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GenomeWideAssociationStudyforBinomiallyDistributedTraits:

ACaseStudyforStalkLodginginMaize

EsperanzaShenstoneandAlexanderE.LipkaDepartmentofCropSciences

UniversityofIllinoisatUrbana-Champaign

UnifiedMixedLinearModel(MLM)inGWAS

2Yu et al. (2006)

AdaptedfromA.Lipka

Phenotype of ithindividual

Grand Mean

Fixed effects: account for population structure

Marker effect

Observed SNP alleles of ith individual

Random effects: account for familial relatedness

Random errorterm

Measures relatedness between individuals

AssumptionsoftheUnifiedMLM

Whatdowedoiftheseassumptionscannotbemet?(Example:Binomiallydistributeddata)

3Yu et al. (2006)

AdaptedfromA.Lipka

BinomialDistribution:#SuccessesinnIndependentSuccess/FailureTrials

MixedLogisticRegressiondoesnotrequirenormalityorequalvariancesConductGWASbyfittingalogisticregressionmodelateachSNP

LogitLinkfunction:Thenaturallog-oddsofasuccess

Thegrandmean

Problem:Fittingthismodelisextremelycomputationallyintensive!!!

Purpose

Developamulti-modelGWASapproachthatwillallowmixedmodelGWAStobeconductedonbinomially

distributedtraits

5

StalkLodgingInMaize

6

StalkStrength

Disease/Pests

EnvironmentalFactors

5-20%yieldlossesworldwide

Flint-Garciaetal.,2003

DataCollection- 2016

7

TwoRepsoftheGoodman-Bucklerdiversitypanelwereplantedusingincompleteblockdesign

TheentireexperimentwasinoculatedwithGoss’swilt

Inthisexperimenttherewasnocorrelationbetweendiseaseandlodging

TheJamannLabatUIUC

LodgingPhenotyping

8

Standcount NumberofPlantsLodged

NumberofplantsNotlodged

LodgingScore(PercentLodged)

23 6 17 26%BeginningofGrowingSeasonEndofgrowingseason

Above:Diagramdepictingoneplot(rep)ofonetaxainthefield

TreatLodgingDataasaBinomialSetupofBinomial Whywethinkbinomialisan

appropriateapproximationforlodging

Theexperimentconsistsofnrepeatedtrials

Withineachplot,eachplantisatrial

Eachtrialhastwooutcomes:successorfailure

Success: planthaslodgedFailure: Planthasnotlodged

Theprobabilityofsuccess, π,isthesameoneverytrial

Theprobabilityofaplantlodging,π,isthesamewithinaplot

Thetrialsareindependent Oneplantlodgingwillnotchangethelikelihoodofanotherplantlodging

9

Multi-ModelApproach

10

Model1FitLogisticRegressionModel

Controlsforpopulation

structureonlyIdentifypeak

SNPs

Model2FitaMixedLinearModelControlsforpopulation

structureandrelatednessIdentifypeak

SNPs

Model3FitMixedLogistic

RegressionModel

UsingPeakSNPsfromModel1andModel2

LogisticRegressionIdentified~50%ofMarkerstobeSignificant

11

Thetop2,796SNPsfromthismodelweresubset

RStudioChromosome

PeakSNPPossibleSNPsofinterest

Motivation:mixedlogisticregressionmodelcanfit2,796modelsin<1day

UnifiedMLMIdentifiedNoSignificantSignals

12GAPITLipkaetal.,2012

Chromosome

MixedLogisticRegressionIdentifies68%ofSNPsIdentifiedinLogisticRegression

toBeSignificant

13

SAS9.4PROCGLIMMIX

Accountingforfamilialrelatednesshelpedrefinelocationofputativegenomicregions

SignalscoincidewiththosepreviouslyidentifiedfortraitsrelatedtolodgingChromosome

14

SimulationStudyinGoodman-BucklerDiversitypanel:

Determinewhichparametersofthebinomialdistributioncontributethemosttoidentificationofgenomic

signals

15

Assign SNP from 4K Set to be QTN

Simulate binomial distributed trait

QTN Effect size Stand count per plot Grand mean

Simulate Data~100 “Traits”

Fit logistic regression model at each of 55K SNPs

ProposedMethodologyforSimulationStudy

Foreachtraitineachsetting:Assessedgenomicpositionsof“top100”markerswithstrongestassociations

HowdoesthetotalnumberofplantsinaplotaffectQTNdetection?

