Evolutionary Applications. 2019;00:1–19.  | 1wileyonlinelibrary.com/journal/eva

Received:7November2018  |  Revised:18April2019  |  Accepted:15May2019DOI: 10.1111/eva.12823

S P E C I A L I S S U E O R I G I N A L A R T I C L E

Multi‐trait genomic selection for weevil resistance, growth, and wood quality in Norway spruce

Patrick R. N. Lenz1,2  | Simon Nadeau1 | Marie‐Josée Mottet3 | Martin Perron2,3 | Nathalie Isabel2,4 | Jean Beaulieu2 | Jean Bousquet2

ThisisanopenaccessarticleunderthetermsoftheCreativeCommonsAttributionLicense,whichpermitsuse,distributionandreproductioninanymedium,providedtheoriginalworkisproperlycited.©2019HerMajestytheQueeninRightofCanada.Environmental DNA publishedbyJohnWiley&SonsLtd.

LenzandNadeauauthorscontributedequallytothiswork.ReproducedwiththepermissionoftheMinisterofNaturalResourcesCanada.

1CanadianWoodFibreCentre,NaturalResourcesCanada,Québec,Québec,Canada2CanadaResearchChairinForestGenomics,InstituteofIntegrativeBiologyandSystems,CentreforForestResearch,UniversitéLaval,Québec,Québec,Canada3MinistèredesForêts,delaFauneetdesParcs,GouvernementduQuébec,Directiondelarechercheforestière,Québec,Québec,Canada4LaurentianForestryCentre,NaturalResourcesCanada,Québec,Québec,Canada

CorrespondencePatrickR.N.Lenz,NaturalResourcesCanada,CanadianWoodFibreCentre,1055duPEPS,POBox10380,Québec,QCG1V4C7,Canada.Email:Patrick.Lenz@canada.ca

Funding informationGenomeCanada,Grant/AwardNumber:6503

AbstractPlantation‐growntreeshavetocopewithanincreasingpressureofpestanddiseaseinthecontextofclimatechange,andbreedingapproachesusinggenomicsmayofferefficientandflexibletoolstofacethispressure.Inthepresentstudy,wetargetedge‐neticimprovementofresistanceofanintroducedconiferspeciesinCanada,Norwayspruce(Picea abies(L.)Karst.),tothenativewhitepineweevil(Pissodes strobiPeck).Wedevelopedsingle‐andmulti‐traitgenomicselection (GS)modelsandselectionindicesconsideringtherelationshipsbetweenweevilresistance,intrinsicwoodqual‐ity,andgrowthtraits.Weevilresistance,acousticvelocityasaproxyformechani‐calwoodstiffness,andaveragewooddensityshowedmoderate‐to‐highheritabilityand lowgenotype‐by‐environment interactions.Weevil resistancewas geneticallypositively correlated with tree height, height‐to‐diameter at breast height (DBH)ratio,andacousticvelocity.TheaccuracyofthedifferentGSmodelstested(GBLUP,thresholdGBLUP,Bayesianridgeregression,BayesCπ)washighanddidnotdifferamongeachother.Multi‐traitmodelsperformedsimilarlyassingle‐traitmodelswhenalltreeswerephenotyped.However,whenweevilattackdatawerenotavailableforalltrees,weevilresistancewasmoreaccuratelypredictedbyintegratinggeneticallycorrelatedgrowthtraitsintomulti‐traitGSmodels.AGSindexthatcorrespondedtothebreeders’prioritiesachievednearmaximumgainsforweevilresistance,acousticvelocity,andheightgrowth,butasmalldecreaseforDBH.Theresultsofthisstudyindicatethatitispossibletobreedforhigh‐quality,weevil‐resistantNorwaysprucereforestationstockwithhighaccuracyachievedfromsingle‐traitormulti‐traitGS.

K E Y W O R D S

breeding,conifers,indexselection,insectresistance,multi‐traitgenomicselection,Norwayspruce,whitepineweevil,woodquality

2  |     LENZ Et aL.

1  | INTRODUC TION

Treesare long‐livedstationaryorganisms thathave towithstandpests and diseases during their lifetime.Host–pest relationshipsmay constantly coevolve over time when organisms share thesame environment (Núñez‐Farfán, Fornoni, & Valverde, 2007;Strauss&Agrawal, 1999).However, exotic speciesmaybemoreexposedtodamagebypestinsectsnativetotheareawheretheyare introduced (Brockerhoff, Liebhold, & Jactel, 2006) becauseresistance mechanisms have usually not evolved in response tothe selective pressure imposed by native insects, which couldpotentially compromise the productivity of exotic tree planta‐tions(Branco,Brockerhoff,Castagneyrol,Orazio,&Jactel,2015).While studies comparing the relative vulnerability of native andexoticconiferstonativeinsectsreportedmixedresults(Fraser&Lawton, 1994; Langström, Lieutier, Hellqvist, & Vouland, 1995;Lombardero, Alonso‐Rodríguez, & Roca‐Posada, 2012; Roques,Auger‐Rozenberg, & Boivin, 2006; Zas, Moreira, & Sampedro,2011),inthemajorityofcases,exoticconifersweremoredamagedthannativeones.

Norway spruce (Picea abies [L.] Karst) is a conifer native toScandinavia,EasternEurope,andthemountainousregionsofcen‐tral Europe. Being the most important commercial softwood forlumber and pulp and paper production in Europe (Hannrup et al.,2004),thespecieswasfoundtobealsohighlyproductiveinEasternNorthAmerica andoneof themost productive conifer in planta‐tioninQuebec,Canada(Thiffaultetal.,2003).However,itishighlysusceptible to the indigenous white pine weevil (Pissodes strobi Peck), awood‐boring insect found in the temperateand southernboreal forests across the North American continent. Larvae feedonleadershoots,causingdieback;eventuallylateralbranchestake

over,causingkinkandcrookedstemsofattackedtrees.Besidesitsprincipalhosteasternwhitepine(Pinus strobusL.),theweevilattacksdifferent native spruces across the North American continent. InNorwayspruce,moderateweevildamageleadstosignificantmon‐etary loss due to stemdefects and the resulting losses in lumbervolumeandquality(Daoust&Mottet,2006).

ThefirstNorwayspruceplantationswereestablishedinNorthAmericainthe19thcenturyandCanadianearlygenetictestingef‐fortsofthisspeciesdatebacktothe1920satthePetawawaNationalResearchForest(Holst,1955).Besidesthescreeningforbestgrow‐ing and frost hardy seed sources, it was quickly recognized thatbreedingeffortsneededtoincludeweevilresistance(Holst,1963).ThegeneticvariationinweevilresistancehasbeendocumentedinNorthAmericansprucespecies,includingSitkaspruce(Picea stichen‐sis[Bong.]Carr.)(Alfaro,King,&VanAkker,2013;Alfaro,VanAkker,Jaquish,&King,2004;King,2004)andinteriorspruce(Picea glauca [Moench] Voss × engelmannii Parry ex Engelm.; white spruce,Engelmann spruce, and their hybrids) (Alfaro et al., 2004; King,Yanchuk,Kiss,&Alfaro,1997).AlthoughNorwaysprucedidnotco‐evolvewiththewhitepineweevilinitsnativeEuropeanrange,mod‐erate‐to‐highgeneticvariationandheritability for resistancewerereported for this species (Holst, 1955;Mottet,DeBlois,&Perron,2015). Current Canadian Norway spruce breeding programs arelargelybasedonresistantselectionsmadebytheCanadianForestService in thepast (Daoust&Mottet, 2006).However, selectionsweremadefollowingconventionalphenotypicevaluationsofmaturetreesandpedigree‐basedapproaches,thusrequiringmanyyearsoftestingingeneticexperiments.Recentdevelopmentsinquantitativegenomicsandbreedingsuchaswhole‐genomepredictionsmayhelpshortentheevaluationstageandbreedingcycles(Park,Beaulieu,&Bousquet,2016).

Box 1 Genomic selection: principles and application in tree breedingGenome‐widepredictionorgenomicselection(GS;Meuwissenetal.,2001)reliesonsimultaneouslyestimatingeffectsofmanythou‐sandmarkers,withsomethatareinlinkagedisequilibrium(LD)withquantitativetraitloci(QTL),inordertoestimatethegeneticmeritofanindividual.AnotherGSapproachreliesonusinggeneticmarkerstoestimatetherealizedgenomicrelationships(G)betweentreestoobtainpredictions(GBLUPs)oftheirgeneticvalue(VanRaden,2008),asopposedtoconventionalmethodsrelyingontheregisteredpedigreetomakesuchpredictions.Genomicselectionmodelsarebuiltusinggenomicprofilesandphenotypicmeasurementsofthesametreesinabreedingpopulation(i.e.,trainingpopulation,Figure1a).Usingthesemodels,thepredictionofgeneticmeritcanbemadebasedonmultilocusgenotypes,thuseliminatingtheneedtophenotypeandevaluatetheperformanceofcandidatesforselection(Figure1b).Whenpredictivemodelshavebeenvalidatedandaresufficientlyaccurate,genomicselectioncanoutperformconventionalpedigree‐basedselectiongiventhatgenomicprofilesfromyoungmaterial(seed,seedling,orembryo)canbeobtainedtopredictgeneticvaluesandmakeselectionsataveryearlystage,thusincreasingdramaticallygeneticgainsperunitoftime(Figure2).Thisisparticularlymoresoforspruces,whichcanbevegetativelypropagatedinanefficientfashionfromselectionsmadeatthejuvenilestage(Parketal.,2016).GSisparticularlyefficientfor(sub‐)borealconifers,whereconventionalbreedingcyclestakeupto30yearsorlonger,largelyduetotheevaluationstagethatcantakeupto25years(Mullinetal.,2011).Hence,undertheapplicationofGS,theroleofphenotypingissignificantlychangedandisonlyneededformodelconstructionandvalidation.Also,withsamegenomicprofiles,modelscanberecalibratedwithlittleeffortfordifferenttraitsaccordingtochangingbreedingpriorities.Selectionintensitycanalsobeincreasedbyscreeninglargenumbersofcandidateswithoutphenotypingcosts,whichisparticularlyrelevantinthecontextofmulti‐traitselection.GSiscurrentlybeingincorporatedintodifferentsprucebreedingprogramsineasternCanada.

     |  3LENZ Et aL.

Theapplicationofgenomicstoforesttreeshasgainedinterestto hasten breeding and better understand the genetic control ofpestresistanceaswellaseconomicallyimportantgrowthandwoodqualitytraits(Plomion,Bousquet,&Kole,2011).Withthecommonlimitationofconventionalmarkerassociationstudiestopredictlargeparts of quantitative genetic variation (e.g., Beaulieu et al., 2011;Gonzalez‐Martinez,Wheeler, Ersoz,Nelson,&Neale, 2007;Porthetal.,2013),effortsintreebreedinghavebeenturningtogenomicpredictionusingdensemarkerpanels.Genomicselection (GS,Box1)approachesrelyonestimatingeffectsofmanythousandmarkers(Meuwissen,Hayes,&Goddard,2001)orusingtherealizedgenomicrelationships(G)betweentreestoobtainpredictionsofgeneticval‐ues (GBLUPs; VanRaden, 2008). Both GS approaches have beensuccessfullytestedinproof‐of‐conceptstudiesinforesttreestopre‐dictgrowthandwoodquality,forexample,inEucalyptus(Resende,Munoz,etal.,2012;Resende,Resende,etal.,2012),pines(Isiketal.,2016;Resende,Munoz,etal.,2012;Resende,Resende,etal.,2012;Zapata‐Valenzuela, Whetten, Neale, McKeand, & Isik, 2013), andspruces(Beaulieu,Doerksen,Clément,MacKay,&Bousquet,2014;Beaulieu,Doerksen,MacKay,Rainville,&Bousquet,2014;Chenetal.,2018;Lenzetal.,2017;Ratcliffeetal.,2015).

