<%BANNER%>

Statistical Model for Mapping Quantitative Trait Loci in Autotetraploid

Permanent Link: http://ufdc.ufl.edu/UFE0022877/00001

Material Information

Title: Statistical Model for Mapping Quantitative Trait Loci in Autotetraploid
Physical Description: 1 online resource (28 p.)
Language: english
Creator: Li, Jiahan
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: autotetraploid, qtl
Statistics -- Dissertations, Academic -- UF
Genre: Statistics thesis, M.S.Stat.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Autotetraploids that include many plant species, such as potato, sugarcane and rose, are of paramount importance to agricultural production and biological research. Quantitative trait locus (QTL) mapping in autotetraploids is challenged by their unique cytogenetic properties, such as preferential pairing and double reduction. In this article, we present a statistical model for mapping autotetraploid QTLs by considering these cytogenetic properties. Our model is built in the mixture model-based framework and implemented with the EM algorithm. The model allows simultaneous estimation of QTL positions, QTL e?ects, the chromosomal pairing factor and the degree of double reduction as well as the assessment of the estimation precision of these parameters. Computer simulation is used to examine the statistical properties of the model. Our model will provide a useful tool for QTL mapping in autotetraploids that undergo double reduction.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Jiahan Li.
Thesis: Thesis (M.S.Stat.)--University of Florida, 2008.
Local: Adviser: Wu, Rongling.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022877:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022877/00001

Material Information

Title: Statistical Model for Mapping Quantitative Trait Loci in Autotetraploid
Physical Description: 1 online resource (28 p.)
Language: english
Creator: Li, Jiahan
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: autotetraploid, qtl
Statistics -- Dissertations, Academic -- UF
Genre: Statistics thesis, M.S.Stat.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Autotetraploids that include many plant species, such as potato, sugarcane and rose, are of paramount importance to agricultural production and biological research. Quantitative trait locus (QTL) mapping in autotetraploids is challenged by their unique cytogenetic properties, such as preferential pairing and double reduction. In this article, we present a statistical model for mapping autotetraploid QTLs by considering these cytogenetic properties. Our model is built in the mixture model-based framework and implemented with the EM algorithm. The model allows simultaneous estimation of QTL positions, QTL e?ects, the chromosomal pairing factor and the degree of double reduction as well as the assessment of the estimation precision of these parameters. Computer simulation is used to examine the statistical properties of the model. Our model will provide a useful tool for QTL mapping in autotetraploids that undergo double reduction.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Jiahan Li.
Thesis: Thesis (M.S.Stat.)--University of Florida, 2008.
Local: Adviser: Wu, Rongling.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022877:00001


This item has the following downloads:


Full Text

PAGE 1

1

PAGE 2

2

PAGE 3

3

PAGE 4

IamgratefultomyadvisorDr.RonglingWu.Withouthim,thisthesiswouldnothavebeenpossible.Ithankhimforhispatienceandencouragementthatcarriedmeonthroughdiculttimes,andforhisinsightsandsuggestionsthathelpedtoshapemyresearchskills.Ialsothanktherestofmythesiscommitteemembers:Dr.ArthurBergandDr.MyronChang.Theirvaluablefeedbackhelpedmetoimprovethethesisinmanyways. 4

PAGE 5

page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 6 ABSTRACT ........................................ 7 CHAPTER 1INTRODUCTION .................................. 8 2THEMODEL ..................................... 10 2.1GeneticDesign ................................. 10 2.2ExtensiontoPartiallyInformativeMarkers .................. 13 2.3QuantitativeGeneticModel .......................... 13 2.4Mixture-BasedLikelihoodandEMAlgorithm ................ 15 2.5HypothesisTesting ............................... 19 3COMPUTERSIMULATION ............................ 20 4DISCUSSION ..................................... 25 REFERENCES ....................................... 26 BIOGRAPHICALSKETCH ................................ 28 5

PAGE 6

Table page 3-1SampleSizen=100.EstimatesofDoubleReduction,RecombinationFraction,OverallMean,AdditiveEects,andDominantEectsfromFullyInformativeMarkers. ........................................ 21 3-2SampleSizen=200.EstimatesofDoubleReduction,RecombinationFraction,OverallMean,AdditiveEects,andDominantEectsfromFullyInformativeMarkers. ........................................ 22 3-3SampleSizen=400.EstimatesofDoubleReduction,RecombinationFraction,OverallMean,AdditiveEects,andDominantEectsfromFullyInformativeMarkers. ........................................ 23 3-4Samplesizen=400.EstimatesofDoubleReduction,RecombinationFraction,OverallMean,AdditiveEects,andDominantEectswithPartiallyInformativemarkers. ........................................ 24 6

