Modeling breed additive and non-additive genetic effects using a Angus x Nellore crossbred

13 Pages·2015·0.35 MB·English

by  Claudia Damo Bertoli

LivestockScience176(2015)1–13
ContentslistsavailableatScienceDirect
Livestock Science
journal homepage: www.elsevier.com/locate/livsci
Modeling breed additive and non-additive genetic effects
using a Angus x Nellore crossbred population
Claudia Damo Bertolia,b,n,1, Jose Braccinib,f,2, Connie McManusc,3,
Jaime Araujo Cobucib,2, Elisandra Lurdes Kernb,2, Mario Luiz Piccolib,d,4,
Flavio Schenkele,5, Vanerlei Rosod,4
aInstitutoFederalCatarinenseCampusCamboriuIFC-CC,RuaJoaquimGarcia,s/nCentro,CaixaPostal2016,CEP88340-055Camboriu,
SC,Brazil
bUniversidadeFederaldoRioGrandedoSul–UFRGSDepartamentodeZootecnia,AvenidaBentoGonçalves,7712agronomia,
CEP91509-900PortoAlegre,RS,Brazil
cUniversidadedeBrasília–UnB,CampusUniversitárioDarcyRibeiro,CEP70910-900Brasília,DF,Brazil
dGenSysConsultoresAssociados,RuaGuilhermeAves,170/304Jardimbotânico,CEP90680-000PortoAlegre,RS,Brazil
eUniversityofGuelph–UofG,CGIL–CentreofGeneticImprovementofLivestock,50StoneRoadEast,Guelph,ON,CanadaN1G2W1
fCNPq,Brazil
a r t i c l e i n f o a b s t r a c t
Articlehistory: Theobjectivesofthisstudyweretoestimatefixedgenetic(bothadditiveandnon-additive)
Received22August2014 effectsandtestdifferentnon-additivemodels.Theseeffectsincludeddirectandmaternal
Receivedinrevisedform joint breed additive effects, direct and maternal complementarity (or profit heterosis),
19March2015 direct and maternal heterosis (dominance) and direct and maternal epistatic loss non-
Accepted23March2015
additiveeffects.AlargecrossbredAngusxNellorepopulationwithapproximately300,000
recordsforweaninggain(WG)and150,000recordsforpost-weaninggain(PG)wasused.
Keywords: Phenotypicscoresforweaning(WC)andpost-weaning(PC)conformation,weaning(WP)
Epistaticloss and post-weaning (PP) precocity, weaning (WM) and post-weaning (PM) muscling and
Heterosis
scrotal circumference (SC) were also used. All models included the fixed contemporary
Non-additivegeneticeffects
group effect and random animal, maternal genetic and permanent environment effects.
Complementarity
Eachmodelwastestedagainstallothermodelsforallninetraitsusingthelikelihoodratio
Crossbreedbeefcattle
test. The complete model,including all additive andnon-additive effects and the model
without complementarity, were seen to be the best options to analyze this crossbred
population. However, least squares may not be the best methodology due to possible
collinearityamongestimates that may inflatethe variance. Inthe complete modelmost
effects were statistically significant (Po0.01) for weaning traits, except for direct and
maternal breed additive effects and direct complementarity effect for WM. For post-
weaningtraits,thedirectcomplementarityeffectforphenotypicscores(PC,PPandPM)and
thematernalheterosiseffectforPG,PC,PM,werenotstatisticallysignificant.Forscrotal
circumferencethematernalcomplementarity,directandmaternalheterosisandmaternal
epistatic loss effects were not statistically significant. All other effects were statistically
significant (Po0.01). For the model without complementarity, the direct breed additive
nCorrespondingto:RuaRioAmazonas,3477RioPequeno,CaixaPostal2139,CEP88340-000Camboriu,SC,Brazil.Tel.:þ554799674595/þ55479977
3086;fax:þ55472104-0800.
E-mailaddresses:[email protected],[email protected](C.D.Bertoli).
1Tel.:þ554721040800.
2Tel.:þ555133086048.
3Tel.:þ556131073300.
4Tel.:þ555133306804.
5Tel.:þ15198244120(cid:2)58650.
http://dx.doi.org/10.1016/j.livsci.2015.03.020
1871-1413/&2015ElsevierB.V.Allrightsreserved.
2 C.D.Bertolietal./LivestockScience176(2015)1–13
effectforPGandPPwasnotstatisticallysignificant,includingthematernalbreedadditive
effectforWC,WD,PPandPMandmaternalheterosis,directandmaternalepistaticloss
effects for SC. Consideringall models,significantdirect breed additive effectwasmostly
positiveforweaningtraitsandwasnegativeforallpost-weaningandSC.Thesignificant
maternalbreedadditiveandmaternalcomplementarityeffectsforSCwereallnegative.The
significantdirectandmaternalepistaticlosseffectswerenegativeforalltraitsandforall
models,exceptforPGinthecompletemodelandforweaningtraitsinthemodelincluding
onlybreedadditiveandepistaticlosseffects.Weconcludethatthefixedgeneticeffectsare
mostly significant, thus it is important to include them in the model when evaluating
crossbreedanimalsandthemodelsincludingbreedadditiveeffects,heterosisandepistatic
losswithorwithoutcomplementaritywerethemoreappropriate.
&2015ElsevierB.V.Allrightsreserved.
1. Introduction complementarity.Alargenumberofstudiesdonotconsider
complementarity as an important effect, but Piccoli et al.
Widelyusedintropicalandsub-tropicalclimatecoun- (2002) found that the magnitude of heterosis estimates is
tries, crossbreeding systemsare based on theexploration reducedwhenthe complementarity(additive*additive inter-
of various genetic effects resulting from existing differ- actions) is included in the model, indicating that under the
encesbetweenbreeds.Amongtheseeffectsarethebreed additive-dominance model the heterosis estimation may be
additiveeffect andthenon-additiveeffects of the combi- duetoanon-linearadditiveeffect.Accordingtotheseauthors
nationoftheinvolvedbreeds(jointadditiveeffect),aswell this effect becomes more evident when the model also
asheterosisandepistaticlosseffects. includesanepistaticlosseffect.
The breed additive effect comprehends the individual The inclusion of the epistatic loss effect in the additive-
effectsofeachoftheinvolvedbreeds;aslong-termselection dominant model was also suggested by Fries et al. (2000)
within a breed increased frequencies of non-allelic genes andreaffirmedbyPiccolietal.(2002)withtheobjectiveof
thatjointlyproducefavorableextraeffects(Friesetal.,2002). achievingabetterexplanationoftheexistinggeneticvaria-
The non-additive effect of the combination of breeds tionamongdifferentbreedcompositions.Thegenotypeata
involved in the crossbreeding, that causes a multiplicative locuscaninfluencethegenotypeeffectofasecondlocusand
relationamongtheadditiveactionswasdefinedbyKinghorn may inhibit gene expression of the second locus in the
(1993)as“profitheterosis”.Theheterosiseffectismainlydue phenotype. Recent studies suggest that the epistatic loss
tothedominanceeffectsonthegenesandcanbeconsidered effectstronglyandnegativelyinfluencedcrossbredanimals´
as the recovery from the depression due to accumulated levelsofproduction(Cardosoetal.,2008,Lemaetal.,2011),
consanguinity. A linear relationship between heterozygosis althoughsomeresearcherschoosedonotincludeepistasisin
and heterosis retention has been found (Fries et al., 2000; the models, such as Vergara et al. (2009b), Legarra et al.