Mostofthegenomicselectionstudiesintreespeciesfocusedonmodelinggrowthandwoodtraits,whicharequantitativetraitslikelytobecontrolledbyalargenumberofgenesofsmalleffects(Namkoong,Kang,&Brouard,1988).Despite the fact thatmanytreebreedingprogramsscreenforbioticresistanceagainstpestsordisease(Mullinetal.,2011),toourknowledge,thereisnostudyon the accuracy ofGS for insect resistance in trees.One studytested different GSmodels to predict resistance to a pathogenin loblolly pine (Pinus taeda L.) (Resende, Munoz, et al., 2012;Resende,Resende, et al., 2012). Theauthors reported that fusi‐formrustresistancewaslikelycontrolledbyafewgenesoflargeeffectssinceitwasbestpredictedwithBayesianregressionmod‐elsthatallowedfordifferentvarianceofmarkereffects.Notonlyisthegeneticarchitectureofthetraitanimportantconsideration

inthechoiceofGSmodel,butonemustalsodealwiththenatureofthephenotypicdata.Screeningdataforpestresistanceismostoften qualitative or semiquantitative, which needs appropriatestatisticalapproachesthatcanhandlenon‐normalityofmodelingerrors.Thus,there isanopportunityfortestingdifferentGSap‐proacheswithweevilresistancedatainNorwayspruce,forexam‐pletheBayesiangeneralizedlinearregressionmodelsthatsupportbinaryorordinaldata(Perez&delosCampos,2014)orthethresh‐oldGBLUPmodeldevelopedforordinaldata (Montesinos‐Lópezetal.,2015).

Inpractice,breedersgenerallyneedtoconsidermultipletraitssi‐multaneouslyintheirselectionsforimprovedgeneticstock.Besidesreducinginsectattack,improvinggrowthandwoodvolumearemajorgoalsforNorwayspruce,asitisforseveralplantation‐grownconi‐fers (Mullinetal.,2011).However, reductionofwoodqualitywasobservedinthepastunderselectionforacceleratedgrowth(Chen

F I G U R E 1   [Box1].Genomicselectionmodelingandintegrationintreebreeding (a) Build GS models

(b) Apply GS models

1∑=

Genomic profileTrees in genetic trials

Treegeneticvalue

GS model

DNA

Assesstrait

DNA

Seedling,seed,embryo Genomic profile

Predictedgenetic value

Select andpropagate

nb markers

Marker effect

F I G U R E 2   [Box1].Estimatedtimeforcompletingabreedingcyclein(sub‐)borealconiferssuchasspruces

4years

20 to 25

years

Crosses

fo noitaruD

gnideerbcy

cle 4

1 to 2 yearsEvaluation

Conventionalbreeding

Genomicselection

4

4Propaga�on

<10 years

>28 years

years

years

years

4  |     LENZ Et aL.

etal.,2014;Lenz,Cloutier,MacKay,&Beaulieu,2010).Therefore,important wood traits for mechanical applications such as woodstiffness should be consideredwhen performing selections (Lenz,Auty,Achim,Beaulieu,&Mackay,2013).Mottetetal. (2015)con‐cludedthatselectionforweevilresistancewouldnotreduceheightgrowth,butcouldaffectdiameterandthereforevolume.However,the genetic relationships between weevil resistance and intrinsicwood properties such as wood density and stiffness have neverbeeninvestigated.Thus,thereisaneedtounderstandthegeneticcorrelationsbetweenweevil resistance,woodquality, and growthtraitsandtolookatthepossibilitytocombinetheminamulti‐traitgenomicselectionframework.

Multivariate genomic selection models can improve the accu‐racyofpredictionsbytakingadvantageofthegeneticcorrelationsbetween traits (Calus&Veerkamp,2011).Thisability isespeciallyadvantageous forpredictionof traits thatarecostlyordifficult tomeasure by conventional means on a large number of candidatetrees,suchasweevilresistanceorwoodquality,byusingavailablecorrelatedindicatortraits.Simulationstudiesshowedthatmulti‐traitmodelscanincreasetheaccuracyofatargettraitof lowheritabil‐itywhen it ismodeledtogetherwithgeneticallycorrelated indica‐tortraitsharboringhighheritability(Guoetal.,2014;Jia&Jannink,2012). In addition, thebenefitsofmulti‐traitGSare increased fortargettraitswithscarcephenotypicrecordswhentheyarecoupledwithintensivelyphenotypedindicatortraits(Guoetal.,2014;Jia&Jannink, 2012; Schulthess et al., 2016). Few studies have appliedmulti‐traitgenomicselectionmethods to realplantbreedingdata‐sets (e.g., Bao, Kurle, Anderson, & Young, 2015; Fernandes,Dias,Ferreira, &Brown, 2018; Schulthess et al., 2016). In tree species,the accuracy ofmulti‐trait versus single‐traitGSmodelswas only

testedonafewtraitsusingbivariatemodelsinloblollypine(Cheng,Kizilkaya,Zeng,Garrick,&Fernando,2018;Jia&Jannink,2012)andin Eucalyptus (Cappaetal.,2018),andthesestudiesdidnot inves‐tigate theeffectsofmissingphenotypicdata.Given theobservedpositivegeneticcorrelationsbetweenweevilresistanceandheightgrowth(Mottetetal.,2015),andthepossiblecorrelationswithwoodqualitytraits,multi‐traitGSmodelscould improvetheaccuracyofpredictionsfortraitsthataredifficultandexpensivetoassessonalargenumberoftrees.

Onceaccurategenomic‐estimatedbreedingvaluesforeachtraithavebeenobtainedfromeithersingle‐traitormulti‐traitmodels,itispossibletocombinethemintoaselectionindex(SI;Hazel,1943)andtorankindividualsbasedontheiroverallperformanceacrossalltraits.Thisstrategyisespeciallyusefulinthepresenceofnegativegeneticcorrelationsinordertoselectmaterialthatachieveagoodbalanceintheirperformanceforalltraitsofinterest.Inaddition,GSisespeciallywellsuitedtoallowidentifyingcorrelationbreakersinsufficient number, given the higher selection intensities that canbe achieved by screening larger numbers of candidates thanwithconventionalmethods(Parketal.,2016).Hence,multi‐traitgenomicselectionmodelsandindexselectionaretwodifferenttoolsthatcanbecombinedtoimproveaccuraciesofbreedingvaluesandoptimizegeneticgains,respectively,inamulti‐traitbreedingprogram.

Here,wepresentacomprehensivegeneticstudyofweevilresis‐tanceinNorwayspruceanditsrelationshipswithgrowthandwoodquality traits in the context of establishing a multi‐trait genomicselectionbreedingprogram.Ourobjectiveswere to (a) betterun‐derstandthegeneticrelationshipsbetweenweevilattackandothergrowthandwoodtraits,inparticularintrinsicwoodqualitytraits;(b)evaluatetheperformanceofdifferentsingle‐traitgenomicselectionmodels, especially for weevil resistance; (c) test the performanceofmulti‐traitgenomicselectionmodelsforpredictingatargettrait(weevil resistanceorwoodquality)whencoupledwithgeneticallycorrelatedindicatortraits(e.g.,heightgrowth);and(d)developmulti‐traitgenomicselectionindicesfortheproductionofhigh‐qualityandweevil‐resistantseedlingstockinNorwayspruce.

2  | MATERIAL AND METHODS

2.1 | Genetic material and phenotyping

Thedataanalyzedinthisstudyareasubsetofalargerbreedingpopu‐lationderived fromapartialdiallelmatingdesign (seeMottetet al.,2015formoredetails).WefocusedourphenotypingandgenotypingeffortsonthetreesplantedontwositesaffectedbywhitepineweevilinQuebec,thatis,Saint‐Modeste(47.85°N;69.38°W;elevation:140m;abbreviated STM) andGrandes‐Piles (46.68°N; 72.68°W; elevation:150m;abbreviatedGPI),respectively,locatedinthebalsamfir–yellowbirchandthesugarmaple–yellowbirchbioclimaticdomains(Figure3).Bothtestsweresetupinyear2000.TheGrandes‐Pilesplantationwasheavilyaffectedbyweevilswith~70%ofthetreesattackedat leastoncebyage16,whiletheSaint‐Modesteplantationwasmoderatelyaffected(~47%ofthetreesattackedbyage16).Todevelopgenomic

F I G U R E 3  LocationofthetestsitesSaint‐Modeste(STM)andGrandes‐Piles(GPI)intheprovinceofQuébec,Canada

_

_

Québec

Montréal

STM

GPI

64°W68°W72°W50°N

46°N

±

0 200 Km

Maine(U.S.A.)

Provinceof Quebec

NewBrunswick

     |  5LENZ Et aL.

selectionmodelsforweevilresistance,weselected40full‐sibfamilies(35parents),20ofwhichwereratedresistantand20ratedsusceptiblebasedonweevilattacksurveysatages10and15onthesetwosites.Atotalof726trees(14to20perfamily,mean=17.85)weresampled.Eachparentwascrossedonaverage2.3times(FigureS1).Thetwotri‐alswereestablishedaccordingtoarandomizedcompleteblockdesign,eachwith fiveblocksand three‐tree rowplots foreach family (treespacing:2.5m×2m).Becauseoftreemortality,notallfamilieswererepresentedineveryblock(i.e.,incompleteblockdesign).

Tree height (Height15) and diameter at breast height (DBH15)weremeasured at age15.Theheight‐to‐diameter ratio (Height15/DBH15)wascalculatedasaproxyofstemtaper.Threewoodqualitytraitsrelatedtomechanicalpropertieswereassessed:averagewooddensityandcellulosemicrofibrilangleweredeterminedfromwoodincrementcoresusingX‐raydensitometryanddiffractometryatage15(Density15andMFA15)asdescribedinLenzetal.(2017);acousticvelocitywasmeasuredatage16(Velocity16)withtheST300Hitmantool.Acousticvelocity isaproxyforwoodstiffnessormodulusofelasticitymeasuredatstandingtrees(Chenetal.,2015;Desponts,Perron,&DeBlois,2017;Lenzetal.,2013).

Foreachoftwosurveysatages10and15,thepresence/absenceofweevil damage in the current year (coded0/1) and in previousyears(coded0/1)wererecorded.Currentyeardamagewasdetectedbyinspectingtheterminalshootforemergenceholesordeathoftheleadershoot.Weevildamageinpreviousyearswasvisiblebyforks,curves,bayonets,ormultiplestems.Wecalculatedthecumulativenumberofattacks(CWA)as:

whereWAcurrent10 andWAcurrent15 are thepresence/absenceofat‐tackatage10and15,respectively;WAprevious10isthepresence/ab‐senceofattackpriortoage10;andWA11–14isthepresence/absenceofattackbetweenages11and14.ThevariableWA11–14,whichwascalculatedtoavoiddouble‐countingpreviousattacks,wasequalto1

(presence)iftherewasanattackpriortoage15,butnoattackatage10orpriortoage10.TheresultingCWAvariableisordinal(orderedcategoriesof0,1,2, and3weevil attacks).Table1andFigureS2providethesummarystatisticsandviolinplots,respectively,forthetraitsassessedinthisstudy.FigureS3showsthespatialdistributionofCWAvaluesinthetestsites.