PAGE 7

7

PAGE 8

1995 )( 1998 )( 2001 )( 1998 )Statisticalmodelsforlinkageanalysisandmapconstructionthatconsideruniquebiologicalpropertiesofpolyploidshavebeendeveloped.( 1998 )( 1999 )( 2001 )Forbivalentpolyploids,Wuetal.( 2002 )incorporatedtheso-calledchromosomalpairingpreference( 1994 )intothelinkageanalysisframework,aimedtoincreasethebiologicalmeaningoflinkagemappingmodels.Therehavebeenseveralstatisticalmodelsdevelopedtomapquantitativetraitloci(QTLs)inbivalentpolyploids.( 2002 )Thereisalsoagroupofpolyploids,calledmultivalentpolyploids,inwhichchromosomespairamongmorethantwohomologouscopiesatmeiosis,ratherthanonlytwocopiesaslikeinbivalentpolyploids.Theconsequenceofthismultivalentpairingistheformationofdoublereduction,i.e.,twosisterchromatidsofachromosomesortintothesamegamete.( 1929 )Fisher( 1947 )proposedaconceptualmodelforcharacterizingtheprobabilitiesof11dierentmodesofgameteformationforaquadrivalentpolyploidintermsoftherecombinationfractionbetweentwodierentlociandtheirdoublereductions.Wuetal.( 2001a )usedFisher'smodeltoderivetheEMalgorithmfortheestimationofthelinkagebetweenfullyinformativemarkers.WuandMa( 2004 )extendedthismodelintoanalyzeanytypeofmarkers,regardlessoftheirinformativenessanddominantorcodominantnature.ThesignicantadvantageofthemodelsbyWuandcolleaguesdirectlyliesintheirgenerality,exibilityandrobustness. 8

PAGE 9

1947 )11classicationsofgameteformation.ThemodelallowstheestimationandtestofnotonlytheQTL-markerlinkage,butalsotheextentofdoublereductionoftheQTL.Becauseoftheinherentcomplexityofclassicationanalysesofgameteformation,wewillfocusonthemodelingandanalysisofone-marker/one-QTLassociations,butbothfullyinformativemarkersandpartiallyinformativemarkersareconsidered.Atwo-stagehierarchicalmodelisderivedtoestimatetheprobabilitiesofgameteformationmodesandthereforedoublereductionintheupperhierarchyandestimatethemarker-QTLrecombinationfractioninthelowerhierarchywithinthemaximumlikelihoodcontextimplementedwiththeEMalgorithm.Computersimulationstudiesareperformedtoinvestigatestatisticalpropertiesofourmodelanditsanalyticalandbiologicalmerits. 9

PAGE 10

1947 )classiedthese136formationmechanismsinto11gametemodes.Ofthese11gametemodes,however, 10

PAGE 11

2001b )inmatrixformexpressedasQ1Q1Q2Q2Q3Q3Q4Q4Q1Q2Q1Q3Q1Q4Q2Q3Q2Q4Q3Q4g=M1M1M2M2M3M3M4M4M1M2=M2M1M1M3=M3M1M1M4=M4M1M2M3=M3M2M2M4=M4M2M3M4=M4M3266666666666666666666666666666641 4g11 12g21 12g21 12g21 12g51 12g51 12g51 12g61 12g61 12g61 12g21 4g11 12g21 12g21 12g51 12g61 12g61 12g51 12g51 12g61 12g21 12g21 4g11 12g21 12g61 12g51 12g61 12g51 12g61 12g51 12g21 12g21 12g21 4g11 12g61 12g61 12g51 12g61 12g51 12g51 12g31 12g31 12g41 12g41 6g71 24g81 24g81 24g81 24g81 6g91 12g31 12g41 12g31 12g41 24g81 6g71 24g81 24g81 6g91 24g81 12g31 12g41 12g41 12g31 24g81 24g81 6g71 6g91 24g81 24g81 12g41 12g31 12g31 12g41 24g81 24g81 6g91 6g71 24g81 24g81 12g41 12g31 12g41 12g31 24g81 6g91 24g81 24g81 6g71 24g81 12g41 12g41 12g31 12g31 6g91 24g81 24g81 24g81 24g81 6g737777777777777777777777777777775; 2{8 ),weseethatthereisno,oneandtworecombinanteventsinthecells(g1),(g3;g5)and(g2;g4;g6;g9),respectively.Thecells(g7)and(g8)areeachamixtureoftwodierentgameteformationmechanismsorcongurations(AandB),i.e.,g7=g7A+g7Bandg8=g8A+g8B,withrelativeproportionsdeterminedbyr.Becausedierentcongurationscontaindierentnumbersofrecombinationevents,theexpectednumberofrecombinationeventsineachcell,i.e.,anobservablegametegenotype,shouldbetheweightedaverageofthenumberofrecombinationeventsforeachconguration.Wuetal.( 2001b )usedamatrixformtocounttheexpectednumberofrecombinationeventsforeachobservablegamete 11

PAGE 12

Basedonmatrices( 2{8 )and( 2{2 ),theexpressionsforthefrequenciesofdoublereduction(and)andtherecombinationfractionrcanbeexpressedintermsofgias (2{5) (2{6) 2[g3+g5+2(g2+g4+g6+g9)+2g7+(1+)g8] (2{7) 12