StandCount:10

Proportionoftimesdetected:1.0

Model1

Top100SNPsfromeachtraitusedtocreatethisfigure


StandCount:15


Model1



StandCount:20


Model1



StandCount:25


Model1


StandcountdoesnotappeartoaffectourabilitytodetectQTN

HowdoesgrandmeanaffectQTNdetection?

GrandMean=0;P{Success}=0.5Proportionoftimesdetected:1.0

Model1




Model1



GrandMean=5;P{Success}=0.99


Model1


GrandmeanvaluesaffectsourabilitytodetectQTN

FutureDirectionsAnyphenotypethatmeasures#successesinaplotofn plantscouldtheoreticallyusetheseapproaches- Trytodesignexperimentsthatresultinabaselineprobabilityofsuccessof0.5

HowcanwefitmixedlinearmodelsinacomputationallyefficientmanneronaWindows/Maccomputer?- Temporarysolution:multi-modelapproachisreasonable- Trytostrivefor:writesoftwarethatusesthescoretest

24

Acknowledgements

25

CommitteeMembersDr.AlexanderE.LipkaDr.TiffanyJamannDr.MartinBohnDr.PatBrown

TheJamannLabJulianCooper

TheLipkaLabBrianRiceAngelaChen

GraduateStudentsAmandaOwings

DepartmentofCropSciencesatUIUC

Model1vs.Model2Comparison

VaryingAdditiveEffectSizes(SameAssignedQTN)

Additiveeffectsize0.5onchromosome8

Proportiontimedetected:0.93

Additiveeffectsize0.1onchromosome8


SummaryofResultsAbletoidentifytwosignificantSNPsintheBPregionofMaizeStalkStrengthQTL

Lietal.,2014,Flint-Garciaetal.,2003,Huetal.,2012PeakSNPsonChromosome7wereinthesamelocationasthemostrobustmarkerassociationwithRPR

Piefferetal.,2013AsignificantSNPonChromosome1wasinthesameregionasacandidategeneforMediterraneanCornBorerstalkdestructionsusceptibility

Samayoaetal.,2015

28

29

HighLDDecayObservedAroundPeakSNPonChromosomeSeven

LimitingFactorsofThisStudyStalklodgingisaputativelylowheritabilitytraitNorepeatabilityacrossreplications

OnlyoneyearofdataincludedinthisanalysisOnlyoneenvironment

MissingdataVariousfactorscontributed

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SummaryofProjectLogisticRegressioniscomputationallyintensiveApproximately30secondstorun1SNPinSAS~17.36daystorun50,000SNPs

Model1andModel2areusedtoidentifywhichSNPsarefitusingthecompletelogisticregressionmodel(Model3)ThenumberofSNPstoincludeisdependentoncomputationalpoweravailable

StalkLodgingdatawasusedtotestthisapproachSomePeakSNPsidentifiedareinthesameregionasQTLassociatedwithstalkstrength,andacandidategeneforMCBStalkDamage

31

DataCollection- 2016

32

2Repsofthe282diversitypanelwereplantedusingincompleteblockdesign

TheentireexperimentwasinoculatedwithGoss’swilt

Inthisexperimenttherewasnocorrelationbetweendiseaseandlodging TheJamannLab

ObservedLodgingintheField

33

Taxaclassifiedasnonstiffstalkwerelodgedmoreoften

Taxaclassifiedasstiffstalkwerelodgedthelessoften

Allplotsrepresentedinthisgraphhadatleast10plantslodged

LodgingScoreResidualsFollowaNon-NormalDistribution

34

The Box-Cox procedure was implemented, and λ=-0.6 was the suggested transformation

Transformation was unsuccessful

352 plots had no lodging

DistributionofLodgingScores

LodgingScoreFreq

uency

Genome-WideAssociationStudy(GWAS)

SearchthegenomeforgeneticmarkerssignificantlyassociatedwithyourtraitofinterestAllowsfortheidentificationofQTLsregionofthegenomeassociatedwiththetrait

35SingleNucleotidePolymorphism(SNP):Atypeofgeneticmarker

http://knowgenetics.org/snps/

36

282DiversityPanel

~75%ofallallelicdiversityinMaize

AdaptedfromFlint-Garciaetal.,2005Romayetal.,2013

OutlineIntroduction

Genome-WideAssociationonStalkLodginginMaize

SimulationStudy

Conclusions

37

UnifiedMixedLinearModelControlsforFalsePositives

38Yuetal.,2006

Simple

Simple

FloweringtimeofMaize(Highpopulationstructure)

EarDiameterofMaize(LowPopulationStructure)

StalkLodginginMaizePredictinglodgingischallenging

Mostmethodsaredestructiveand/oruseothertraitsasproxies

Canphenotypinglodgingstillyieldinterestingresults?