2.2 | SNP genotyping

The726treesweregenotypedusinganInfiniumiSelectSNParray(Illumina),whichwasassembledfromacatalogofhigh‐confidencegeneSNPsobtainedfromexomecaptureandsequencing(Azaiezetal.,2018).Thegenotypingreproducibilityratewashigh(99.94%),asestimatedfromtwopositivecontrolsreplicatedoneachgenotypingplate.From5,660successfullymanufacturedSNPsrepresentingasmanydistinctgenelociwelldistributedoverthe12sprucelinkagegroups(Pavyetal.,2017),weretainedatotalof3,914SNPswithcallrate≥90%(averagecallrateof99.6%),minorallelefrequency(MAF)≥0.005,andafixationindex|FIS|<0.50.SNPswerewelldistributedacrossMAFclasseswith86%oftheSNPswithMAF≥0.05(FigureS4). Missing genotypes (only 0.4% of genotypes) were imputedusingak‐nearestneighbormethodbasedonlinkagedisequilibrium(LD‐kNNi)withthesoftwareLinkImpute (Moneyetal.,2015).Thesoftwareestimatedanaccuracyof0.83for imputedgenotypesbyrandomlymaskinggenotypes.

2.3 | Relationship matrices and pedigree verification

Allanalyseswereperformed in theRv.3.3.1environment (RCoreTeam,2016).Apedigree‐basedrelationshipmatrix(A)anditsinversewerefirstcomputedbasedontheregisteredpedigree informationusing the function “asreml.Ainverse” of the R package ASReml‐Rv.3.0 (Butler, Cullis, Gilmour, & Gogel, 2007). For use in genomicselection (GS)models, therealizedgenomic relationshipmatrix (G,Figure S5) was computed from themarker data with the “A.mat”

(1)CWA=WAprevious10+WAcurrent10+WA11−14+WAcurrent15

TA B L E 1  Phenotypicmeans,standarddeviations(SD),andcoefficientsofvariation(CV)foreachsiteandacrosssitesforthe714treesretainedforanalyses

Traita Units

GPIb (n = 388) STMb (n = 326) Across sites (n = 714)

Mean SD CV (%) Mean SD CV (%) Mean SD CV (%)

Velocity16 km/s 3.71 0.33 8.96 3.69 0.31 8.54 3.70 0.32 8.77

Density15 kg/m3 344.78 24.77 7.19 395.45 29.30 7.41 367.91 36.91 10.03

MFA15 degrees 10.98 4.59 41.81 13.22 6.47 48.96 12.01 5.64 46.98

DBH15 mm 148.05 20.08 13.56 106.73 20.49 19.19 129.19 28.89 22.36

Height15 cm 908.09 128.12 14.11 788.90 111.64 14.15 853.67 134.61 15.77

Height15/DBH15 — 62.08 10.01 16.13 75.46 11.61 15.39 68.19 12.67 18.57

CWA Numberofattacks 0.99 0.80 80.79 0.63 0.76 121.65 0.83 0.81 97.46

aMeasuredtraitsindescendingorderareacousticvelocityatage16asaproxyforwoodstiffness,averagewooddensityatage15,microfibrilangleatage15,diameteratbreastheightatage15,treeheightatage15,theheight‐to‐diameterratioatage15,andthecumulativenumberofweevilattacks.bExperimentalsitesGrandes‐Piles(GPI)andSaint‐Modeste(STM).

6  |     LENZ Et aL.

functionoftheRpackagerrBLUP(Endelman&Jannink,2012)withthedefaultoptions,whichwasequivalenttotheformuladescribedbyVanRaden(2008).AcomparisonoftheA and Gmatricesrevealed11“misclassified”treesthatpresumablydidnotbelongtotheirex‐pectedcross.Inaddition,onetreewasdeemedanoutlierbecauseithadabnormallyhighaveragewooddensity(Density15),aftercheck‐ingmodelresiduals(seeEquation(2)below).Afterremovingmisclas‐sifiedandoutlier trees,714 treesgenotypedon3,914SNPswereused insubsequentanalyses.TheresultingA and GmatriceswerehighlycorrelatedwithaPearson r=0.94 (FigureS6).LargevaluesofGwithineach classofA aremostlydue to two inbred families(FigureS7).

2.4 | Heritability and genotype‐by‐environment interactions

First, variance components, heritability, andbreeding valueswereestimated using the conventional pedigree‐based (ABLUP) or thegenomic‐based(GBLUP)individual‐treemixedmodels(theso‐called“animalmodel”)inASReml‐Rv.3.0:

where yisthephenotype;μistheoverallmean;sisthefixedsiteef‐fect;b(s)istherandomeffectofblockwithinsite,withb (s)∼N(0,�2

bIb);

a is the random additive genetic effect, with a∼N(0,�2

aA); sa is

the random interaction of site with additive genetic effects, withsa∼N(0,𝜎2

saIs⊗A); and e is the residual term, assuming homogene‐

ityacrosssiteswithe∼N(0,�2eIe).FortheABLUPmethod,thematrix

A is the pedigree‐based relationshipmatrix,whichwas replaced bythe realized genomic relationship matrixG for the GBLUP method(a∼N

(0,�2

aG) and sa∼N(0,�2

saIsG)).TheX and Zmatricesareincidence

matricesoftheircorrespondingeffects,andIxisanidentitymatrixofitsproperdimension.Thesymbol⊗referstotheKroneckerproduct.Totestthehypothesisofgreaterthanzerovarianceforeacheffect(H0: σ2=0;H1: σ2>0),weperformedalikelihood‐ratiotestwithonede‐greeoffreedombetweenthefullmodelinEquation(2)andareducedmodelwithouttheeffecttobetested.Thedominanceeffectwasnotincluded inmodelsbecause itwasnotsignificantforall traitsunderstudy (Table S1), and, according to BIC, the fit of models includingdominancewassimilarorworsethanthemodelsincludingtheadditiveeffectonly(TableS2).Wecomparedmodel(1)withamodelfittingadifferentresidualvarianceforeachsiteandfoundthatthelattermodelwasslightlybetterforthreeoutoftheseventraitsstudied(TableS3).However,thebreedingvaluesbetweenbothapproacheswerehighlycorrelatedforalltraits,withr>0.99.Thus,weoptedforthesimplermodelinEquation(2)tokeepABLUPandGBLUPmodelscomparablewithmarker‐basedgenomicselectionmodels.Finally,inspectionoftheresidualsfromEquation(2)versusthedistanceinXandYinthetrialsshowednodetectablespatialpatterns(notshown).

Narrow‐senseindividualheritabilitywasestimatedas:

The sizeof genotype‐by‐environment interaction (GxE), or type‐Bcorrelation(rB),wasestimatedas:

Standarderrorsofheritabilityandtype‐Bcorrelationestimateswereobtainedusingthedeltamethod(pinfunctionfromtheRpackagenadiv;Wolak,2012).

2.5 | Correlations between weevil resistance, wood quality, and growth traits

Toestimatesingle‐sitephenotypicandgeneticcorrelationsbetweentraits, bivariatemodelswere run for all pairs of traits in ASReml.Bivariatemodelswererunforeachsiteseparatelybecauseofcon‐vergenceproblemsofthemulti‐sitemodelduetolargeGxEforsometraits(e.g.,DBH15,seeResults).Thefollowingmodelwasfitted:

where yi and yjarethestackedvectorsofphenotypicobservationsfortrait iandtrait j, respectively;t isthevectoroffixedeffectsoftraits (i.e., thegrandmean foreach trait);b(t) is the randomeffectofblocknestedwithintrait,withb (t)∼N

(0,IbVB

); a(t)istherandom

additiveeffectwithintrait,witha (t)∼N(0,AVA

); and eistheresidual

error,withe∼N(0,IeVR

).ThematrixA(ABLUP)wasreplacedbythe

realizedgenomicrelationshipmatrix(G)fortheGBLUPmethod.ThematricesVB,VA,andVRare2x2variance–covariancematricesde‐finedbythecorrelationofeffectsbetweentraits(rb,ra,andre,respec‐tively)anduniquevariancesforeachtrait(i.e.,CORGHinASReml).Tofacilitateconvergence,weprovidedstartingvaluesforthevariancecomponentsinVB,VA,andVRmatricesthatweretakenfromthere‐sultsofthesingle‐traitmodels(Equation(2),TableS4).Forrb,ra,andre,thestartingvaluewassetto0(nocorrelation).Thegeneticcorrela‐tionbetweentraitswasdirectlyprovidedbytheestimatedparameterraandthephenotypiccorrelationwascalculatedas:

whereCOV(i,j)pisthephenotypiccovariancebetweentraits,and��2

pi,

��2bi,��2

ai,and��2

eiaretheestimatedphenotypic,block,additive,andre‐

sidual varianceof trait i (same for trait j), respectively. The signif‐icanceof thegeneticcorrelation (H0: ra=0;H1: ra≠0)wastestedby performing a likelihood‐ratio testwith one degree of freedombetweenthefullmodelinEquation(5)andareducedmodelassum‐ingra=0(i.e.,adiagonalVAmatrix).Thesignificanceofthepheno‐typiccorrelation(H0: rp=0;H1: rp≠0)wastestedbyperformingalikelihood‐ratiotestwiththreedegreesoffreedombetweenthefullmodelinEquation(5)andareducedmodelassumingnocorrelationbetweentraits(rb=0,ra=0,andre=0).Thesingle‐siteheritabilityoftraitiwasgivenby:

(2)y=�+Xs+Z1b (s)+Z2a+Z3sa+e

(3)h2ind

= ��2a∕

(��2a+ ��2

sa+ ��2

e

)

(4)rB= ��2a∕

(��2a+ ��2

sa

)

(5)⎡⎢⎢⎣yi

yj

⎤⎥⎥⎦=Xt+Z1b (t)+Z2a(t)+e

(6)rP=COV(i,j)p√

��2pi��2pj

=

rb

√��2bi��2bj+ ra

√��2ai��2aj+ re

√��2ei��2ej√(

��2bi+ ��2

ai+ ��2

ei

) (��2bj+ ��2

aj+ ��2

ej

)

     |  7LENZ Et aL.

2.6 | Single‐trait genomic selection models

We evaluated four single‐trait GS methods: GBLUP, Bayesianridge regression (BRR), BayesCπ, and, in addition for CWA,thresholdGBLUP(TGBLUP)developedforordinaltraits.GBLUPwas implemented as described in Equation (2) in ASReml. TheGmatrix describes the realizedgenomic relationshipsbetweentrees, which better account for within‐family Mendelian sam‐pling, as well as deeper (unknown) pedigree relationships.GBLUP relies on the “infinitesimal” model of quantitative ge‐netics, assuming that the genetic control of complex traits isequallydistributedacrossmany(infinite) lociwithsmalleffects(Falconer&Mackay,1996).TheGBLUPmodelassumedthatre‐sidualsarenormallydistributedforalltraits.ForthetraitCWA,we tested the threshold GBLUP model (TGBLUP) for ordinaldata,asdescribedbyMontesinos‐Lópezetal. (2015).Toimple‐mentTGBLUP,thesamemodelasinEquation(2)wasfitted,butthe response typewas set to “ordinal” (probit link function) intheBGLRRpackagev.1.0.5(delosCampos,&Pérez‐Rodríguez,2016). Conventional‐estimated breeding values (EBVs) of indi‐vidual trees for the ABLUP method or the genomic‐estimatedbreeding values (GEBVs) for theGBLUP and TGBLUPmethodswereobtainedfromthebestlinearunbiasedpredictions(BLUPs)oftherandomadditiveeffect(a).