Gregoryetal.,1991).Theepistaticlosseffectcomprehendsan (2007)andArthuretal.(1999).
additionaldeviationfromthegenotypicvalueoccasionedby As the main objective of crossbreeding systems is
thenon-additivecombinationwhenmorethanonelocusis takingadvantagefromnon-additivegeneticeffectsamong
considered in the analysis (Falconer and Mackay, 1996). breeds, obtaining reliable estimates of the parameters
According to VanRaden (2006), talking about crossbred involvedin crossbreeding systemsandthusbeingable to
animals, “If non-additive effects are subtracted and only predict the performance of the crossed genotypes is an
additiveeffectsarereported,selectionmaynotbeoptimal”. importantstepforthesuccessfuldevelopmentofabreed-
The models that estimate simultaneously additive and ingprogram(Cardosoetal.,2008).
heterosiseffectsorestimatedirectadditiveeffectsafterthe The main objective of this study was to test different
adjustmentof thedataforheterosisbasedontheexpected additiveandnon-additivegeneticmodels.Wealsoaimto
heterozygosisarethemostcommonbasicmodelsofmulti- estimate the fixed genetic effects (joint breed direct and
racial populations breeding programs for beef cattle. These maternal additive effects and complementarity (or profit
models have been used in crossbred populations in Brazil heterosis),heterosisandepistaticlossdirectandmaternal
(Lopesetal.,2010),Africa(Theunissenetal.,2013),Australia non-additive effects), involving crosses between Angus
(Arthur et al.,1999), Canada (Roso et al., 2005a), Colombia andNellorebeefcattlebreeds.
(Vergara et al., 2009a, 2009b), Ethiopia (Demeke et al.,
2003a,2003b),USA(ElzoandWakeman,1998)andUruguay 2. Materialsandmethods
(Lemaetal.2011).
Theinclusionofcomplementarityeffectinthemodelwas 2.1. Data
suggestedbyFriesetal.(2000)andreaffirmedbyPiccolietal.
(2002).AccordingtoPimenteletal.(2006),whenreferringto Datafromdifferentbreedcompositionsresultingfrom
crossbredanimalsinatropicalenvironment,wecanconsider crosses between Angus and Nellore cattle was used. This
that two groups of genes were acting, one related to the data came from more than 200 herds distributed in the
growth potential and the other to adaptation. The multi- BrazilianprovincesofRioGrandedoSul,Paraná,SãoPaulo,
plicativerelationamongtheireffectscouldbeinterpretedas MatoGrossodoSul,MatoGrossoandGoiásandalsofrom
C.D.Bertolietal./LivestockScience176(2015)1–13 3
cts, Paraguay.Allherdswereparticipantsof“ProgramaNatura
36.2)0.0)8.3)9.4)42.6)2.2)1.2)0.0)0.0)100.00) eticeffe dBereeMdienlhgoPraromgernamto).GAebnséotliucotedaendBorveilnatoisv”e (fNreaqtuuerancCieasttolef
(((((((((( en observationsamongcoefficientsarepresentedinTable1.
g
em 10320962379526693121670627335271305285,309 n-additive 2.1.1N.inTeratirtasits were used in this analysis: weaning gain
o (WG), post-weaning gain (PG), phenotypic scores of con-
n
(19.2)(0.0)(23.3)(3.5)(42.1)(7.3)(4.4)(0.2)(0.0)(100.00) aticloss facootrcwmiteyaat(inoPinPn)g(,WanpCdh)e,mnpourtesyccpoliicncigtsyc(P(oWMreP)s)aoatfnpcdoosmntf-uowrsmcelaianntgiino(gnWa(MPsCw))t,eaplklreaens-
pist scrotalcircumference(SC)adjustedforanimalweightand
ea 548523566553992412006020810125764946285,309 osisande apscgooeinr.etThsfoecrapleeh,aecwnhohtmeyrpaeincoasngceeomriesenftohtregerwaocouhrpst.tr,Taaihtneidsngfuiivmveebniesortnohfaeufbisveeesd-t
0) eter observationispresentedinTable3.
oupedinclassesof0.125,rangingfromzerotoone. hahm (31.4)27107(9.5)89598(31.4)(0.1)17(0.0)3(0.0)(68.5)731(0.3)98(0.0)3110(1.1)24370(8.5)136291(47.8)132697(46.5)43545(15.3)9490(3.3)36052(12.6)14284(5.0)3120(1.1)232(0.1)35335(12.4)14538(5.1)(100.00)285,309(100.00)285,309(100.0 vegeneticeffects,directandmaternalcomplementarity,hnparentheseswereexpressedasrelativefrequencies. 22staNd2b(Tch2iva...hyeet2220eoiv¼el...oTT1lF02iidodnadrhha..8Piritiaere)eeirrodBeCo*esewccfec(rnodcco1oetptemeiot.nehecf(e0trercdatfptene-offooraalafidiamerulacmi)ba.cemdinsvaui)en(pdeeitanet2nmchlidnairndte0toeientisatmatv0nmadolbieApw0rneoalarien)eetnatfno,tshsgyfistedNftpnPueaeiorocmieruscntfciismtlhsdatclbfaeeoyeiloetradxdri(nele(tereia,ceebcdtmdaeredgyghnat)geie)Kvpmmaencagicnelioenlnsaeor.esecgtfngmtwf(ooriihef2icnrmiuxpetoc0miserltircp0eeechfnafl2meaoneeneunf)l(ctmcfu,e1gsteeienm9seCsece.dn9ttasndnat3erotterisdt)aomfi,sitorcabcyoieasnrtrcsntoiyeedoebtlfeiymfeem(udeacdtsp.ctsamheTtaoatsdoeleas-)..
fixedgeneticeffects,gr cm (9.5)89677(0.4)200(90.1)195431 (100.00)285,309 dmaternalbreedadditinedvalue.Percentagesi tcN2ehof.e2feeel.Tl3fcofoNt.isrce,eeiHletslhfetnorietmarteechriatoseitfsoterdieansretcohestozicfefofiregnitdcbohitsereoeidtfcdytaatch(smoheecafbm)afirncae¼iineemdandamt.sml*wba(1tree.er0reen-dauamlsae(n)dhdmwasah)dmehereestciesrariaobthseiidess
frequenciesofobservationsamongcoefficientsof amca (9.5)37561(13.2)27135(0.2)145(0.1)1013(2.5)2385(0.8)257161(41.6)84046(29.5)(29.5)65641(23.0)(4.2)8575(3.0)(11.8)34416(12.1)(0.7)420(0.1)(0.0)52120(18.3)(100.00)285,309(100.00)285,309 m,ea,em:coefficientsusedtoestimatedirectanncludefractionsequalorsmallerthanthementio TFtbhiayxMAAAAAAibseCHECClBodesHEdetu2gerdeltony.eliti(ca1xxxxxxae9f9fe1c)tasaxxxxxxminndcluSdccexxxhadeEninffkeetcchxxxmtlse(i1ng9ec9lnuho3dxxta)ey,dpaioclsnomhγxxmoudseelsdecxxboaynsCidaeerrxxmdedosion
relative aa 271355227140118626842591186833676205032285,309 m,ha,hClassesi AAHCHEE xx xx x x xx xx xx xx
Table1Absoluteand Classes 0.0000.1250.2500.3750.50006250.7500.8751.000Total aa,am,ca,crespectively. aggdreaeeirsnn,epeecaetttmciiccti,evafecenfafledyf,ce.tccstmm,sd,a,itrdheeiracrnt,eaachltnmdea,mnpeidasatt,eamrtenimcaatle:hrlodnesiatrselercoctnsoioasmnnn-pdoalendmmd-aaietdtinedvtreiantiraviltegyebgnreneenteoeidncti-caaeeddffddffeeiittcciivvttssee,,
4 C.D.Bertolietal./LivestockScience176(2015)1–13
Table3
Numberofanimals(A)andcontemporarygroups(CG)usedintheanalysis.
