Simulation analysis to test the influence of model adequacy and data structure on the estimation of genetic parameters for traits with direct and maternal effects

Clément Virginie, Bibé Bernard, Verrier Étienne, Elsen Jean-Michel, Manfredi Eduardo, Bouix Jacques, Hanocq, Hanocq Éric

Description

Simulations were used to study the influence of model adequacy and data structure on the estimation of genetic parameters for traits governed by direct and maternal effects. To test model adequacy, several data sets were simulated according to different underlying genetic assumptions and analysed by comparing the correct and incorrect models. Results showed that omission of one of the random effects leads to an incorrect decomposition of the other components. If maternal genetic effects exist but are neglected, direct heritability is overestimated, and sometimes more than double. The bias depends on the value of the genetic correlation between direct and maternal effects. To study the influence of data structure on the estimation of genetic parameters, several populations were simulated, with different degrees of known paternity and different levels of genetic connectedness between flocks. Results showed that the lack of connectedness affects estimates when flocks have different genetic means because no distinction can be made between genetic and environmental differences between flocks. In this case, direct and maternal heritabilities are under-estimated, whereas maternal environmental effects are overestimated. The insufficiency of pedigree leads to biased estimates of genetic parameters.

Sujets

• Animal model
• Maternal effect
• Connectedness

Informations

• Publié par: biomed
• Publié le: 01 janvier 2001
• Nombre de lectures: 7
• Langue: English

Extrait

G©eInNetR.AS,elE.DEPvoSl.ci3e3nc(e2s0,0210)03169–395

369Originalarticle
Simulationanalysistotesttheinfluence
ofmodeladequacyanddatastructure
ontheestimationofgeneticparameters
fortraitswithdirectandmaternaleffects
VirginieC
LÉMENT
a
,
∗
,BernardB
IBÉ
a
,
ÉtienneV
ERRIER
b
,
c
,
Jean-MichelE
LSEN
a
,
EduardoM
ANFREDI
a
,
JacquesB
OUIX
a
,ÉricH
ANOCQ
a
a
Stationd’améliorationgénétiquedesanimaux,Institutnationaldelarecherche
agronomique,BP27,31326Castanet-TolosanCedex,France
b
Stationdegénétiquequantitativeetappliquée,Institutnationaldelarecherche
agronomique,78352Jouy-en-JosasCedex,France
c
Départementdessciencesanimales,InstitutnationalagronomiqueParis-Grignon,
16rueClaudeBernard,75231ParisCedex05,France
(Received3May2000;accepted5May2001)

Abstract–
Simulationswereusedtostudytheinfluenceofmodeladequacyanddatastructure
ontheestimationofgeneticparametersfortraitsgovernedbydirectandmaternaleffects.
Totestmodeladequacy,severaldatasetsweresimulatedaccordingtodifferentunderlying
geneticassumptionsandanalysedbycomparingthecorrectandincorrectmodels.Results
showedthatomissionofoneoftherandomeffectsleadstoanincorrectdecompositionofthe
othercomponents.Ifmaternalgeneticeffectsexistbutareneglected,directheritabilityis
overestimated,andsometimesmorethandouble.Thebiasdependsonthevalueofthegenetic
correlationbetweendirectandmaternaleffects.Tostudytheinfluenceofdatastructureonthe
estimationofgeneticparameters,severalpopulationsweresimulated,withdifferentdegreesof
knownpaternityanddifferentlevelsofgeneticconnectednessbetweenflocks.Resultsshowed
thatthelackofconnectednessaffectsestimateswhenflockshavedifferentgeneticmeansbecause
nodistinctioncanbemadebetweengeneticandenvironmentaldifferencesbetweenflocks.In
thiscase,directandmaternalheritabilitiesareunder-estimated,whereasmaternalenvironmental
effectsareoverestimated.Theinsufficiencyofpedigreeleadstobiasedestimatesofgenetic
parameters.
geneticparameters/animalmodel/maternaleffects/simulations/connectedness
∗
Correspondenceandreprints
E-mail:[e-mail]

V.Clément
etal.