BRRandBayesCπarefromadifferentclassofmodels,inwhichmarker effects are estimated andused topredict breedingvaluesbasedontreegenotypes.WefittedthefollowingBayesianmodelintheBGLRpackage:

where yisthephenotype;μistheoverallmean;sisthefixedsiteeffect(i.e.,modeledwithaflatprior);b(s)istherandomeffectofblockwithinsite,withb (s)∼N(0,�2

bIb); am is therandomadditive

effect of markers; and e is the residual term, with e∼N(0,�2eIe).

NotethatcomparedwithABLUPandGBLUPmodels,thegeno‐type‐by‐environmentinteraction(GxE)componentwasnotfittedinBRRandBayesCπmodels, thusassumingthatmarkereffectswerestableacrossenvironments.Toaccountfordifferentdistri‐butionsofmarkereffects,thepriorforamchangesdependingonthemethod(seeAppendixS1forafulldescription).Briefly, themethodBRR isaBayesianversionof ridge regression, inwhichmarkereffectsarenormallydistributed(i.e.,Gaussianprior)andhaveidenticalvariance(am∼N(0,�2

mIm)).InBRR,allmarkershavea

nonzeroeffect,andsothismethodisappropriatefortraitscon‐trolledbyalargenumberofgeneswithsmalleffects.Incontrast,themethodBayesCπtakesintoaccountthatonlyaproportionπ ofmarkershaveaneffect,whileaproportion (1−π)ofmarkereffects are shrunk toward zero (Habier, Fernando, Kizilkaya, &Garrick,2011).FortheBRRandBayesCπmethods,theresponsetypewassetto“ordinal”(probitlinkfunction)forthetraitCWA,

and to “gaussian” for all other traits.BGLRwas run for50,000iterations and a thinning interval of 20, with the first 15,000iterations discarded as a burn‐in. Genomic‐estimated breedingvalues(GEBVs)wereobtainedbysummingovertheeffectsofallmarkers,withGEBVi=

∑m

j=1Z’ijaj,whereajistheestimatedeffectof

thejthmarker,andZ′

ijisanindicatorofthegenotypeofindividual

iatthejthmarker.

2.7 | Multi‐trait genomic selection models

Genomic selection models that incorporated the information ofmultiplecorrelatedtraitsintoasingleanalysiswereevaluatedusingGBLUPmultivariatemodelsinASReml.Tofacilitatetheconvergenceofmultivariatemodels, themodelingwasdone intwosteps.First,phenotypeswereadjustedforblockandsiteeffects (y*)bytakingtheresiduals(e)ofamodelthatincludedafixedsiteeffect(s)andarandomblockwithinsiteeffect(b(s)):y=�+Xs+Zb (s)+e.Afterad‐justingphenotypes,theportionofGxEduetorankchangesindif‐ferentsitesremains,butthe“level‐of‐expressionGxE”(i.e.,spreadofbreedingvaluesacrossenvironments)iscontrolledfor(Li,Suontama,Burdon,&Dungey,2017).Second,amultivariatemodelwithptraitswasfitted:

where y*i are the stacked vectors of adjusted phenotypes from

trait i totraitp; t is thevectorof fixedeffectsof traits (i.e., thegrand mean for each trait); a(t) is the random additive effectwithintrait,witha (t)∼N

(0,GVA

); and eistheresidualerror,with

e∼N(0,IeVR

).ThematricesVA,andVR are p×p variance–covari‐

ancematrices,definedbycorrelationsbetweenallpairsoftraitsanduniquevariances for each trait.GxE (as rank‐changes inter‐action)wasnotfittedtosimplifythemodelandfacilitateconver‐gence.Weprovidedstartingvaluesforthevariancecomponentsin VA and VRmatricesthatweretakenfromtheresultsofthesin‐gle‐traitmodels.WeobtainedGEBVsofindividualtreesforeachtraitseparatelyfromtheBLUPsoftherandomadditiveeffect(a)withintrait.

Weevaluatedtheperformanceofmulti‐traitGSmodelsforpre‐dictingatargettrait,whencoupledwithgeneticallycorrelatedindi‐catortraits.Wechosethreetargettraits,thecumulativenumberofweevilattacks(CWA),averagewooddensityatage15(Density15),andmicrofibrilangleatage15(MFA15),forwhichmeasurementsaredifficultorcostlytoobtainforalargenumberofcandidatetrees.Foreachtargettrait,fourmulti‐traitGSmodelwastested:(a)atwo‐traitmodelincludingoneofthetargettraitsandHeight15asanindicatortrait;(b)atwo‐traitmodelwithoneofthetargettraitsandHeight15/DBH15ratio;(c)atwo‐traitmodelwithoneofthetargettraitsandVelocity16;and(d)athree‐traitmodelwithoneofthetargettraits,Height15/DBH15ratio,andVelocity16.Tosimulateasituationwhere

(7)h2indss

= ��2ai∕

(��2ai+ ��2

ei

)

(8)y=�+Xs+Z1b (s)+Z2am+e

(9)

⎡⎢⎢⎢⎢⎣

y* i

…

y*p

⎤⎥⎥⎥⎥⎦=Xt+Za(t)+e

8  |     LENZ Et aL.

thetargettraitwasonlymeasuredforasmallersubsetofthetrees,thepercentageofmissingdata in the trainingset (seebelow)wasvaried from0% to90%by randomlyaddingmissingvalues to thephenotypesofthetargettrait.Werepeatedthisprocess100timesforeachtraitandlevelofrandommissingvaluesincross‐validation(seebelow).

2.8 | Cross‐validation and estimation of accuracy

ThepredictionaccuracyofABLUP,GBLUP (singleandmulti‐trait),TGBLUP,BRR,andBayesCπmodels’predictionswastestedusingatenfoldcross‐validation(CV)schemecombiningdataacrosssitesasinBeaulieu,Doerksen,Clément,etal.(2014)andLenzetal.(2017).Thefullsetofindividualtreeswasrandomlysplitintotenfold,eachcontaining~10%of the trees fromeach family.Foreach roundofCV,ninefold(~642treesor90%)wasusedinmodeltraining,whichwasusedtopredictthebreedingvaluesfortheremainingfold(~71validationtreesor10%).ThistenfoldCVwasrepeatedtentimes,foratotalof100modelsforeachtrait.

Thepredictiveability(PA)ofthemodelswasevaluatedasthe Pearson correlation coefficient between the predictedbreedingvaluesofthevalidationtreesandtheadjustedphe‐notypes(y*)forblockandsiteeffects.Thepredictiveaccuracy(PACC)ofmodelswasestimated fromPAasPACC=PA∕

√h2ind

(Dekkers, 2007; Legarra, Robert‐Granie, Manfredi, & Elsen,2008). For all themethods tested (ABLUP, GBLUP, TGBLUP,BRR,BayesCπ , andmulti‐traitGBLUP),weused the h2

ind esti‐

matedfromtheGBLUPmodel(Equations2and3)asourbestestimateofheritabilityforthecalculationofpredictiveaccu‐racy (PACC). PA and PACCwere calculated within each foldto avoid including a fold effect, then averaged across foldsand repetitions to obtain standard errors (Isik, Holland, &Maltecca,2017).

Formulti‐traitmodels,thepredictionability(PA)andpredictionaccuracy(PACC)ofmulti‐traitGBLUPmodelswerecomparedwiththe equivalent single‐trait GBLUP models using adjusted pheno‐typesasaresponsevariable(seeAppendixS2).

2.9 | Genetic gains and multi‐trait selection indices

Expectedgenetic gains from single‐trait selectionwere calculatedasthemeanestimatedbreedingvalueofthetop5%treesforeachtraitseparately,asestimatedfromthesingle‐traitABLUP(EBVs)orGBLUP(GEBVs)analysis(Equation2).Theseestimatedgainsrepre‐sentedthemaximumpossiblegainforeachtrait.Toestimategeneticgains inamulti‐traitselectioncontext,wecombinedfour traitsofeconomicinterestintoaSIasfollows:

where Height15EBV, CWA6.15EBV, Velocity16EBV, and Density15EBV are theBLUPestimatedbreedingvalues fromthesingle‐traitABLUPorGBLUPanalysis(Equation2)forthecorrespondingtrait;andwiaretherelativeweightgiventoeachtrait,withtherestrictions:

0≤wi≤1foralltraits,andw1+w2+w3+w4=1.

WeassignedanegativesigntoCWAsinceadecreaseinthevalueof this trait (fewer weevil attacks) represents an improvement.Breedingvaluesforeachtraitwerescaledtoavarianceofone(al‐ready centered)prior toSI calculations.DBH15 is aneconomicallyimportanttrait,butwasexcludedfromtheSIscenariosbecauseitsheritability was not significantly different from zero (see results).Thefourweightcoefficientswerevariedbetween0and1byinter‐valsof0.05,resultingin1,771differentselectionindices.ForeachSI,treeswererankedaccordingtodecreasingvaluesoftheindex(I)andthetop5%treeswereselectedtocalculatetheexpectedgeneticgain.Foreachtrait, therelativegeneticgain (%)wascalculatedastheratioof theexpectedgaintothemaximumpossiblegainfromsingle‐traitselection.Wepresent,afirstSIscenario(SI‐1)thatcor‐respondedtotheprioritiesfortheNorwaysprucebreedingprograminQuébec,whichputmoreemphasisonweevilresistance(w2=0.6),followedbygrowth,representedherebyheightgrowth(w1=0.3),

(10)SI=w1Height15EBV−w2CWA6.15EBV+w3Velocity16EBV+w4Density15EBV

Traitc

ABLUP GBLUP

h2ind

rB h2ind

rB

Velocity16 0.37(0.12)** 0.79(0.15) 0.29(0.08)*** 0.76(0.16)

Density15 0.25(0.11)* 0.65(0.2)* 0.26(0.08)** 0.76(0.17)

MFA15 0.08(0.06) 0.47(0.32)* 0.06(0.05) 0.43(0.32)**

DBH15 0.00(0.00) 0.00(0.00)*** 0.00(0.00) 0.00(0.00)**

Height15 0.47(0.16)** 0.65(0.15)*** 0.22(0.08)** 0.52(0.17)***

Height15/DBH15 0.40(0.14)** 0.68(0.16)** 0.20(0.08)* 0.56(0.20)**

CWA 0.47(0.12)*** 0.97(0.08) 0.27(0.07)*** 0.86(0.15)

aThemodelfittedisdescribedinEquation(2).bLevelofstatisticalsignificance:*p<0.05;**p < 0.01; ***p < 0.001. cSeeTable1forfulldescriptionoftraits.

TA B L E 2   Individualnarrow‐senseheritability(h2

ind)andtype‐Bgenetic

correlation(rB)estimates(standarderrorsinparentheses)usingthesingle‐traitABLUPandGBLUPmethodsfortheacross‐siteanalysesa.Forheritabilityestimates,thesignificanceoftheadditivevariancecomponentisshown(seeTableS4).Fortype‐Bgeneticcorrelations,thesignificanceofthesite×additivevariancecomponentisshownb.Asignificantsite×additivevarianceindicatessignificantgenotype‐by‐environmentinteraction(i.e.,smallervaluesofrB)

     |  9LENZ Et aL.

andacousticvelocity (w3=0.1).Wechose topresent two furtherSIs that maximized the total relative gain of the following traits:Height15,CWA,andVelocity16 (SI‐2)andintheothercaseHeight15,CWA,Velocity16,andDensity15(SI‐3).