Trait Weightgain Conformation Precocity Muscling Scrotalcircumference
TOTAL CONNEC(%) TOTAL CONNEC(%) TOTAL CONNEC(%) TOTAL CONNEC(%) TOTAL CONNEC(%)
A W 294,045 284,628(97) 288,182 279,582(97) 276,264 268,333(97) 286,350 277,734(97)
PW 148,443 138,102(93) 149,091 144,264(98) 141,188 136,802(97) 147,392 142,580(97) 46,269 40,092(87)
CG W 9242 6615(72) 8840 6433(73) 8312 6011(72) 8807 6398(73)
PW 11,398 7044(62) 3535 2496(71) 3304 2318(70) 3506 2471(70) 4222 2445(58)
W:weaningphenotypes;PW:post-weaningphenotypes;CONNEC.(%):number(andpercentage)ofanimals(A)/contemporarygroups(CG)connectedto
theanalyzeddata.
α
etal.(2008),CardosoandTempelman(2004),Pimenteletal. geneticeffects; isthevectorcombiningtherandomdirect
(2006(cid:2))andPRosoetal.(2005b).Thesecoeff(cid:3)icientsaregivenby (a),maternal(m)andpermanent(p)environmentaleffects,
hPa¼ 1– 2i¼1ðSirebreedinDambreediÞ and hm¼ð1(cid:3) i.e. α¼[a0 m0 p0]0, and ε is the vector of random residual
2i¼1ðMaternalGrandSirebreedin MaternalGrandDam effects. Incidence matrices X, W and Z relate records to
breedÞÞ where i¼1 refers to Angus breed proportion and fixedenvironmental effects, to fixed genetic effects and to
i
i¼2 refers to Nellore breed proportion. When the breed random direct and maternal additive genetic and perma-
composition of a cow was not known (all products had nentenvironmenteffects,respectively.
knownbreedcomposition)thecowwasconsideredasinter Thevectorsofrandomeffectsαandεwereassumedto
2 3
semating. A(cid:4)Ga A(cid:4)Gam 0
6 7
have(co)variance¼V(α)¼4 A(cid:4)Gam A(cid:4)Gm 0 5
2.2.4. Epistaticlosseffect 0 0 I(cid:4)Pe
Toestimatethedirect(ea)andmaternal(em)epistatic and V(ε)¼I(cid:4)R. A is the additive numerator relation-
loss effects, the epistazygosity coefficients were used as
ship matrix among animals and I is the identity matrix;
" # " #
proposed by Fries et al. (2000,2002) and also used by σ2 σ σ2 σ
Cardoso et al. (2008), Pimentel et al. (2006), Carvalheiro G ¼G ¼ a1 a1a2 ;G ¼ m1 m1m2 ; G ¼
a a σ σ2 m σ σ2 am
etal.(2006)andRosoetal.(2005a,b).Thesecoefficientsare " a1a#2 a22 m1m32 m2
wgivheenrebHyseais¼th½e[Hsisreþ'sHdh]etaenrodzyegmos¼is,½Hd[HmisgtshþeHdmagmd']s, σσa1m1 σσa1m2 ;Pe¼4σσ2p1 σσp12p25andR¼"σσ2e1 σσe12e2#
heterozygosis, Hmgs is the maternal grand sire heterozy- a2m1 a2m2 p1p2 p2 e1e2 e2
gosisandHmgdisthematernalgranddam heterozygosis. where σ2 refers to variance and σ refers to covariance; a
Whenthebreedcompositionofacowwasnotknown(all refers to direct additive genetic, m to maternal additive
products had known breed composition) the cow was genetic p to permanent environmental effects and e to
consideredasintersemating. residual;1referstothefirstand2tothesecondtraitona
two-traitanalysis.
The complete general model above (1) was analyzed
2.3. Statisticalanalysis
andalsowithreductions.Thedifferenceamongcompared
γ
2.3.1. The(co)variancecomponents models was in vector, which includes different fixed
The(co)variancecomponentswerepreviouslyestimated geneticeffects.Eightmodelswereanalyzed:modelAwhich
γ
using model (1), including all effects (fixed effects of includes in only the breed additive effect (direct and
γ
environment,fixedgeneticeffects,randomdirect,maternal maternal);modelACwhichincludesin thebreedadditive
and permanent environmental effects and residual). The effect (direct and maternal) and complementarity (joint
Restricted Maximum Likelihood (REML) method with the additive) effects (individual and maternal); model AH
γ
DMU (Madsen and Jensen, 2000) software was used. The which includes in the breed additive effect (direct and
convergencecriterionwas10(cid:3)12. maternal)anddominance(heterosis)effects(individualand
γ
maternal);modelAEwhichincludesin thebreedadditive
2.3.2. Genotypicmodels effect(directandmaternal)andepistaticlosseffects(indi-
γ
The general model is described by Eq. (1). The pair- vidualandmaternal);modelACHwhichincludesin the
traitsWG–PG,WC–PC,WP–PP,WM–PMandWG–SCwere breedadditiveeffect(directandmaternal),complementar-
analyzedinatwo-traitanalysisusingthismodelwiththe ity effects (individual and maternal) and dominance (het-
systematic inclusion of fixed genetic terms, in order to erosis)effects(individualandmaternal);modelACEwhich
γ
comparemodelsandeffects. includesin thebreedadditiveeffect(directandmaternal),
y¼XβþWγþZαþε ð1Þ complementarity effects (individual and maternal) and
epistatic loss effects (individual and maternal); model
β γ
whereyisthevectorofobservationsoftrait1andtrait2; AHE which includes in the breed additive effect (direct
isthevectoroffixedeffectsofenvironment,whichincludes and maternal), dominance (heterosis) effects (individual
contemporary group (herd, year, season, sex, phenotype and maternal) and epistatic loss effects (individual and
γ
collect date and manage group); is the vector of fixed maternal) and the complete model ACHE which includes
C.D.Bertolietal./LivestockScience176(2015)1–13 5
γ
in the breed additive effect (direct and maternal), com- matrix between predictor variables of the fixed genetic
plementarityeffects (individualand maternal), dominance effects.Theconditionnumber(k)istheconditionindexof
(heterosis) effects (individual and maternal) and epistatic thehighestvalue.VIFwasgivenbyVIF¼1/(1(cid:3)R2),where
i
losseffects(individualandmaternal).(Table2)Intotal,eight R is the determination coefficient. (Schabenberger and
i
modelswereanalyzedforeachtraitusingtheleastsquares Pierce,2002).
methodologyinatwo-traitanalysis.Datawaspre-adjusted
for fixed effects of animal age, dam age and birth date
(julian).Scrotalcircumferencewaspre-adjustedforageand
3. Resultsanddiscussion
weight.GenSysConsultoresAssociadosdevelopedtheana-
lysisprogramsinFortran95.