0731.INTRODUCTION
Theanimalmodelisextensivelyusedforpredictinggeneticvaluesand
estimatinggeneticparameters,becausetheoptimumcombineduseofall
relationshipsandperformancesimprovesaccuracy.However,despitethe
theoreticaladvantagesofthismodel,somedataandmodelconditionscan
affectthevalidityandprecisionoftheestimationofvariancecomponents.
Thefirstsourceofbiasliesinthechoiceofthegeneticmodelusedto
analysedata.Concerningmaternallyinfluencedtraits,thereisstilldiscrepancy
betweenthetheoreticalstudiesaboutgeneticparameterestimationandpractical
applications.Thereasonsforthiscanbeproblemsofconvergencewithvariance
componentsestimationsoftware,ordatastructure(forexampleincompleteped-
igree),orunavailabilityofefficienttechniques(softwareorhardware)asisthe
caseinsomedevelopingcountries.Whentraitsaregovernedbybothdirectand
maternaleffects,fittingonlydirecteffectsleadstoanoverestimationofdirect
heritability.Forgrowthtraits,mostoftheestimationsofdirectheritability
withbothdirectandmaternaleffectsvarybetween0.20and0.30[30,38,47].
Whenmaternaleffectsareignored,directheritabilitiespublishedcanreach
0.73fordailygainbeforeweaning,[23],0.48or0.50forbirthweight[29],
0.35forfour-monthweight[27],0.56forweightsbeforeweaning[6]or0.45
forweaningweight[7].However,therelativepartofdirectandmaternal
effects(geneticorenvironmental)andthenatureandmagnitudeoftherelation
betweentheseeffectsaredeterminingconditionsfortheeffectivenessofa
selectionscheme.Literatureontheinfluenceofmodeladequacyinorderto
estimatevariancecomponentsislimited.Therearesomepublicationsinwhich
variousmodelsweretestedinordertofindthemostadaptedtoanalysedata.
Forexample,simulationswereusedtostudybiometricalaspectsofdirectand
maternaleffects[41,43].Meyer[33]studiedtheprecisionofgeneticpara-
meterestimationwithdifferentfamilystructures.Robinson[41]andLeeand
Pollak[28]testedthesire
×
yearvariationonthegeneticcorrelationbetween
directandmaternaleffects.QuintanillaAguado[39]studiedtheimportanceof
themodelsonmaternaleffectsanalysisbyfittinganenvironmentalcorrelation
betweenthedamandtheoffspring.Thesepreviouspublicationsreportedbiases
whenusingincorrectmodels.Inthisarticle,wequantifythisbiasfordifferent
valuesoftruegeneticparameters.
Datastructureisthesecondsourceofbiaslikelytoaffecttheestimationof
variancecomponents.Intraditionalfarmingsystems,itissometimesdifficult
toidentifyanimalsandtorecordperformancesand/orgenealogy.Theamount
andthequalityofthedataarethenaffectedbypracticalconstraints.Although
thisisoftenthecaseindevelopingcountries,thiscanalsoconcernindustrialised
countries,inparticularasregardshardybreedsmanagedinlargeflockswith
severalmalesusedsimultaneouslyfornaturalservice.Oneoftheconsequences

