genome wide association study for binomially distributed

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

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StalkLodgingInMaize

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StalkStrength

Disease/Pests

EnvironmentalFactors

5-20%yieldlossesworldwide

Flint-Garciaetal.,2003

DataCollection- 2016

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TwoRepsoftheGoodman-Bucklerdiversitypanelwereplantedusingincompleteblockdesign

TheentireexperimentwasinoculatedwithGoss’swilt

Inthisexperimenttherewasnocorrelationbetweendiseaseandlodging

TheJamannLabatUIUC

LodgingPhenotyping

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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

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Multi-ModelApproach

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Model1FitLogisticRegressionModel

Controlsforpopulation

structureonlyIdentifypeak

SNPs

Model2FitaMixedLinearModelControlsforpopulation

structureandrelatednessIdentifypeak

SNPs

Model3FitMixedLogistic

RegressionModel

UsingPeakSNPsfromModel1andModel2

LogisticRegressionIdentified~50%ofMarkerstobeSignificant

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Thetop2,796SNPsfromthismodelweresubset

RStudioChromosome

PeakSNPPossibleSNPsofinterest

Motivation:mixedlogisticregressionmodelcanfit2,796modelsin<1day

UnifiedMLMIdentifiedNoSignificantSignals

12GAPITLipkaetal.,2012

Chromosome

MixedLogisticRegressionIdentifies68%ofSNPsIdentifiedinLogisticRegression

toBeSignificant

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SAS9.4PROCGLIMMIX

Accountingforfamilialrelatednesshelpedrefinelocationofputativegenomicregions

SignalscoincidewiththosepreviouslyidentifiedfortraitsrelatedtolodgingChromosome

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SimulationStudyinGoodman-BucklerDiversitypanel:

Determinewhichparametersofthebinomialdistributioncontributethemosttoidentificationofgenomic

signals

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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

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Acknowledgements

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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

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HighLDDecayObservedAroundPeakSNPonChromosomeSeven

LimitingFactorsofThisStudyStalklodgingisaputativelylowheritabilitytraitNorepeatabilityacrossreplications

OnlyoneyearofdataincludedinthisanalysisOnlyoneenvironment

MissingdataVariousfactorscontributed

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SummaryofProjectLogisticRegressioniscomputationallyintensiveApproximately30secondstorun1SNPinSAS~17.36daystorun50,000SNPs

Model1andModel2areusedtoidentifywhichSNPsarefitusingthecompletelogisticregressionmodel(Model3)ThenumberofSNPstoincludeisdependentoncomputationalpoweravailable

StalkLodgingdatawasusedtotestthisapproachSomePeakSNPsidentifiedareinthesameregionasQTLassociatedwithstalkstrength,andacandidategeneforMCBStalkDamage

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DataCollection- 2016

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2Repsofthe282diversitypanelwereplantedusingincompleteblockdesign

TheentireexperimentwasinoculatedwithGoss’swilt

Inthisexperimenttherewasnocorrelationbetweendiseaseandlodging TheJamannLab

ObservedLodgingintheField

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Taxaclassifiedasnonstiffstalkwerelodgedmoreoften

Taxaclassifiedasstiffstalkwerelodgedthelessoften

Allplotsrepresentedinthisgraphhadatleast10plantslodged

LodgingScoreResidualsFollowaNon-NormalDistribution

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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/

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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?

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StangerandLauer,2006

BinomialDataAllowsforLogisticRegression

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Methods

OneSNPsfrom4K markersetwasassignedtobeQTN

Taxafromthe282diversitypanelweresimulatedtoexperiencelodging

The55Kmarkersetwasusedtogenotypethetaxausedinthesimulation

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ObjectivesEvaluatetheefficacyofthethreemodelapproachtomixedlogisticregression

EvaluatetheuseofthediversitypanelforuseinlogisticregressionGWAS

ExaminehowvariableswithinthedataseteffecttheabilitytodetectaQTN

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SimulationStudySettings

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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)

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Model2

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• Model2mayhavehadenoughpowertosuccessfullydetectQTNdespitemodelassumptionsbeingviolated•Previousstudieshaveshownthatlinearmodelscansometimesbeapproximatedbylogisticregressionmodels

Conclusion➢TraditionalGWASrequiresnormaldata

➢Logisticregressionhasthepotentialtoanalyzenon-normallydistributedtraits

➢Thebiggestlimitationofusinglogisticregressionisthecomputationalpower

required

➢ SimulationStudyshowtheneedforincreasedvariabilityofphenotypicdata- this

isespeciallyhardtoachieveinabinarytrait

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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

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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

genome wide association study for binomially distributed

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