3  | RESULTS

3.1 | Heritability and genotype‐by‐environment interaction

Intheacross‐siteanalyses,heritabilityrangedfrom0to0.47usingthe ABLUP method and from 0 to 0.29 using GBLUP (Table 2).DetailsofestimatedvariancecomponentsareinTableS4.Wefoundmoderate‐to‐high heritability (ABLUP: h2

ind = 0.25–0.47; GBLUP:

h2ind=0.20–0.29)forthecumulativenumberofweevilattacks(CWA),

woodqualitytraits(Velocity16;Density15),heightgrowth(Height15),and height‐to‐DBH ratio (Height15/DBH15), whereas microfibrilangle(MFA15)wasunderlowadditivegeneticcontrol(theadditivevariancewasnotsignificantlydifferentfromzero).ForDBH15,the

estimatedheritabilitywasnullandthetype‐Bcorrelationwaszero(rB=0)duetolargegenotype×environmentinteraction(GxE).Usingthe GBLUP method, weevil resistance (CWA), acoustic velocity(Velocity16),andaveragewooddensity (Density15)hadthehighestheritabilities(h2

ind=0.26–0.29).ThelowestGxEestimateswerealso

found for these traits (rB=0.76–0.86usingGBLUP), indicating lit‐tle rankchangesof familiesbetweensites.GxEwasmoderate forHeight15andHeight15/DBH15(rB=0.52–0.56usingGBLUP)andwashigherforMFA15 and DBH15(rB<0.43usingGBLUP).

3.2 | Correlations between weevil resistance, growth, and wood quality traits

PhenotypicandgeneticcorrelationsbetweentraitsusingtheGBLUPmethodarepresentedforeachsiteseparately,inTable3forGPI,themostseverelyaffectedsitebyweevilattacks,andinTable4forSTM,thesitethatwasmoderatelyaffected.ResultsusingABLUPweresimi‐lar(GPI:TableS5;STM:TableS6),andsowepresentbelowonlythere‐sultsusingGBLUP.Weevilresistancewassignificantlycorrelatedwith

TA B L E 3  SiteGPI:phenotypic(rp,abovediagonal)andgeneticcorrelations(ra,belowdiagonal)betweentraitscalculatedwiththeGBLUPmethod.Diagonalelementsindicatethesingle‐sitenarrow‐senseheritability(h2

ind ss)foreachtrait.Standarderrorsofestimatesarein

parentheses.Geneticandphenotypiccorrelationsweretestedforsignificance.Forh2ind ss,thesignificanceoftheadditivevariancecomponent

isshown

Traitc Velocity16 Density15 MFA15 DBH15 Height15 Height15/DBH15 CWA

Velocity16 0.38(0.09)*** 0.32(0.06)*** −0.10(0.05) −0.16(0.06)** 0.28(0.06)*** 0.41(0.05)*** −0.19(0.06)*

Density15 0.61(0.14)*** 0.49(0.10)*** −0.04(0.05) −0.46(0.05)*** −0.07(0.07) 0.39(0.05)*** −0.12(0.06)

MFA15 −0.16(0.38) −0.11(0.40) 0.06(0.05) 0.02(0.05) 0.01(0.05) −0.03(0.05) 0.04(0.05)†

DBH15 −0.02(0.28) −0.38(0.23) −0.52(0.48) 0.18(0.09)* 0.40(0.05)*** −0.56(0.04)*** 0.11(0.06)

Height15 0.6(0.17)** 0.00(0.18) 0.29(0.34) 0.33(0.22) 0.54(0.09)*** 0.52(0.05)*** −0.48(0.05)***

Height15/DBH15 0.62(0.14)*** 0.36(0.16)* 0.37(0.34) −0.35(0.21) 0.74(0.12)*** 0.44(0.09)*** −0.54(0.04)***

CWA −0.52(0.18)* −0.20(0.19) −0.14(0.38)† 0.49(0.25) −0.69(0.12)*** −0.99(0.04)*** 0.44(0.09)***

aThemodelfittedisdescribedinEquation(5).bLevelofstatisticalsignificance:*p<0.05;**p < 0.01; ***p < 0.001; †Convergencefailed.cSeeTable1forfulldescriptionoftraits.

TA B L E 4  SiteSTM:phenotypic(rp,abovediagonal)andgeneticcorrelations(ra,belowdiagonal)betweentraitscalculatedwiththeGBLUPmethoda.Diagonalelementsindicatethesingle‐sitenarrow‐senseheritability(h2

ind ss)foreachtrait.Standarderrorsofestimatesarein

parentheses.Geneticandphenotypiccorrelationsweretestedforsignificance.Forh2ind ss,thesignificanceoftheadditivevariancecomponent

isshownb

Traitc Velocity16 Density15 MFA15 DBH15 Height15 Height15/DBH15 CWA

Velocity16 0.47(0.11)*** 0.26(0.07)*** −0.32(0.05)*** −0.18(0.08)* 0.23(0.07)* 0.41(0.07)*** −0.22(0.07)**

Density15 0.16(0.27) 0.21(0.09)*** 0.14(0.06) −0.43(0.06)*** −0.16(0.07)** 0.40(0.06)*** −0.22(0.06)***

MFA15 −0.78(0.16)** 0.18(0.32) 0.19(0.08)*** −0.07(0.06) −0.14(0.06) −0.01(0.06) −0.02(0.06)

DBH15 −0.29(0.32) 0.08(0.38) 0.71(0.32)* 0.14(0.08)** 0.62(0.04)*** −0.69(0.04)*** 0.25(0.06)***

Height15 0.62(0.22)* 0.15(0.36) −0.16(0.33) 0.05(0.44) 0.21(0.10)** 0.11(0.07) −0.23(0.06)**

Height15/DBH15 0.58(0.19)* 0.02(0.28) −0.65(0.23)* −0.69(0.19)* 0.71(0.24)* 0.34(0.10)*** −0.52(0.05)***

CWA −0.57(0.21)* −0.06(0.30) 0.25(0.29) 0.55(0.27) −0.60(0.25) −0.79(0.12)*** 0.29(0.10)***

aThemodelfittedisdescribedinEquation(5).bLevelofstatisticalsignificance:*p<0.05;**p < 0.01; ***p < 0.001. cSeeTable1forfulldescriptionoftraits.

10  |     LENZ Et aL.

growthandwoodqualitytraits.Onbothsites,wefoundamoderatenegativegeneticcorrelation(GPI:ra=−0.52;STM:ra=−0.57)betweenthecumulativenumberofweevilattacks(CWA)andacousticvelocity(Velocity16),andastrongnegativegeneticcorrelationbetweenCWAandHeight15/DBH15 (GPI: ra=−0.99;STM: ra=−0.79).TherewasanegativegeneticcorrelationbetweenCWAandHeight15onbothsites(GPI: ra = −0.69; STM: ra = −0.60), although this genetic correlationwasonlysignificantonthemostseverelyaffectedsiteGPIbyweevilattacks.Conversely,therewasapositive,butnotsignificant,geneticcorrelationbetweenCWAandDBH15(GPI:ra=0.49;STM:ra=0.55).Overall,theseresultsindicatedthatweevil‐resistantgenotypesweretaller,with larger height‐to‐DBH ratio and higherwood stiffness asmeasuredbyacousticvelocity.

Significant genetic correlations between wood quality andgrowthtraitswerefoundforbothsites.Acousticvelocity(Velocity16)wasstronglypositivelycorrelatedwithHeight15andHeight15/DBH15 forbothsites(ra>0.58).Averagewooddensity(Density15)wasalsoweaklypositivelycorrelatedwithHeight15/DBH15(ra=0.36)forsiteGPI, but this genetic correlationwas not significant for site STM.MFAwasstronglypositivelycorrelatedwithDBH15 (ra=0.71)andnegativelycorrelatedwithHeight15/DBH15(ra=−0.65)forsiteSTM,butthesecorrelationswerenotsignificantforsiteGPI.

3.3 | Accuracy of single‐trait genomic selection models

Thefourtestedsingle‐traitgenomicselection(GS)methods(GBLUP,TGBLUP, BRR, BayesCπ) and the conventional pedigree‐basedmethod (ABLUP) resulted in similarpredictiveabilitiesandpredic‐tive accuracies. ThePA,whichwasdefined as the correlationbe‐tween the predicted breeding values for the validation trees andthe phenotypic values, ranged from 0.10 for DBH15 to 0.46 forVelocity16 (Figure 4). Low heritability traits (MFA15, DBH15) hadthesmallestPA,whilePAforallothertraitswasabove0.35.AfterstandardizingPAwiththesquarerootofheritability,theestimatedpredictiveaccuracy(PACC)wasobtainedanditwashighforalltraits(PACC>0.69).PACCwasveryhigh(0.97)forHeight15/DBH15 and above0.80forCWA,Velocity16,Height15,andMFA15.HoweverforMFA15,thestandarderroroftheestimatedPACCwashigh,whichislikelyduetoalowheritabilityestimatewithlargestandarderror.PACCforDBH15wasnotestimatedbecauseofthenullheritabilityobservedforthistrait.

For the cumulative number of weevil attacks (CWA), thethree methods that considered ordinal data, namely TGBLUP,BRR,andBayesCπ,hadPAandPACCsimilartothoseofGBLUP,whichassumednormalityofresiduals(Figure4).Inaddition,ge‐nomic‐estimated breeding values obtained from TGBLUP andGBLUPwerehighlycorrelated(Pearsonr=0.997),andtheheri‐tabilityestimateswerewithinthesamerange(GBLUP:h2

ind=0.27

(0.07);TGBLUP:h2ind=0.30(0.08)).Thus,theassumptionofthe

normality of residuals in GBLUP (Figure S8) did not appear toaffectheritabilityestimatesand theperformanceof themodelinourdataset.

3.4 | Accuracy of multi‐trait genomic selection models

Multi‐traitGBLUPmodelswereusedtopredictthebreedingvaluesofatargettrait (CWA,Density15,orMFA15),whencombinedwithgeneticallycorrelatedindicatortraits(Height15,Velocity16,Height15/DBH15ratio).Thecumulativenumberofweevilattacks(CWA),av‐eragewooddensity at age15 (Density15), andmicrofibril angle atage15(MFA15)werechosenastargettraitsbecausetheyarerathercumbersomeandexpensive to assesson a largenumberof trees,whereasindicatortraitsareeasiertotrackforthemajorityoftreesinabreedingpopulation.Themulti‐traitmodelswerecomparedwiththesingle‐traitGBLUPmodels.Asexpected,whenthepercentageofmissingphenotypicdataincreasedfrom0%to90%forthetargettraitsCWA,Dens15,andMFA15,thepredictiveaccuracy(PACC)ofthesingle‐traitmodels(dashedgraylineinFigure5)sharplydroppedfrom0.83to0.59,from0.71to0.43,andfrom0.91to0.55,respec‐tively.SimilartrendswerefoundforthePA(FigureS9).