Modeladequacyanddatastructure
371
canbetheuseofaveryincompletepedigreeresultinginalessthorough
relationshipmatrixusedintheanimalmodel.Moreover,thelackofartificial
inseminationandapoorexchangeofsiresacrossbreedingunitslimitgeneflow
andcauseapartialorcompletelackofgeneticconnectedness.Eveninselection
schemesunderintensivebreedingconditions,disconnectednesscanbeaprob-
lemwhenpredictionofgeneticvaluesisdoneonanationalscaleandartificial
inseminationisorganisedintoregions,asisthecaseforinstancefortheMont-
béliardeandHolsteincattlebreedsinFrance[19,20]orinNorth-American
breeds[3,24,44].Theeffectofdatastructurehasbeenextensivelystudiedin
thecontextofgeneticevaluationofanimals.Absenceofconnectednessand
poorgenealogicalinformationareresponsibleforbiasesandlossofaccuracyin
thepredictionofgeneticvaluesbyananimalorsiremodel[1,21,44].However,
notmuchisknownabouttheeffectofdatastructureontheestimationofgenetic
parametersbyananimalmodel,especiallyinthepresenceofmaternaleffects.
Diaz
etal.
[10]andEccleston[11]studiedtheinfluenceofdisconnectednesson
modelswithdirecteffectsandfoundthatitwouldactonlyontheprecisionofthe
estimation.Now,toproposestrategiesforimprovement,itisnecessarytoassess
therelativeimportanceofdeviationsfromtheidealsituation.Thesecondpur-
poseofthisarticleistotest,bysimulation,theinfluenceofdatastructureonthe
estimationofgeneticparametersfortraitssubjecttodirectandmaternaleffects.

2.MODELADEQUACY
2.1.Datasimulation
2.1.1.Simulatedpopulation
ThesimulationprogramwaswritteninFortranandNAGLibrarieswere
usedforallrandomprocesses.
Asmodeladequacycanbearealprobleminpopulationsunderextensive
conditionswheredatastructureandunavailabilityofefficienttechniquescan
beaconstraintfortheuseofthecorrectmodel,weusedaknownAfrican
sheeppopulation[12,13,35]tosetsomeparametersofthesimulatedpopula-
tion(prolificacy,replacementrate,male/femaleratio).Comparedtothereal
population,thenumberofanimalsperflockwasincreasedinordertoavoid
confusionbetweenanimalandflockeffects.Thebasepopulationconsisted
of1260unrelatedanimals(60malesand1200females)assignedrandomly
to20flocksof63animalseach(3malesand60females).Oncethebase
populationwascreated,thesimulationwascarriedoutover6years.Eachyear,
randommating(nomatterwhatflockanimalscamefrom)waspractisedwitha
ratioofonemalefortwentyfemales.Theoffspringweregeneratedaccording
toaprolificacyof115%.Eachyear,1/3ofthemalesand1/5ofthefemales
werereplacedbyoffspringatrandom.Theremainingoffspringwasdiscarded

372
V.Clément
etal.
sothatthenumberofanimalsperflockandthenumberofflockswereconstant
overtime.Theaveragenumberofoffspringperfemalewasequalto2.7.The
datasetcorrespondstoafullyconnectedpopulationwithcompletepedigree.
2.1.2.Modelsusedforsimulatingdata
ThesimulatedmodelsweresimilartothoseusedinRobinson’sstudy[41],
with
A
representingthegeneticdirecteffects,
M
thegeneticmaternaleffects,
R
thegeneticcorrelationbetweendirectandmaternaleffects,and
C
thematernal
environmentaleffects.Someauthors(HohenbokenandBrinks[22],Koch[25],
FoulleyandMénissier[17]andCantet[8])haveshownthatamorecomplex
biologicalmodelcouldexist,thismodelincludinganongeneticcorrelation
betweenmaternaleffectsofdamsanddaughters.Severalbiometricalmodels
havebeenproposedtoconsiderthiscorrelation[8,40,41].Wecouldhaveused
thismodelinoursimulations,butwewantedtolimitthisworktothemodels
mostfrequentlyusedforthestudyofmaternaleffects.Themodelsandthe
corresponding(co)variancesarepresentedinTableI.
Forthebasepopulation(whichrepresentsfounderparents),randomeffects
weresampledfromnormaldistributionswithzeromeanandvariancescor-
respondingtoeachrandomeffect.Directgeneticvalue
A
i
forindividuals
i
wassimulatedinadistribution
N
(
0
,
σ
Ao
)
andmaternalgeneticvalue
M
i
for
individuals
i
wassimulatedusing:
qM
i
=
r
AoAm
×
(
σ
Am
/
σ
Ao
)
×
A
i
+
1
−
r
A
2
oAm
×
Q
i
×
&