3.1. Themodels
TheLikelihoodRatio,asdescribedbyRegazziandSilva
(2004), was used to compare the models for each
The significance of the comparisons of the models
modelpair.
against reductions is presented in Table 4. Of the 198
realized comparisons (22 between each two of the eight
2.3.3. Connectednessanalysis
models, for each of the nine analyzed traits), using the
A connectedness analysis between contemporary
Likelihoodratiotestandtestingunderasignificancelevel
groups was carried out according to Roso et al. (2004), ofP40.001,40comparisons(20%)werenotsignificant.Of
using the total number of direct genetic links between
these, 45% were for scrotal circumference. The nullity
contemporary groups due to common sires and dams.
hypothesis was rejected, indicating that for each of the
Contemporarygroupswithmorethan2calvesandwithat
158significantcomparisonsthetestedmodelspresenteda
least 5 ten direct links and two classes of direct or
significant difference in at least one of the considered
maternal fixed effects were considered connected and
parameters.
retained for analysis. Roso et al. (2004) found that as the
AllmodelstestedagainstreducedA,ACandAEmodels,
degreeofconnectednessamongtestgroupsdecreases,the
presented significant differences except for SC, showing
accuracy of comparisons of EBVs of bulls in different test
that for all other traits these models are not the best
groups also decreases. As one of the final objectives of a
modelstousetocrossbreedanimals.
geneticevaluationistoobtainaccurateEBVs,wetestedthe
The AH reduction model did not show significant
connectedness, using only connected animals and con-
difference from ACH for most traits, but did with ACE,
temporarygroupsinthisanalysis.Thenumberofanimals
AHE and ACHE models. If AH and ACH are not truly
and contemporary groups for each trait before and after
different,wemaysupposethatcaand/orcmarenotreally
theconnectednessanalysisispresentedinTable3.
important to these traits. Lopes et al. (2010), testing
different models to estimate genetic effects in Angus x
2.3.4. Collinearitydiagnosis Nellore crosses, found that the “joint additive effect does
Principal components (PC), condition index (CI) and not substantially improve the adjustment”. Carvalheiro
variance inflation factor (VIF) were used to perform a et al. (2006), studying Hereford–Nellore crosses, suggest
collinearitydiagnosisp.CffiffiIffiffiffiwffiffiffiffiaffiffiffisffiffiffiffiobtainedforeacheigenvalue that complementarity seems to be important but should
by computing CI ¼ λ =λ, where λ is the largest be further investigated to better comprehend the effect
i max i max
λ
eigenvalue and is the ith eigenvalue of the correlation andhowtomodelit.
i
Table4
Significanceofthemodelstestedagainsttheeachpossiblereducedmodel.
model AC AH AE ACH ACE AHE ACHE ACH ACE AHE ACHE ACH ACE AHE ACHE ACH ACE AHE ACHE ACHE ACHE ACHE
reduction A A A A A A A AC AC AC AC AH AH AH AH AE AE AE AE ACH ACE AHE
trait
WG nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn ns nnn nnn nnn nnn nnn nnn nnn nnn ns ns
WC nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn ns nnn
WP nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn ns nnn nnn nnn nnn nnn nnn nnn nnn ns ns
WM nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn nn nnn nnn nnn nnn nnn nnn nnn nnn ns nnn
PG nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn ns nnn nnn nnn nnn nnn nnn nnn nnn ns ns
PC nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn nn nnn nnn nnn nnn nnn nnn nnn nnn ns ns
PP nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn ns nnn ns nnn nnn nnn nnn nnn nnn ns nnn
PM nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn nnn ns ns ns ns nnn nnn nnn nnn nnn ns ns
SC nnn nn nn nn ns ns ns ns ns ns ns ns ns ns ns ns ns ns ns ns ns ns
ns:nonsignificant;A:modelincludingonlythebreedadditive(directandmaternal)effect;AC:modelincludingthebreedadditive(directandmaternal)
andcomplementarity(directandmaternal)effects;AH:modelincludingthebreedadditive(directandmaternal)andheterosis(directandmaternal)
effects;AE:modelincludingthebreedadditive(directandmaternal)andepistaticloss(individualandmaternal)effects;ACH:modelincludingthebreed
additive(directandmaternal),complementarity(individualandmaternal)andheterosis(individualandmaternal)effects;ACE:modelincludingthebreed
additive(directandmaternal),complementarity(directandmaternal)andepistaticloss(directandmaternal)effects;AHE:modelincludingthebreed
additive(directandmaternal),heterosis(directandmaternal)andepistaticlosseffects(directandmaternal)andthecompletemodelACHE:thebreed
additive(directandmaternal),complementarity(directandmaternal),heterosis(directandmaternal)andepistaticloss(directandmaternal)effects.
nnPo0.01.
nnnPo0.001.
6 C.D.Bertolietal./LivestockScience176(2015)1–13
Table5
Correlationbetweenthecoefficientsusedonestimationoffixedgeneticeffects.Weaninggainbelowandpost-weaninggainabovediagonal.
aa am ca cm ha Hm ea em
aa 1 0.7552 0.7172 0.1195 0.6607 0.1165 0.2652 0.0884
am 0.7435 1 0.5577 (cid:3)0.1375 0.7379 (cid:3)0.1200 (cid:3)0.1077 (cid:3)0.1281
ca 0.6726 0.5298 1 0.5073 0.7559 0.4548 0.5513 0.4241
cm 0.0724 (cid:3)0.1810 0.4774 1 (cid:3)0.0052 0.9013 0.8373 0.8362
ha 0.6015 0.6970 0.7288 (cid:3)0.0323 1 (cid:3)0.0025 (cid:3)0.0425 (cid:3)0.0012
hm 0.0711 (cid:3)0.1628 0.4247 0.8998 (cid:3)0.0242 1 0.8760 0.5367
ea 0.2210 (cid:3)0.1416 0.5259 0.8305 (cid:3)0.0792 0.8719 1 0.5630
em 0.0521 (cid:3)0.1610 0.4000 0.8339 (cid:3)0.0248 0.5345 0.5540 1
aa,am,ca,cm,ha,hm,ea,em:directandmaternalbreedadditiveeffect,directandmaternalcomplementarity,heterosisandepistaticlossnon-additive
effects,respectively.
The comparison of ACHE/ACE did not present any importantastheothernon-additiveeffects;however,Lopes
significanceandACHE/AHEpresentednon-significantcom- et al. (2010) concluded “The inclusion of joint additive
parisonsforalargernumberoftraits.ObservingACHE/ACE effects does not substantially improve the adjustment
wemightsupposehaorhmwerenotimportanttoimprove promoted by the analysis models, besides inserting a bias
the adjustment of the tested models thus the models are attributed to multicollinearity”. Carvalheiro et al. (2006)
equivalent.However,ifweconsiderthesignificanceofthe arguethatcomplementarityseemsimportantbutshouldbe
comparison ACH/AC a possible confounding may exist furtherinvestigated.
when ha/hm or ea/em are not present in the model.
