vs.Loge(TLmax)

residualplot

SEDAR48BlackGrouperLengthandWeight 10

Figure2.(continued)Predictedfitsandrawresiduals(inlogekg)forloge-transformedlength-weightregressions.

a. Loge(Guttedwt.)vs.Loge(FL)predictedfit b. Loge(Guttedwt.)vs.Loge(FL)residualplot

c. Loge(Guttedwt.)vs.Loge(TLnatural)

predictedfitd. Loge(Guttedwt.)vs.Loge(TLnatural)residual

plot

e. Loge(Guttedwt.)vs.Loge(TLmax)

predictedfitf. Loge(Guttedwt.)vs.Loge(TLmax)

residualplot

SEDAR48BlackGrouperLengthandWeight 11

Figure3.Predictedfitsforloge-transformedFL(mm)-wholewt.(kg)regressionsbeforeandafterdeletingMRFSS/MRIPspecimens<400mm.

a. Loge(Guttedwt.)vs.Loge(FL)predictedfitwithallspecimens.Highlightedboxframesspecimens<400mmFL

b. Loge(Guttedwt.)vs.Loge(FL)predictedfitafterdeletingMRFSS/MRIPspecimenswithFL<400mm.

c. Comparisonofback-transformedregressionlinesbeforeandafterexcludingMRFSS/MRIP

specimens<400mm.InsetshowslocationsofallexcludedspecimensinrelationtotheSEDAR48predictedregressionline,andmostwerewithinthe99%predictioninterval.