The PACC ofmulti‐trait models was not improved over single‐traitmodelswhenallofthephenotypicdataforthetargettraitwere

F I G U R E 4   (a)Predictiveability(PA)and(b)predictiveaccuracy(PACC)ofthesingle‐traitgenomicselectionmodels(GBLUP,BRR,BayesCπ)andtheconventionalpedigree‐basedmodel(ABLUP)testedinthisstudy.Forthecumulativenumberofweevilattacks(CWA),threemodelsaccountedforordinaldatatype,namelythethresholdGBLUPmodel(TGBLUP),BRR,andBayesCπ,whileABLUPandGBLUPassumedthaterrorswerenormallydistributed.Errorbarsindicatethestandarderrorsoftheestimates.ThePACCofmodelsforthetraitDBH15wasnotcalculatedbecausetheestimatedheritabilitywasnull.SeeTable1forfulldescriptionoftraits

(a)

(b)

     |  11LENZ Et aL.

includedformodeltraining(0%missingdata)(Figure5;standarder‐rorsaregiven inTableS7).However, for thetarget traitCWAwith40%ormoremissingdata,theaccuracyofmulti‐traitmodelswasim‐provedas comparedwith thatof the single‐traitmodel (Figure5a).PACCwasthehighestwhenCWAwascoupledwiththehighlyge‐neticallycorrelatedHeight15/DBH15ratio(ra=−0.89,averageofsin‐gle‐siteestimates)asanindicatortrait(bluelineinFigure5a).Forthistwo‐traitmodel,PACCwasmaintainedhigh(0.74)anddecreasedonlymarginallywhen90%ofCWAdatawasmissing, ascomparedwith

the full dataset. The two‐traitmodelwithHeight15 as an indicatortrait (ra =−0.65, red line)outperformed the single‐traitmodelonlywhenCWAhad80%ormoremissingdata.WhenCWAwascoupledwiththemoderatelycorrelatedtraitVelocity16(ra=−0.55,greenline),PACCwas similar to that of the single‐trait model. The three‐traitmodelincludingtraitsCWA,theHeight15/DBH15ratio,andVelocity16 (purple line) outperformed the single‐trait model for 40% ormoremissingdata,butitsPACCwasslightlylowerthanthatofthetwo‐traitmodelconsideringCWAandtheHeight15/DBH15ratio(blueline).

F I G U R E 5  Predictiveaccuracy(PACC)ofGBLUPmulti‐traitgenomicselectionmodelsforpredictingthetargettraits:(a)thecumulativenumberofweevilattacks(CWA);(b)Density15;and(c)MFA15. Thedifferentcoloredlinesrepresentdifferentmulti‐traitmodelswithdifferentindicatortraits.Thedashedgraylineisthesingle‐traitGBLUPmodel.Thepercentageofmissingphenotypicdataforthetargettraitinthetrainingsetswasvariedfrom0%to90%(x‐axis),while100%ofthetrainingdatawasretainedfortheindicatortraits.SeeTable1forfulldescriptionoftraits

(b) (c)(a) 15 15

M

TA B L E 5  Geneticgainsforeachtraitawhenselectingthetop5%treesinthreeselectionindexscenarios(SIs)usingtheABLUPandGBLUPmethods.Gainsareexpressedasapercentageofthephenotypicmean.Apositivepercentageindicatesanimprovementinthevalueofthetrait.DBH15wasnotconsideredbecauseofthenullheritabilityandassociatednullgeneticgains

Selection indexbVelocity16 (%)

Density15 (%)

MFA15b

(%)Height15 (%)

Height15/DBH15 (%)

CWAb (%)

ABLUP

SI−1:emphasisonweevilresistance (w1=0.3;w2=0.6;w3=0.1;w4=0)

4.27 0.08 1.70 12.13 10.97 67.97

SI−2:maximizeHeight15,CWA,Velocity16 (w1=0.25; w2=0.4; w3=0.35; w4=0)

6.32 0.14 4.91 12.36 11.09 56.89

SI−3:maximizeHeight15,CWA,Velocity16,Density15 (w1=0.2; w2=0.3; w3=0.25; w4=0.25)

5.77 1.87 0.25 11.51 11.10 53.77

GBLUP

SI−1:emphasisonweevilresistance (w1=0.3; w2=0.6; w3=0.1; w4=0)

5.30 0.62 3.61 7.82 9.74 54.57

SI−2:maximizeHeight15,CWA,Velocity16 (w1=0.3; w2=0.35; w3=0.35; w4=0)

6.17 0.51 5.62 8.10 10.30 50.33

SI−3:maximizeHeight15,CWA,Velocity16,Density15 (w1=0.25; w2=0.25; w3=0.25; w4=0.25)

5.60 2.60 2.09 7.93 10.18 45.84

aSeeTable1forfulldescriptionsoftraits.bIndexselectionformula(Equation10):SI=w1Height15EBV−w2CWA6.15EBV+w3Velocity16EBV+w4Density15EBV , where Height15EBV,CWA6.15EBV,Velocity16EBV,andDensity15EBVaretheBLUPestimatedbreedingvaluesfromthesingle‐traitABLUP(EBVs)orGBLUP(GEBVs)analysisforthecorrespondingtrait(Equation2).cForMFAandCWA,animprovement(positivepercentage)isassociatedwithadecreasingvalueofthetrait(i.e.,areductionofthemicrofibrilangleandareductionofthecumulativenumberofweevilattacks,respectively).

12  |     LENZ Et aL.

For the target traitsDensity15 andMFA15 (Figure 5b,c),multi‐traitmodels did not improve PACC over single‐trait GBLUP, evenwhenthetargettraithadlargeamountofmissingdata.ForMFA15,someofthemulti‐traitmodelsshowedevenalowerPACCthanthesingle‐traitmodels.

3.5 | Genetic gains and multi‐trait selection indices

Theexpectedgeneticgains,expressedasapercentageofthepheno‐typicmeanwhenselectingthetop5%treesforeachtraitseparately(single‐traitselection),aregiveninTableS8.Forthecumulativenum‐berofweevilattacks(CWA),apositivegainrepresentsareductionofthenumberofattacks(i.e.,higherresistance).CWAcouldbeim‐provedby asmuch as78% (ABLUP)or66% (GBLUP),whileothertraits showedmuchsmallergains in the4%–20%range.The largeobservedgainsforCWAarelikelyduetoamoderate‐to‐highherit‐abilityofCWA,alargecoefficientofphenotypicvariation(Table1),andthenon‐normaldistributionofthetrait.

The expected gains from themulti‐trait selection indices (SIs)areshowninTable5.ResultsfromABLUPandGBLUPweresimilar,andso,wepresentonlytheGBLUPresultsbelow.Thefirstselectionindex scenario (SI‐1)presents theplannedbreeding focusandputmostemphasisonweevilresistance(w2=0.6),followedbyHeight15 (w1=0.3),andbyVelocity16 (w3=0.1).Thisscenarioachievedthelargest gains in terms of reduction of cumulative weevil attacks(CWAs)(83%ofmaximumpossiblegainsfromsingle‐traitselectioninTableS8),whilestillyieldingdesirablegainsforHeight15(86%ofmaximum)andVelocity16(74%ofmaximum).TheSI‐2scenariothatsimultaneouslymaximized thegeneticgain inHeight15,Velocity16,andCWAreachedasmuchas89%,87%,and76%ofthemaximumpossible gains for each trait, respectively. In this scenario,MFA15 was also improved by 5.6% (62%ofmaximum). For SI‐1 and SI‐2,thegain inDensity15wasmarginal.ForSI‐3,Density15wasaddedas an important trait tomaximize alongwithHeight15, Velocity16,andCWA.ThisSIscenarioslightly improvedgains inDensity15 by 2.6%(51%ofmaximum),butatthecostofsmallerimprovementsforHeight15,Velocity16,CWA,andMFA15. InallthreeSIs,stemtaper,asestimatedbytheHeight15/DBH15ratio,wasimproved(i.e.,lowerstemtaper)by~10%.

4  | DISCUSSION

4.1 | Genetic control of weevil resistance and its relationships to growth and wood quality traits

Tree breeding uses the existing natural intraspecific variation toidentify superior genotypeswith desirable attributes. In this con‐text,theheritabilityofnaturalresistancetopestsmaybeseenasanindicatorfortheevolutionarypotentialofthespecies(Charmantier&Garant, 2005;Geber&Griffen,2003). In a recently introducedspeciessuchasNorwaysprucetoNorthAmerica,naturalselectionfor resistancetonativepestsmayhaveactedonly foroneor twogenerations at best. Nevertheless, we showed that resistance to

whitepineweevilattackwasundermoderate‐to‐highgeneticcon‐trol. Individual heritability estimates (ABLUP)were slightly higherthaninanearlierstudybyMottetetal.(2015),whocombineddatafrommorefamiliesandteststhanthisstudy,butvalueswereinthesamerangethanthoseobservedinthenativeinteriorspruce(Kingetal.,1997)andslightlyhigherthanthoseinthenativeSitkaspruce(King, 2004). In its native range, Norway spruce suffers damagesfromanotherweevilspecies,thelargepineweevil(Hylobius abietis),mostly at the seedling stage after clearfelling operations (Day &Leather,1997).Althoughbothweevilspeciesdonotattacktreesatthesamedevelopmentalstage,bothfeedonthebarkandphloem,soitislikelythatresistancemechanismstodifferentweevilsarepartlyrelated.Zasetal.(2017)foundmoderatefamilyheritabilityandlowGxE for resistance to the pineweevil in Norway spruce. Norwaysprucehasalsofacedoutbreaksofbarkbeetles,suchasIps imitinus and Ips typographus,aftermajorstormssuchasthosethatoccurredin Central Europe in the 1990s (Wermelinger, 2004). Resin canaltraitsrelevantforconstitutiveresistanceagainstbarkbeetleswerefoundtobeunderstronggeneticcontrol(Rosner&Hannrup,2004).Thus, it is likely that genetic variation at resistance genes for theNorthAmericanwhitepineweevilwasalreadyavailableatthetimeofintroductionofNorwayspruceinNorthAmerica,astheresultofnaturalselectionagainstinsectpestsinEurope,withopportunitiesforrapidchangeinallelefrequenciesatresistanceloci.

Inourstudy,bothCWAandtreeheightatage15wereundersig‐nificantgeneticcontrolandthegeneticcorrelationbetweenthesetraitswasnegative,butsignificantonlyforthesitethatsufferedthemostfrequentweevilattacks(GPI).Theseresultsarenotsurprisinggiventhatheightgrowthismechanisticallystuntedinconsequenceof attack, while the tree continues to grow in DBH and volume.Indeed,with increasingage,ahigherheight/DBHratioand thusalowerstemtaperwasobservedinmoreweevil‐resistanttrees(Holst,1955;Mottetetal.,2015;thisstudy).Kingetal.(1997)alsoreportednegativegeneticcorrelationsbetweenCWAandtreeheightforinte‐riorspruceinBritishColumbia,bothbeforeandaftertheoccurrenceof weevil attacks. They concluded that inherently faster growingfamilieshavehigher levelofgeneticresistance. InNorwayspruce,Mottetetal. (2015) foundnegligiblegeneticcorrelationsbetweenweevil attacks and tree height measured before the majority ofweevilattacks(age5)andconcludedthatgeneticimprovementforresistancetowhitepineweevilwouldnotadverselyaffectgrowth.Ontheotherhand,thestrongpositivegeneticcorrelationbetweenresistancetoweevilattacksandheightatage15foundonsiteGPIinthisstudymayindicatethattheyarecontrolledbycommongenes,whichwasalsosuggestedbyanearlierQTLstudyininteriorspruce(Porthetal.,2012).Inaddition,resistancemechanismstoEuropeanbarkbeetlessuchas resincanal traitswere foundtobepositivelygeneticallycorrelatedwithbothheightgrowthandDBH(Rosner&Hannrup,2004).Overall,ourresultssuggestthatacceleratedbreed‐ingofresistantseedstockthroughgenomicselectiontoolswillre‐sultintallertrees,eitherbecausetheleadersofresistanttreeswillbe less affected by attacks, or because alleles underlying growthgeneswillbesimultaneouslyfavored.

     |  13LENZ Et aL.