According to VanRaden (2006) “Breed differences contain 3.1.1. Collinearityanalysis
additive, dominance, and epistatic effects that are con- 3.1.1.1. Correlationbetweenpredictorvariables. Thecorrelation
foundedifonlytwobreedsareconsidered…”.Whenusing betweenthecoefficientsusedfortheestimationofthefixed
simpler models, joint additive and epistatic effects appear geneticeffectsforWGandPGarepresentedinTable5.
tobemixedintheheterosiseffect(Pimenteletal.2006). Intotal,46%of thecorrelationsbetweenthepairsfor
For weaning traits, the determination coefficient (R2) WG and 50% for PG, present values superior to 0.5,
(notshown)washighestandthemeansquareerror(MSE) indicating medium to high correlations between the
waslowerfortheACEmodelandforpostweaningtraits pairs.Thishighcorrelationmayindicatemulticollinearity
theAHEmodelhadthehighestR2andlowestMSE. between the coefficients; therefore, the coefficient pairs
AlthoughACHEdidnotdifferstatisticallyfromACEand must not be the only verified factor as the existing
AHE for most traits, the ACE model produced very high relationship between three or more coefficients can also
magnitude of the estimates. These high estimates hinder beinterferinginthismulticollinearity.
thebiologicalinterpretationandleadustoassumethatthis For all analyzed traits (WG, WC, WP, WM, PG, PC, PP,
is not the best model to use. The ACHE and AHE models PM and SC), the highest correlation was found between
seemmoreparsimonioustousewithcrossbredanimals. thecoefficientsformaternalcomplementarityandmater-
A wide variety of forms of interactions may be mani- nalheterosis,followedbythecorrelationofmaternaland
fested in a crossbred animal, often estimated as a single direct epistatic loss with maternal complementarity. This
component,calledheterosis.Thisestimatedheterosisvalue high correlation might be the reason why significant
is, actually, the liquid balance of all the gene interactions differences were not detected between the ACH/AH and
that are present in the animal. Models that include non- ACHE/ACEreductions.
additiveeffectscanbemoreprecise,butalsomoreconfus- Whencomplementarityisremovedfromthemodel(not
ing.Althoughgeneticinteractionsarecomplicatedtermsto shown), the highest correlation is between maternal het-
extractfrommodels,theycanprovideusefulpredictionsif erosisanddirectepistaticloss,keepingvaluesaround0.85
used carefully. Breeders must continue selecting for addi- for all traits. This high correlation may be due to the
tive merit, but can also improve non-additive merit, con- difficulty in separating the coefficients of maternal com-
sidering these interactions in breeding programs where plementarity and maternal heterosis and direct epistatic
crossbredanimalsareused(VanRaden,2006). loss,resultingfromdatastructureandfromapossiblelinear
Buenoetal.(2011),studyingepistasisongeneticevalua- dependence(multicollinearity)involvingthepredictors.
tion models, concluded that simpler models used to eval- Whenweremovethematernalcomponentofheterosis
uate bovine composites might wrongly identify various from the analysis of PG, PC and PM (maternal heterosis
additiveandnon-additiveeffectsasaheterosiseffect.Breed wasnotsignificantforthesetraits)thehighestcorrelation
additive,heterosisandepistaticlosseffects,aswellasdirect remainsbetweencomplementarityandepistaticloss,with
and maternal effects, should be included in models to veryclosevalues.
evaluate crossbreed beef cattle. (Bueno et al., 2012; Lema
etal.,2011;Cunhaetal.,2009;Cardosoetal.,2008;Kippert 3.1.1.2. Principalcomponentsandconditionalindex. Thefirst
etal.,2008;Carvalheiroetal.,2006) principal component allows us to perceive a possible
Complementarityeffectsaremorecontroversal.Cardoso collinearity between the values of the direct (ca) and
etal.(2008)andPiccolietal.(2002)foundthattheyareas maternal complementarity (cm), maternal heterosis (hm),
C.D.Bertolietal./LivestockScience176(2015)1–13 7
1st and 2nd Principal 1st and 2nd Principal
Components WG Components PG
Second component --00000000,,,,,,,,234021561 0 am 0,1 ha 0,2a a 0,3 em c0a,4 hmea c0m,5 Second component ---000000000,,,,,,,,,2340321561 0 0,1 am 0h,2a aa0 ,3 em 0,h4cm ae a cm0 ,5
-0,3 -0,4
First component First component
Fig.1. First and second principal components for weaning gain (WG) and post-weaninggain (PG) traits. aa: direct breedadditiveeffect, ca, direct
complementarityeffect,ha:directheterosiseffect,ea:directepistaticlosseffect.am:maternalbreedadditiveeffect,cm:maternalcomplementarityeffect,
hm:maternalheterosiseffect,em:maternalepistaticlosseffect.
direct(ea)andmaternal(em)epistaticlossestimates.These The variance inflation factor (VIF) analysis for the
estimates may be confounded for these traits. The second modelsACHE,AHEandACEarepresentedinTable6.
principal component shows that the breed direct (aa) and The VIF shows that the estimates had their variance
maternal(am)additiveeffect,directheterosis(ha)anddirect inflateupto110times(SC)whencomparedtoanorthogo-
complementarity(ca)effectopposestothematernalcomp- nal condition (VIF¼1) for the model ACHE.(Table 6) Roso
lementarity (cm), maternal heterosis (hm) and direct (ea) etal.(2005b)suggestedtheuseofridgeregressiontosolve
and maternal (em) epistatic loss effects, showing again a the problem of multicollinearity; however, Cardoso et al.
possibleconfoundingbetweentheseestimators(Fig.1). (2008), comparing the least squares and ridge regression
When there is no collinearity, the eigenvalues, condition methodologies,showedthat,althoughthemostconsistent
index and condition numbers are all one. With increasing results were generated by the ridge regression technique,
collinearity,eigenvaluesarebothlargerandsmallerthanone theestimatesofgenotypiceffects,withandwithouttheuse
(eigenvalueclosetozeroindicatesmulticollinearityproblem) ofthistechnique,generatesimilarpredictedvalues,andthis
and the condition index and number will increase (Scha- occurredforalltestedtraits.
benbergerandPierce,2002).AccordingtoSchabenbergerand Thispossiblecollinearitycanbepartiallyexplainedasall
Pierce (2002), if the value of the condition number of the estimators are based on the breed composition of indivi-
matrixislowerthantheupperthresholdof30,thisindicates duals,whichisrestrictedto1.Inaddition,thefactthatthe
problemsofmulticollinearity.Thehighestconditionindexwe breedcompositionofanindividualisequaltotheaverage
found was 21.2493 for WG. The other CIs were 21.0631 for of the breed composition of their parents interferes with
WC, 20.4443 for WP, 20.8205 for WM, 24.4637 for PG, thiscollinearity.Inpractice,weareusingthesameinforma-
22.8341 for PC, 21.9954 for PP, 22.3479 for PM and 28.5690 tiontopredictdifferenteffectsseenfromdifferentangles.
forSC.Lemaetal.(2011)alsousedthethresholdof30.They FortheACEmodel,exceptPP,allothertraitspresented
foundconditionnumberof28.3andconcludedthatcollinear- FIV higher than ten for maternal complementarity and
itywasnotaproblem. higherFIVfordirectandmaternalepistaticlossthanAHE
Multicollinearitycanoccurwhenoneormorevariables model. For the AHE and ACH models, onlySC produced a
aredependentonotherspresentinthesamemodel.When FIVhigherthanten.TheAC,AH,AEandAmodelsdidnot
using non-additive models, we are using breed composi- presentanyFIVaboveten.Theseresultsmayindicatethat
tion(individual,parentsandgrandparents)toestimateall the greatest problem for collinearity is complementarity,
coefficients (breeddirect,complementarity, heterosis and ascmalwaysshowedthehighestvalues.
epistatic loss). High correlations between variable pairs
maybeindicativeofmulticollinearity(Rosoetal.,2005b).