39

StangerandLauer,2006

BinomialDataAllowsforLogisticRegression

40

Methods

OneSNPsfrom4K markersetwasassignedtobeQTN

Taxafromthe282diversitypanelweresimulatedtoexperiencelodging

The55Kmarkersetwasusedtogenotypethetaxausedinthesimulation

41

ObjectivesEvaluatetheefficacyofthethreemodelapproachtomixedlogisticregression

EvaluatetheuseofthediversitypanelforuseinlogisticregressionGWAS

ExaminehowvariableswithinthedataseteffecttheabilitytodetectaQTN

42

SimulationStudySettings

43

Setting GrandMean

StandCount

Additiveeffectsize

1 0 10 0.92 1 10 0.93 3 10 0.94 5 10 0.95 0 15 0.96 0 20 0.97 0 25 0.9

Model1identifiesPeakSNPsWhileAccountingforPopulationStructure

44

Whatdoeschangingtheinterceptdotoourdata?

Model3FailedtoConvergeinSASProcGLIMMIXPossiblereasonsforthisfailure:• “therewasnotenoughvariationintheresponsetoattributeanyvariationtotherandomeffect”•EstimatedGmatrixisnotpositivedefinite:“procedureconvergedtoasolutionswherethevarianceoftherandomeffectis0”AlternativeSolution:• UsetheGMMATpackage(Chenetal.2015)(OnlyrunsonUNIXOS)

47

Model2

48

• Model2mayhavehadenoughpowertosuccessfullydetectQTNdespitemodelassumptionsbeingviolated•Previousstudieshaveshownthatlinearmodelscansometimesbeapproximatedbylogisticregressionmodels

Conclusion➢TraditionalGWASrequiresnormaldata

➢Logisticregressionhasthepotentialtoanalyzenon-normallydistributedtraits

➢Thebiggestlimitationofusinglogisticregressionisthecomputationalpower

required

➢ SimulationStudyshowtheneedforincreasedvariabilityofphenotypicdata- this

isespeciallyhardtoachieveinabinarytrait

49

Model1identifiesPeakSNPsWhileAccountingforPopulationStructure

50

BinomialDataAllowsforLogisticRegression

LogisticRegressiondoesnotrequirenormalityorequalvariancesConductGWASbyfittingalogisticregressionmodelateachSNP

LogitLinkfunction:Thenaturallog-oddsofaplantislodgedornotlodged

Thegrandmean

Model2IdentifiesPeakSNPsWhileControllingforPopulationStructureandRelatedness

52

Phenotype of ithindividual

Grand Mean

Fixed effects: account for population structure

Marker effect

Observed SNP alleles of ith individual

Random effects: account for familial relatedness

Random errorterm

Yu et al. (2006)

Measures relatedness between individuals

AdaptedfromA.Lipka

Model3isFitUsingSubsetofPeakSNPs

53

SAS9.4PROCGLIMMIX

Model3isfitusingtopSNPsfromModel1

Recommendation:NumberofSNPsthatcanberuninapproximately24hours

ResultsofSimulationStudyinContextofStalkLodgingData

• Itispossiblethatourmodel’sabilitytoaccuratelydetectQTLwascompromisedbecauseofanobservedlowrateoflodging• Canwecontrol•Ifthisbaselineprobabilityoccurs,thentheinabilityofourmodeltodetectQTLmayhavebeenexacerbatedbyaninterceptvaluethatisfarremoved0.

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PeakSNPsthatCoincidewithSignalsAssociatedwithRelatedTraits

TypeofRegionidentified

Chr LocationinLiterature LocationinModel3 Notes

Marker 7 159.4Mb 161.9Mb155.8Mb164.9Mb

ThreemostsignificantSNPsonChr7

qRPR2QTL 2 236.4-237.0Mb 236.8Mb 14th mostsignificantSNPonChr2

qRPR3-1QTL 3 181.1Mb-184.7 181.7Mb182.0Mb 92nd and98th mostsignificantSNPOnChr3

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