Thegeneticcontrolofvariationinwoodqualitytraits,suchasav‐eragewooddensityandacousticvelocityasaproxyforwoodstiff‐ness,wasinthesamerangeasthatforweevilresistance.ComparedtorecentwoodqualitystudiesofNorwaysprucefromScandinavia(Chenetal.,2014,2015),ourheritabilityestimateswerelowerforaveragewooddensity,buthigherforacousticvelocity.HeritabilityestimatesforMFAwerelowcomparedwiththosereportedinprevi‐ousstudies(Chenetal.,2014;Lenzetal.,2010),whichismostlikelyrelatedtothemeasuringapproachusedinthepresentstudywhereonly the last ringwasassessed.Themoderateheritabilityand theresulting sizeablegeneticgainobservedhere foracousticvelocitymakeitapromisingquick‐assessmenttraitforimprovingwoodstiff‐nessandproductquality(Lenzetal.,2013).Inaddition,woodstiff‐nesscanbeimprovedtogetherwithweevilresistancesinceacousticvelocitywasnegativelygenetically correlatedwith thecumulativenumber ofweevil attacks.Moreover, weevil resistance andwoodtraits showed low genotype‐by‐environment interactions, whichshould facilitate reforesting selected planting stock across largerbreedingzones.AveragewooddensitydidnotappeartobethebesttraitforoverallimprovementofNorwayspruceinthetestedcondi‐tionsgivenitsnegativecorrelationswithgrowthtraitsandslightlyhigher genotype‐by‐environment interaction. Overall, given theirpositivegeneticcorrelationsandmoderate‐to‐highheritability,wee‐vilresistance,acousticvelocity,andheightgrowthappearasexcel‐lentcandidatetraitsforsimultaneousgeneticimprovement.

4.2 | Genomic selection models for accurate and hastened selection of best genotypes

Genomic selection can significantly shorten breeding cyclesthrough the prediction of breeding values of nonphenotypedmaterial using their genomic profiles and allows screeningmorecandidates for increase selection intensity or multi‐trait selec‐tion. Comparedwith the conventional pedigree‐based approach(ABLUP),genomicselectionmodelsusingGBLUP,BRR,orBayesCπ hadcomparablePAandaccuracy,confirmingearlyproof‐of‐con‐cept studies in other conifers and spruces (Beaulieu, Doerksen,Clément, et al., 2014;Beaulieu,Doerksen,MacKay, et al., 2014;GamalEl‐Dienetal.,2015;Lenzetal.,2017;Ratcliffeetal.,2015).InBRRandBayesCπ,wedidnotfitgenotype‐by‐environmentin‐teractionsasopposedtoABLUPandGBLUPmethods,butthisdidnotaffectPAnorpredictiveaccuracy.

PredictiveabilitywasrelatedtoheritabilityandwaslowestforthelowheritabilitytraitsMFA15 and DBH15.Thisisbecausethepro‐portion of phenotypic variation that can be explained by additivegeneticeffectsissmallerforthesetraits.Comparisonsofpredictiveaccuracyofbreedingvaluesacrossstudiesaredifficultbecauseoftheabsenceofastandardwayofdetermination.Forsimilargrowthandwoodqualitytraits,predictiveaccuracywasslightlyhigherthanpreviouslyobservedfornativeNorwayspruce(Chenetal.,2018)orforwhitespruce(Beaulieu,Doerksen,Clément,etal.,2014;Beaulieu,Doerksen,MacKay,etal.,2014;GamalEl‐Dienetal.,2015;Ratcliffeetal.,2015),anditwaslowerandmorevariablethanthatobserved

forblack spruce (Picea mariana [Mill.]B.S.P.) (Lenzet al., 2017). IncontrasttothosepreviousGSstudies,weassumedhereinthattruebreedingvalueswereunknownandcalculatedthepredictiveaccu‐racybydividingthePAbythesquarerootofheritability(Dekkers,2007;Legarraetal.,2008).Hence,predictiveaccuracyshouldnotbecorrelatedwithheritability,butdependsonothercharacteristicsofthedataset,suchastheaccuracyofphenotypicmeasurements,theeffectivepopulationsize,andthegeneticarchitectureoftraits(Grattapaglia&Resende,2011).However,theprecisionofthepres‐entestimatesofpredictiveaccuracymaybeaffectedbythepreci‐sionofheritabilityestimates.

Intheory,GSshouldperformbetterthanpedigree‐basedmod‐els because it allows correcting pedigree errors and capturingthe within‐family variation resulting from Mendelian segregation(Grattapagliaetal.,2018).Thus,inaforwardselectionscenariowithnonphenotypedyoungmaterial,theselectionofthebestindividu‐alswithin families becomes possiblewithGS. In the present con‐textofsmallsizeofthebreedingpopulation,weconcludethattheestimatedgenomicpredictionsforresistancetoweevilattack,treeheight,height/DBHratio,andwoodqualitytraitsallowforaccurateandhastenedselectionofbestcandidatesbasedontheirgenomicprofiles.

4.3 | Evidence for polygenic control of weevil resistance in spruces

To our knowledge, the present study is the first one applyinggenomic selection to breed for insect resistance in conifers. Wethereforehadparticularinterestintestingdifferentalgorithmsthatconsidered the ordinal distribution of this trait and that reflecteddifferentdistributionsofmarkereffects.First,wefoundnoadvan‐tagesofusingmethods thataccounted forordinaldata (thresholdGBLUP,BRR,andBayesCπ),ascomparedwithapproachesthatas‐sumed normality of residuals (ABLUPs andGBLUPs). Second, theBayesCπalgorithm,whichassumedthatonlyaportionofgeneshadaneffect,didnotleadtoimprovementofPAoraccuracycomparedwithmethods assuming that all genes had small effects (GBLUPs,BRR). InBayesCπ, the estimated proportion ofmarkers having aneffect(� ≅ 0.50)forweevilresistancewasinthesamerangeasthatforothertraits(TableS9).Incontrast,Resende,Munoz,etal.(2012)andResende,Resende,etal.(2012)obtainedahigherpredictiveac‐curacyusingBayesCπ for fusiform rust resistance in loblolly pine,which suggested the presenceof large effect genes.Our findingscanbeexplainedbytwopossiblephenomena:(a)weevilresistanceiseffectivelycontrolledbymanygenesofsmalleffects,withnode‐tectablemajorgeneeffects;or(b)noneofthesampledSNPswasincloselinkagewithgeneshavingeffectsforresistance.Itisdifficulttodiscriminatebetweenbothhypotheses,especiallysinceGSmodelswith the current genome coverage and small size of the breedingpopulation shouldmostly retrace relatedness between trees fromlong‐rangelinkagedisequilibrium(e.g.,Beaulieu,Doerksen,MacKay,etal.,2014;Lenzetal.,2017)andcouldthusprovidehighpredictiveaccuracies following both sets of conditions. However, polygenic

14  |     LENZ Et aL.

control of weevil resistance seems plausible since earlier reportsassociated resistance to weevil attack with different constitutiveandinducedmechanisms.Physicaldefensebarrierstoweevilweredescribedthroughsclereidsandstonecellsinthebarkofsitkaandhybridspruces(King,Alfaro,Lopez,&VanAkker,2011;Whitehilletal.,2016). Inaddition, chemicaldefensestrategiesarealsoatplaythroughthepresenceofabundantconstitutiveresinducts(Kingetal.,2011;Rosner&Hannrup,2004)andtheadditionalformationoftraumatic resinducts (Poulin,Lavallee,Mauffette,&Rioux,2006),togetherwith increase interpenoidmetaboliteproduction(Robertetal.,2010) following insect feeding.Porthetal. (2012) identifiedmany candidate genes forweevil resistance in interior spruce, in‐cluding some master regulatory genes. Moreover, transcriptomestudies inSitkasprucerevealedseveralthousanddifferentiallyex‐pressedgenesbetweenresistantandsensiblegenotypes,aswellasfollowingweevilwoundingandfeeding(Ralphetal.,2006;Whitehillet al., 2019). Hence, weevil resistance in Norway spruce is mostlikelypolygenicgiventhecomplexnatureofphysicalandchemicaldefensemechanisms,butwhethersomelargergeneeffectsexistre‐mainstobeelucidated.

4.4 | Multi‐trait GS as a tool to improve accuracy of scarcely phenotyped traits

The jointmodelingofmultiple traitscanbenefit fromgeneticcor‐relationsbetweentraitsand increasepredictiveaccuracy (Calus&Veerkamp,2011;Guoetal.,2014;Jia&Jannink,2012).InEucalyptus,Cappa et al. (2018) reportedmodest improvements in thepredic‐tive accuracy of breeding values frommulti‐trait over single‐traitGS models (~2%–4%) when a low heritability target trait (treeheight)wascoupledwithahighlygeneticallycorrelatedtrait(DBH,ra=0.92).Otherempiricalplantortreebreedingstudiesfoundlittlebenefitsofusingmulti‐traitGStopredictnonphenotypedselectioncandidateswhen100%of the individuals in the training setwerephenotyped(Baoetal.,2015;Chengetal.,2018;Fernandesetal.,2018; Jia & Jannink, 2012; Schulthess et al., 2016). Similarly, wefoundthatmulti‐traitGBLUPdidnotoutperformsingle‐traitmod‐elswhenallindividualsinthetrainingsetwerephenotypedforthetargettrait.Thus,incaseswhenphenotypicinformationisbalancedacross traits, single‐trait modeling is the recommended methodgiventhattheyharborreducedmodelcomplexity(Schulthessetal.,2016).

Multi‐trait GS models present an interesting strategy to copewithtraitsthathavelargeamountofmissingvaluesbecausetheyaredifficultorcostlytomeasure,suchastraitsrelatedtoresistancetobioticandabioticfactors,orwoodqualitytraits.Wefoundthatwhenwe includedahighlygeneticallycorrelatedgrowthtrait (Height15/DBH15 ratioorHeight15)asan indicator trait, themulti‐traitmod‐els predicted resistance to weevil attacks more accurately whentherewasalargeamountofmissingdataforthistrait.However,theadvantageofmulti‐traitoversingle‐traitGSdisappearedasthege‐neticcorrelationbetweenweevil resistanceandthe indicator traitdecreasedtora=−0.55whenusingVelocity16astheindicatortrait.

Similarly, there was no advantage of using multi‐trait models topredict the target traitsDensity15orMFA15,whichwas likelyduetoweak or inconsistent genetic correlations across sites betweenthetargetandindicatortraits.Previousstudiessimilarlyfoundthatmulti‐traitmodelsperformedbestwhenthegeneticcorrelationbe‐tweentraitswashigh(ra>0.5;Calus&Veerkamp,2011;Guoetal.,2014;Montesinos‐Lópezetal.,2016).Thus,ourresultsandthoseofpreviousstudiessuggestthat,inthecaseofatargettraitwithmod‐erateheritabilitysuchasweevilresistance,multi‐traitGSmodelsareonly advantageous when a highly genetically correlated indicatortraitisavailable.