Thehigherthecollinearity,thehigherthestandarderrors 3.2. Fixedgeneticeffectsestimates
and,widertheconfidenceintervals.Thetstatisticstendto
be very small in this case. When multicollinearity is Estimates of fixed genetic effects are presented in
present,itisthereforedifficulttorejectthenullhypothesis Table 7. All regression coefficients for WG and WM are
(Schabenberger and Pierce, 2002). Even if there is multi- statisticallysignificant (Po0.01), as are most coefficients for
collinearityamongtheusedestimators,werejectmostof theothertraits(WC,WP,PG,PC,PP,PM).Scrotalcircumfer-
ournullhypothesesinthepresentstudy. ence presents 30% of the total statistically non-significant
coefficients. Among the non-significant effects, there were
3.1.1.3. Varianceinflationfactor. Thevarianceinflationfactor some maternal components for post-weaning traits, which
(VIF) indicates the variance inflation of each regression werenotexpectedtobesignificant.Contrarytothis,thenon-
coefficient compared with an orthogonal situation. Usually significance of the direct and maternal breed additive and
valuesabove10forVIFsuggestthatmulticollinearitymaybe direct complementarity effects for WM (models ACHE, ACH
causing problems in the estimation (Schabenberger and andAHE)wasnotexpectednorwasthedirectbreedadditive
Pierce,2002). effectforPG(modelAHE)andforPP(modelsACEandAHE).
8 C.D.Bertolietal./LivestockScience176(2015)1–13
Table6
Varianceinflationfactor(VIF)estimated(ACHE,AHEandACEmodels).
ModelACHE
WG WC WP WM PG PC PP PM SC
aa 3.544 3.593 3.455 3.503 4.174 4.024 3.823 3.853 6.054
am 3.712 3.892 4.024 3.844 4.030 4.323 4.854 4.230 4.773
ca 13.730 13.935 13.815 13.355 21.228 19.661 19.140 18.183 22.848
cm 69.093 67.611 62.564 66.808 86.393 75.271 68.870 74.077 110.851
ha 8.896 8.886 8.460 8.672 13.638 12.444 11.416 11.911 13.541
hm 36.929 36.343 34.335 36.021 45.887 41.392 38.361 40.770 51.637
ea 13.924 14.158 13.918 13.975 18.166 17.214 16.603 16.795 21.906
em 17.169 16.908 15.957 16.755 20.864 18.359 17.366 18.199 28.671
modelAHE
aa 3.544 3.592 3.454 3.502 4.165 4.010 3.798 3.837 6.053
am 3.481 3.606 3.659 3.561 3.775 3.993 4.317 3.902 4.415
ha 2.216 2.285 2.370 2.249 2.568 2.596 2.839 2.521 3.421
hm 5.124 5.172 5.073 5.132 5.383 5.301 5.177 5.218 6.661
ea 6.330 6.380 6.250 6.313 7.012 6.784 6.586 6.655 10.,394
em 1.496 1.491 1.453 1.481 1.511 1.474 1.448 1.459 1.705
modelACE
aa 3.465 3.502 3.369 3.414 4.008 3.865 3.675 3.699 5.686
am 3.672 3.849 3.980 3.802 3.960 4.254 4.781 4.164 4.588
ca 3.399 3.561 3.840 3.441 3.973 4.080 4.728 3.831 5.716
cm 10.189 10.147 9.704 10.032 10.926 10.329 9.781 10.147 15.204
ea 5.745 5.764 5.726 5.689 6.341 6.124 6.134 5.988 9.462
em 4.501 4.477 4.291 4.439 4.673 4.467 4.278 4.418 5.917
aa,am,ca,cm,ha,hm,ea,em:directandmaternalbreedadditivegeneticeffects,directandmaternalcomplementaritynon-additivegeneticeffects,
directandmaternalheterosisnon-additivegeneticeffects,directandmaternalepistaticlossnon-additivegeneticeffects,respectively;WG:weaninggain;
PG:post-weaninggain;WC:weaningconformation;PC:post-weaningconformation;WP:weaningprecocity;PPpost-weaningprecocity;WM:weaning
muscling;PM:post-weaningmuscling;SC:scrotalcircumferenceadjustedtoage.
ThebreedadditiveeffectrelatestotheAngusandmust Nelloregenesproportionincreasethecalfperformancealso
be considered as a deviation from Angus performance as increase, but with a small scrotal circumference. Negative
the Nellore gene proportion increases. The direct breed valuesofamforWC(modelACE),WP(modelsACHE,ACE
additive direct effect (aa) was positive for weaning traits and AHE) and WM (models ACE and AHE) may indicate
andnegativeforpost-weaningtraitsandSCformostofthe poorer performance in conformation, precocity and mus-
tested models, showing that as the Nellore (B. indicus) cling at weaning for the Nellore genes. We did not find
gene proportion increases, the general weaning growth literature testing these models with these traits. Positive
rate increases and the general post-weaning growth rate values of am for 205 day and 550 day weights were
decreases.ForA,ACandAEmodels,aawasnegativeforall reported by Kippert et al. (2008) and for weaning weight
traits. The positive or negative effect does not mean that by Lopes et al. (2010). Lema et al. (2011), using a model
theanimalsareheavierorlighter;itisjustthegeneeffect. withoutacomplementarityeffect,foundstronglynegative
The final animal weight will be a balance of all involved valuesforNellorebreedasadeviationfromHereford.They
effects.Negativevalueswerereportedforweaningweight suggest their environment was less restricted, explaining
for Nellore (Lopes et al., 2010) and positive for Brahman the better performance for the British breed compared to
(ElzoandWakeman,1998),bothasdeviationfromAngus. Zebu. All models presented negative values of am for SC.