Inabreedingcontext,ourresultsopenuppossibilitiestoconsidermaterialtestedonsiteswherenorecordofweevilattackshavebeentaken.Accuratephenotypingofweevil resistance requiresnumer‐ousvisitsateachtrialandatdifferentplantationages.Furthermore,anappropriatelevelofattackateachsite,ideallymorethan50%ofattackedtrees,isdesirabletoproperlyevaluategeneticresistance.These constraints imply that resistance toweevil attacks is oftenrecordedonlyforapartofavailabletestsitesandmaterial.Insuchcases,multi‐traitGSmodelscanbeusedtomoreaccuratelypredictweevilresistanceforthetreesinnonphenotypedsiteswhenanin‐dicatortraithasbeenmeasuredinallsites(Montesinos‐Lópezetal.,2016).Furthermore,the lowgenotype‐by‐environment interactionofresistancetoweevilattacksfoundinthisstudyandinMottetetal.(2015)wouldensurerelativelyhighaccuraciesofpredictionsbe‐tweensites (Beaulieu,Doerksen,MacKay,etal.,2014;Lenzetal.,2017).

Due to convergence issues for the three‐trait models, we didnotaccountforgenotype‐by‐environmentinteractions(GxE)inourmulti‐traitmodels.Weadjustedthephenotypesforsiteandblockeffects,butthisstandardizationdoesnotcontrolforGxEduetorankchangesbetweensites.Nevertheless, thisseemedtobeareason‐ablemodelsimplification inthepresentcase,giventhatwefoundthe same predictive accuracy for single‐trait GBLUP models thataccountedforGxE(Equation2)comparedwithGBLUPmodelsthatusedtheadjustedphenotypeasaresponsevariableanddidnotac‐countforGxE(Equation11inAppendixS2,TableS10).

Modelswithmore than two traits have only been tested in ahandfulofstudies(Baoetal.,2015;Schulthessetal.,2016;Tsuruta,Misztal,Aguilar,&Lawlor,2011).Inparticular,Schulthessetal.(2016)didnot findanybenefitofusing three‐traitover two‐traitmodelswhen theaimwas topredictonlyone target trait.However, theyfoundthatthethree‐traitmodelwasbettertopredicttwoscarcelyphenotyped target traits, when a third correlated trait was fullyavailable. In this study, the three‐trait model with indicator traitsHeight15/DBH15 ratio andVelocity16 did not outperform our besttwo‐traitmodelusingonlyHeight15/DBH15ratioasanindicatortraitto predict resistance toweevil attacks. This is becauseVelocity16 wasmuch less correlatedwithweevil resistance (ra = −0.55) thanwas the Height15/DBH15 ratio (ra = −0.89), and thus, Velocity16 added little information to thepredictions.Becauseof the rapidlyincreasingcomplexityofmodelsasthenumberofcorrelatedtraitsincreases,computerresourcelimitationsandconvergenceproblems

     |  15LENZ Et aL.

duetocollinearitycanarise (Schulthessetal.,2016). Inthisstudy,convergenceproblemsprecludedustofitsimultaneouslymorethanthree traits.Multi‐trait Bayesianmodels are expected to bemoreefficientthanmulti‐traitGBLUPwhenthenumberoftraitsincreases(Calus&Veerkamp,2011).Overall,thebenefitsofaddingmoretraitsseemslimited,butthisneedstobefurthertestedwithdifferentGSmodelsandwithtraitscombinationsofdifferentlevelsofheritabilityandgeneticcorrelations.

4.5 | Index selection provided positive gains for most focus traits

Indexselectionisacommonlyusedtoolintreeimprovementtose‐lectindividualsthatcombinesuperiorgeneticvalueforseveraltraitsofinteresttothebreeder.Thisstrategyusuallyresultsinlowerge‐neticgainforeachtraitcomparedwithsingle‐traitselection,becausecorrelationsamongtraitsarenotperfectandareoftennegative.OurscenarioSI‐1 reflected theprioritiesof theNorwaysprucebreed‐ersoftheprovinceofQuébec.Besidesthecurrentfocusonweevilresistance and growth,woodquality traitswill be included in thenextgenerationselectioncriteriaforthisplantation‐grownspeciestoavoida reduction inmechanicalpropertiesof lumberextractedfromfastergrowingtrees.However,determiningeconomicweightsforeachtraitischallenging.Economicstudieshavebeenconductedfordifferentconiferbreedingprograms(e.g.,Aubry,Adams,&Fahey,1998; Ivković,Wu,McRae,&Powell, 2006;Petrinovic,Gélinas,&Beaulieu,2009),buttheresultingeconomicweightsarenottrans‐ferabletootherspeciesandregionssincetheydependmuchonthewood production and transformation systems. Because of thesedifficulties, economic weights have not been established yet forNorwayspruceintheCanadianbreedingandforestrycontexts,andtherelativeweightsthatwehavechosenfortheSI‐1scenarioarecurrentlythemostlikelytobeimplementedintheshorttermbutarestillofanindicativenature.

Inthisstudy,favorablecorrelationsbetweenweevilresistance,heightgrowth,andacousticvelocity resulted inonlyminor trade‐offsamongthosetraitsinthetestedselectionindices.However,theimprovementforDBHorthecloselyrelatedvolume(notestimatedin this study) appears more challenging. The low genetic controland the importantgenotype‐by‐environment interactionobservedforDBH (see alsoMottet et al., 2015)make it difficult to predicttheeffectofselectingforweevilresistanceonthistrait.However,thepossiblelossinlumbervolumewouldlikelybecompensatedbylesslogdefectsduetoincreasedresistanceofplantationstoweevilattacks(Daoust&Mottet,2006).Thus,improvingforweevilresis‐tancewouldundoubtedlybenefitNorwayspruceasanexoticplan‐tationspeciesineasternCanada.

5  | CONCLUSIONS

Inthisstudy,weinvestigatedthegeneticcontrolofweevilresistanceanditsrelationshipwithwoodandgrowthtraitsinNorwayspruceas

anexoticplantationspecies.Wefurtherintegratedthesetraitsintoamulti‐traitgenomicselection(GS)framework.Wefoundthatinsucharealisticcontext,itwaspossibletoimprovesignificantlyforwee‐vilresistanceusingGS,giventhatweevilresistancewasmoderatelytohighlyheritableandthat itwaspositivelygeneticallycorrelatedwiththeheight/DBHratioandwoodstiffness(acousticvelocity).Bytakingadvantageoftheseexistinggeneticrelationships,weshowedthatmulti‐traitgenomicselectionmodelscould improve theaccu‐racyofthepredictionforascarcelyphenotypedtargettrait(weevilresistance)byusingtheinformationfromareadilyavailableindicatortrait.Finally,bycombiningmultiplecorrelatedtraitsintoaselectionindex,weobtainedthebestcompromiseforalltraitsofinterestthatcorrespondedtotheprioritiesofthebreeders.Thus,thisintegratedapproachshowedhowgenomicselectioncanbeusedtobreedsi‐multaneously for taller, stiffer, andmoreweevil‐resistantNorwayspruces.We conclude that single/multi‐traitGSmodels and indexselectionareefficientselectiontoolsthatcanbeintegratedintoop‐erationalbreedingprogramstoacceleratetherealizationofgeneticgainsformosttraitsofinterest.

Anotheradvantageofintegratinggenomicselectiontoabreed‐ingprogram is that,once thebreedingpopulationhasbeengeno‐typed,modelscaneasilybe recalibrated foradditional traits, suchaspestresistanceorresiliencetoepisodicclimateextremessuchasdroughts.Suchtraitsmaybecostlyanddifficulttomeasureinforesttrees(e.g.,Houssetetal.,2018)andtheuseofcorrelatedindicatortraits inmulti‐traitmodelswould reducephenotypingcosts.Massphenotypingusingremotesensingtechnologiescouldalsohelpiden‐tifyindicatortraitsthatarecorrelatedwitheconomicallyimportantones(Dungeyetal.,2018).Theincreaseofinformationfrommultiplecorrelatedtraitswillprovideopportunitiestotestnovelmulti‐traitmodelsandtoimprovegenomicselectionaccuracies.Finally,giventhatlargenumbersofcandidatetreescanbegenotypedattheveryjuvenile stage,multi‐traitGSwill result inhighly significant reduc‐tions in testing time for such long‐lived species,while allowing toincreaseselection intensitycompared tomoreconventional selec‐tionapproaches.

ACKNOWLEDG EMENTS

We thank Gaëtan Daoust (Natural Resources Canada), AnteStipacinic, Jean‐Sébastien Joannette, and Johanne Claveau(Ministère des Forêts, de la Faune et des Parcs du Québec) fortheestablishmentof the field trialsanddatacollection,aswellasFrançoisBeaulieu(CanadaResearchChairinForestGenomics,Univ.Laval,andNaturalResourcesCanada)andJasonMiccocci (NaturalResourcesCanada) forhelpwith samplingandphenotypicassess‐mentsof test trees.Our thanks to JosianeDeBlois (MinistèredesForêts, de la Faune et de Parcs du Québec), Sébastien Clément(CanadianWoodFibreCentre),andJeremyMartel(CanadaResearchChair in Forest Genomics, Univ. Laval, and Natural ResourcesCanada)forhelpwithdatabasingandstatisticalanalysesofquantita‐tivetraitdata.WealsothankM.Deslauriers(CanadianWoodFibreCentre), S. Blais, and A. Azaiez (Canada Research Chair in Forest

16  |     LENZ Et aL.

Genomics,Univ.Laval)forDNAextractionsandvalidationofgeno‐typicdata,andD.Vincent,F.Bacot,andtheirteamforgenotypingNorwaysprucesamplesattheGenomeQuébecInnovationCentre(McGill Univ.,Montreal). This researchwas part of the FastTRACproject, fundedbyGenomeCanadaandGenomeQuébecthroughthe national Genomics Applied Partnership Program (GAPP). Theproject was also supported by contributions from the Ministèredes Forêts, de la Faune et des Parcs du Québec, FPInnovations,J.D.IrvingLtd,theNewBrunswickTreeImprovementCouncil,theCanadianWoodFibreCentre,andtheLaurentianForestryCenterofNaturalResourcesCanada.

DATA ARCHIVING S TATEMENT

SNPdataandthedescriptionofthegenotypingarrayweredepos‐itedintheEuropeanVariationArchive(EVA,https://www.ebi.ac.uk/eva/, accession number PRJEB27427).More details can be foundinAzaiezetal. (2018).ThephenotypicandgenotypicoriginaldatabelongtotheNorwaysprucebreedingprogramoftheprovinceofQuébecandhavebeenstoredinourinstitutions’databases.Itcanbesharedupon request to thecorrespondingauthoraccording totheintellectualpropertypolicies(IPP)ofparticipatinggovernmentalinstitutions.Therefore,datahavethereforenotbeendepositeddi‐rectlyintoapublicdomain.

ORCID

Patrick R. N. Lenz https://orcid.org/0000‐0002‐0184‐9247

R E FE R E N C E S

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How to cite this article:LenzPRN,NadeauS,MottetM‐J,etal.Multi‐traitgenomicselectionforweevilresistance,growth,andwoodqualityinNorwayspruce.Evol Appl. 2019;00:1–19. https://doi.org/10.1111/eva.12823