Apositivevalueofaaforweaningweightwasreportedby Cardoso et al.(2008), studying crosses between Hereford
Lema et al. (2011) and negative values for average pre- and Nellore found negative values of am only for post-
weaningdailygainwerereportedbyCardosoetal.(2008) weaningprecocity.
and for pre-weaning gain by Carvalheiro et al. (2006). Complementarity can be considered as what Kinghorn
TheseeffectsconsideredNelloreasadeviationfromHere- (1993)called“profitheterosis”.Ifweconsiderthiseffectas
ford. Kippert et al. (2008) studying 205 dayand 550 day thejointactionoftwogenepools,assuggestedbyPimentel
weights found negative values for both periods, weaning et al. (2006), these results can be interpreted as additive
and post-weaning, even though neither the complemen- interaction between two different traits, independent of
tarity nor epistatic loss effects were considered. Cardoso dominance (heterosis) or epistasis. When we consider a
et al. (2008), studying Nellore x Hereford crosses also tropicaloratemperateenvironment,thechangeinperfor-
foundnegativevaluesofaaforalltraits(WC,WP,WM,PC, mancewhenwemovethegeneticcompositionfrom0.00to
PP,PMandSC). 0.25Bosindicusisnotnecessarilyequivalentforthe move
Thematernalbreedadditiveeffect(am)waspositivefor from 0.75 to 1.00. What we are considering here is a
mostofmodelsandtraitsexceptforSC,showingthatasthe quadratic effect between two breeds as suggested by
Table7
Regressioncoefficientsofbreedadditiveandnon-additivegeneticeffectsofpreandpost-weaningtraitsinAngusxNellorecrosses.
ACHE ACH ACE AHE AC AH AE A
WG
aa 1.405 (0.323) ** 1.881 (0.302) ** 4.776 (0.319) ** 4.429 (0.323) ** (cid:3)1.504 (0.295) ** 1.810 (0.271) ** (cid:3)5.551 (0.295) ** (cid:3)2.535 (0.257) **
am 2.111 (0.195) ** 4.322 (0.183) ** 1.513 (0.194) ** 2.957 (0.189) ** 6.085 (0.172) ** 4.238 (0.181) ** 6.970 (0.172) ** 4.739 (0.152) **
ca 16.269 (1.605) ** 3.350 (1.079) ** 58.021 (0.798) ** 40.823 (0.768) **
cm 36.701 (2.339) ** 5.190 (0.747) ** 90.059 (0.898) ** 27.964 (0.395) **
ha 8.079 (0.365) ** 14.437 (0.245) ** 11.356 (0.182) ** 14.573 (0.174) **
hm 3.872 (0.665) ** 15.026 (0.251) ** 21.465 (0.248) ** 16.346 (0.116) **
ea (cid:3)3.821 (0.541) ** (cid:3)20.403 (0.347) ** (cid:3)10.531 (0.365) ** 8.096 (0.194) **
em (cid:3)11.616 (0.559) ** (cid:3)24.588 (0.286) ** (cid:3)3.070 (0.165) ** (cid:3)5.002 (0.163) **
PG
aa (cid:3)1.090 (0.405) ** (cid:3)4.681 (0.371) ** (cid:3)1.115 (0.397) ** (cid:3)0.172 (0.405) ns (cid:3)10.265 (0.362) ** (cid:3)3.038 (0.326) ** 0.638 (0.357) ns (cid:3)6.705 (0.303) **
am 1.892 (0.235) ** 2.529 (0.217) ** 1.457 (0.232) ** 1.373 (0.227) ** 6.577 (0.202) ** 2.468 (0.214) ** 4.734 (0.204) ** 11.593 (0.179) **
ca 21.586 (2.204) ** 17.294 (1.365) ** 55.084 (0.953) ** 52.577 (0.919) ** C
cm (cid:3)12.820 (3.018) ** (cid:3)6.783 (0.889) ** (cid:3)6.212 (1.073) ** (cid:3)28.680 (0.467) ** .D.
hheaam 60(cid:3)..15819.24452 (((000...587025628))) *n***s 1(cid:3)25.2.01255 ((00..239213)) **** (cid:3)15.337 (0.417) ** 1(cid:3)(cid:3)325.1..46852876 (((000...242932748))) ****** 1(cid:3)45.5.66170 ((00..123156)) **** (cid:3)13.226 (0.227) ** Bertolie
t
em 1.496 (0.714) * (cid:3)1.854 (0.338) ** (cid:3)0.510 (0.192) ** (cid:3)1.097 (0.190) ** al.
/
aacaam W000...103C072763 (((000...000160478))) ****** 00(cid:3)..10029.36199 (((000.,.000140358))) ****** 01(cid:3)..42094.00111 (((000...000130348))) *n***s 00..202044 ((00..001048)) *n*s 00(cid:3)..18061.00902 (((000...000130237))) n****s 00..008679 ((00..001018)) **** 0(cid:3).102.0299 ((00..001027)) **** 0(cid:3).009.0930 ((00..001016)) **** LivestockS
cm 1.310 (0.097) ** 0.160 (0.031) ** 2.808 (0.037) ** 0.725 (0.017) ** cie
ha 0.222 (0.015) ** 0.471 (0.010) ** 0.251 (0.008) ** 0.406 (0.007) ** nce
hm 0.091 (0.028) ** 0.418 (0.010) ** 0.677 (0.010) ** 0.427 (0.005) ** 17
ea (cid:3)0.229 (0.023) ** (cid:3)0.737 (0.014) ** (cid:3)0.524 (0.015) ** 0.150 (0.008) ** 6
em (cid:3)0.423 (0.023) ** (cid:3)0.779 (0.012) ** (cid:3)0.131 (0.007) ** (cid:3)0.178 (0.007) ** (20
1
5
PC )
1
aa (cid:3)0.123 (0.019) ** (cid:3)0.185 (0.,018) ** (cid:3)0.062 (0.019) ** (cid:3)0.046 (0.019) * (cid:3)0.412 (0.017) ** (cid:3)0.270 (0.016) ** (cid:3)0.261 (0.018) ** (cid:3)0.371 (0.015) ** 1–
am 0.142 (0.012) ** 0.215 (0.011) ** 0.126 (0.012) ** 0.130 (0.012) ** 0.360 (0.010) ** 0.214 (0.011) ** 0.284 (0.010) ** 0.415 (0.009) ** 3
ca 0.190 (0.106) ns (cid:3)0.918 (0.066) ** 1.526 (0.048) ** 0.955 (0.046) **
cm 0.665 (0.139) ** 0.084 (0.043) ns 1.425 (0.051) ** (cid:3)0.195 (0.024) **
ha 0.336 (0.025) ** 0.648 (0.015) ** 0.385 (0.011) ** 0.526 (0.011) **
hm 0.027 (0.040) ns 0.113 (0.014) ** 0.346 (0.014) ** 0.077 (0.007) **
ea (cid:3)0.326 (0.034) ** (cid:3)0.788 (0.020) ** (cid:3)0.529 (0.021) ** (cid:3)0.204 (0.011) **
em (cid:3)0.235 (0.033) ** (cid:3)0.467 (0.016) ** (cid:3)0.089 (0.009) ** (cid:3)0.100 (0.009) **
WP
aa 0.036 (0.015) * 0.029 (0.014) * 0.189 (0.014) ** 0.170 (0.015) ** (cid:3)0.092 (0.013) ** (cid:3)0.005 (0.012) ns (cid:3)0.146 (0.014) ** (cid:3)0.099 (0.012) **
am (cid:3)0.045 (0.010) ** 0.023 (0.009) * (cid:3)0.105 (0.009) ** (cid:3)0.087 (0.009) ** 0.084 (0.008) ** 0.005 (0.009) ns 0.038 (0.008) ** 0.038 (0.007) **
ca 0.180 (0.073) * (cid:3)0.914 (0.049) ** 1.144 (0.039) ** 0.311 (0.037) **
cm 1.063 (0.103) ** (cid:3)0,191 (0.034) ** 3.149 (0.041) ** 0.635 (0.019) **
ha 0.196 (0.016) ** 0.483 (0.011) ** 0.170 (0.009) ** 0.388 (0.008) **
hm 0.200 (0.030) ** 0.528 (0.011) ** 0.770 (0.011) ** 0.442 (0.005) **
ea (cid:3)0.305 (0.025) ** (cid:3)0.858 (0.016) ** (cid:3)0.709 (0.017) ** 0.116 (0,009) **
em (cid:3)0.432 (0.025) ** (cid:3)0.919 (0,013) ** (cid:3)0.216 (0.007) ** (cid:3)0.261 (0.007) **
PP
9
1
Table7(continued) 0
ACHE ACH ACE AHE AC AH AE A
aa (cid:3)0.122 (0.022) ** (cid:3)0.195 (0.020) ** 0.000 (0.021) ns (cid:3)0.020 (0.022) ns (cid:3)0.442 (0.020) ** (cid:3)0.289 (0.018) ** (cid:3)0.227 (0.020) ** (cid:3)0.394 (0.017) **
am 0.042 (0.015) ** 0.111 (0.014) ** (cid:3)0.015 (0.015) ns 0.002 (0.014) ns 0.290 (0.013) ** 0.118 (0.014) ** 0.192 (0.012) ** 0.385 (0.010) **
ca 0.187 (0.120) ns (cid:3)1.189 (0.075) ** 1.873 (0.060) ** 0.974 (0.056) **
cm 0.402 (0.155) ** (cid:3)0,153 (0.050) ** 1.728 (0.058) ** (cid:3)0.379 (0.030) **
ha 0.406 (0.027) ** 0.782 (0.017) ** 0.456 (0.014) ** 0.636 (0.013) **
hm 0.113 (0.044) * 0.164 (0.015) ** 0.386 (0.016) ** 0.059 (0.008) **
ea (cid:3)0.410 (0.038) ** (cid:3)1.028 (0,023) ** (cid:3)0.658 (0.024) ** (cid:3)0.290 (0.012) **
em (cid:3)0.225 (0.037) ** (cid:3)0.607 (0.018) ** (cid:3)0.148 (0.011) ** (cid:3)0.156 (0.010) **
WM
aa 0.017 (0.014) ns 0.011 (0.013) ns 0.151 (0.014) ** 0.125 (0.014) ** (cid:3)0.092 (0.013) ** (cid:3)0.030 (0.012) * (cid:3)0.199 (0.013) ** (cid:3)0.109 (0.011) **
am 0.005 (0.009) ns 0.082 (0.008) ** (cid:3)0.027 (0.009) ** (cid:3)0.016 (0.009) ns 0.134 (0.008) ** 0.056 (0.008) ** 0.092 (0.008) ** 0.048 (0.007) **
ca 0.089 (0.071) ns (cid:3)0.882 (0.048) ** 0.886 (0.036) ** 0.174 (0.035) **
cm 1.248 (0.102) ** 0.130 (0.033) ** 3.211 (0.040) ** 0.931 (0.018) **
ha 0.178 (0.016) ** 0.415 (0.011) ** 0.131 (0.008) ** 0.314 (0.008) ** C
hm 0.161 (0.029) ** 0.496 (0.011) ** 0.771 (0.011) ** 0.481 (0.005) ** .D.
eeam (cid:3)(cid:3)00..242029 ((00..002244)) **** (cid:3)(cid:3)00..784511 ((00..001153)) **** (cid:3)(cid:3)00..164161 ((00..001067)) **** 0(cid:3).201.1391 ((00..000079)) **** Bertoli
e
PM ta
aa (cid:3)0.206 (0.021) ** (cid:3)0.267 (0.019) ** (cid:3)0.144 (0,021) ** (cid:3)0.158 (0.021) ** (cid:3)0.461 (0.019) ** (cid:3)0.335 (0.017) ** (cid:3)0.293 (0.019) ** (cid:3)0.414 (0.016) ** l.
/
am 0.042 (0.013) ** 0.093 (0.012) ** 0.014 (0.013) ns 0.022 (0.013) ns 0.225 (0.011) ** 0.091 (0.012) ** 0.160 (0.011) ** 0.286 (0.010) ** Liv
cchama 000...053953132 (((000...110152507))) n****s 00(cid:3)..05029.86636 (((000...000174772))) *n***s 11..422614 ((00..005563)) **** 0.368 (0.012) ** 0(cid:3).805.2145 ((00..002560)) **** 0.488 (0.012) ** estockS
hm 0.007 (0.043) ns 0.092 (0.015) ** 0.272 (0.015) ** 0.049 (0.007) ** cie
ea (cid:3)0.261 (0.036) ** (cid:3)0.738 (0.022) ** (cid:3)0.443 (0.023) ** (cid:3)0.204 (0.012) ** nce
em (cid:3)0.202 (0.036) ** (cid:3)0.426 (0.017) ** (cid:3)0.088 (0.010) ** (cid:3)0.093 (0.010) ** 17
6
SC (2
aa (cid:3)1.589 (0.121) ** (cid:3)1.909 (0.107) ** (cid:3)1.649 (0.117) ** (cid:3)1.648 (0.121) ** (cid:3)2.010 (0.105) ** (cid:3)1,846 (0.087) ** (cid:3)1.776 (0.095) ** (cid:3)1,864 (0.073) ** 01
5
am (cid:3)0.889 (0.062) ** (cid:3)0.938 (0.052) ** (cid:3)0.904 (0.060) ** (cid:3)0.949 (0.059) ** (cid:3)0.984 (0.046) ** (cid:3)0.993 (0.051) ** (cid:3)0.943 (0.051) ** (cid:3)0.875 (0.042) ** )
1
ca 1.187 (0.489) * 1.156 (0.337) ** 1.039 (0.245) ** 1.736 (0.236) ** 1–
cm (cid:3)0.345 (0.797) ns (cid:3)0.566 (0.215) ** 0.219 (0.295) ns (cid:3)0.623 (0.109) ** 3
ha (cid:3)0.092 (0.114) ns 0.048 (0.078) ns 0.151 (0.057) ** 0.250 (0.055) **
hm 0.197 (0.222) ns 0.055 (0.074) ns 0.095 (0.080) ns (cid:3)0.014 (0.034) ns
ea (cid:3)0.367 (0.175) * (cid:3)0.269 (0.115) * (cid:3)0.198 (0.121) ns (cid:3)0.142 (0.059) *
em (cid:3)0.037 (0.194) ns (cid:3)0.172 (0.088) ns (cid:3)0.082 (0.047) ns (cid:3)0.098 (0.047) *
ns:nonsignificant;aa,am,ca,cm,ha,hm,ea,em:directandmaternalbreedadditivegeneticeffects,directandmaternalcomplementarity,heterosisandepistaticlossnon-additivegeneticeffects,respectively.
WG,WC,WP,WM:weaninggain,conformation,precocity,musclingrespectively;PG,PC,PP,PM:post-weaninggain,conformation,precocity,musclingrespectively;SC:Scrotalcircumference;standarderrorare
inparenthesis.
nPo0.05.
nnPo0.01.