PAGE 13

4g11 12g21 12g21 12g21 12g51 12g51 12g51 12g61 12g61 12g6g2 13

PAGE 14

whereistheoverallmean,a1,a2,anda3aretheadditivegeneticeectsofallelesQ1,Q2,andQ3relativetoalleleQ4,andd12,d13,d14,d23,d24,andd34arethedominantgeneticeectsduetointeractionsbetweendierentallelesQ1andQ2,Q1andQ3,Q1andQ4,Q2andQ3,Q2andQ4,andQ3andQ4,respectively. 14

PAGE 15

4(11+22+33+44); 4(311223344); 4(322113344); 4(333112244); 4(333+3441122); 4(322+3441133); 4(322+3331144); 4(311+3442233); 4(311+3332244); 4(311+3223344): wherej1j4jiistheindicatorvariablethatisdenedas1ifindividualihasaQTLgenotypej1j2(j1j2=Q1;Q2;Q3;Q4),and0otherwise,j1j2isthegenotypicvalueofQTLgenotypej1j2asdenedinequation( 2{9 ),andeiistheresidualerrorassumedtobenormallydistributedwithmeanzeroandvariance2.Weusetodenotetheunknownvector(11;22;33;44;12;13;14;23;24;34;2).ForaQTLmappingexperiment,markergenotypesareobservable.Letnl1l2betheobservationofmarkergenotypel1l2(l1l2=M1;M2;M3;M4).Thelikelihoodofthephenotypic(y)andmarkerdata(M)isconstructed,withinthemixturemodelframework, 15

PAGE 16

wherej1j2jl1l2istheconditionalprobabilityofQTLgenotypej1j2givenmarkergenotypel1l2,andfj1j2(yi)isassumedtofollowanormaldistributionwithmeanj1j2andvariance2.Priorconditionalprobabilityj1j2jl1l2iscalculatedasthefrequencyofjointmarker-QTLgenotypel1l2j1j2,expressedintermsofninegprobabilitiesinmatrix( 2{2 ),dividedbythefrequencyofmarkergenotypel1l2.Markergenotypefrequenciesare=4foreachofdoublereductiongametesM1M1,M2M2,M3M3,andM4M4,and(1)=6foreachofnon-doublereductiongametesM1M2,M1M3,M1M4,M2M3,M2M4,andM3M4.Theestimatesofunknownparametersthatmaximizethelikelihood( 2{21 )canbeobtainedbyimplementingtheEMalgorithm.InstepE,wecalculatetheposteriorprobabilityofaQTLgenotypegivenaspecicmarkergenotypeofindividualiby j1j2jl1l2i=j1j2jl1l2fj1j2(yi) 16

PAGE 18

Basedon 2{8 ,theMLEsofg1;g2;;g9intheproblemofpartiallyinformativemarkerscanbeexpressedinasimilarway.Theseleadtotheestimatesofthefrequenciesofdoublereduction ^=^g1+^g2+^g3+^g4=1 ^=^g1+^g2+^g5+^g6; ^r=1 2[^g3+^g5+2(^g2+^g4+^g6+^g9)+2^g7+(1+)^g8]: ThegenotypicvalueofQTLgenotypej1j2andresidualvarianceareestimatedby ^j1j2=Pni=1PM4l1=M1PM4l2=M1j1j1jl1l2iyi ^2=1 TheiterationisrepeatedbetweentheEstep,equations( 2{3 ),( 2{4 ),and( 2{22 ),andMstep,equations( 2{23 ){( 2{28 ),untilstableestimatesareobtained.Thestableestimatesarethemaximumlikelihoodestimates(MLEs)ofparameters. 18

PAGE 19

Thedierencebetweenthelog-likelihoodfunctionsunderthenullandalternativehypothesesarecalculated.Butthedistributionofthislog-likelihoodratio(LR)isnotknownbecauseoftheviolationofregularityconditionsforthemixturemodel.Forthisreason,acommonlyusedempiricalapproachbasedonpermutationtestsbyreshuingtherelationshipsbetweenthemarkergenotypesandphenotypes( 1994 )isusedtodeterminethecriticalthreshold,inordertojudgewhetherthereisaQTLforthetrait.AfterasignicantQTLisdetected,thenexthypothesisisabouttheadditivegeneticeectoftheQTL.Thiscanbetestedbyformulatingthenullhypothesis,H0:a1=a2=a3=0;underwhichtheestimatesofgenotypicvaluesofQTLgenotypescanbeobtainedwiththeEMalgorithmasdescribedabove,butposingthreeconstraintsderivedfromequations( 2{11 ),( 2{12 )and( 2{13 ).Similarly,thedominantgeneticeectscanbetestedwiththenullhypothesis,H0:d12=d13=d14=d23=d24=d34=0;withestimatesofgenotypicvaluesundertheconstraintsderivedfromequations( 2{14 ){( 2{19 ).Allthesegeneticeectscanbetestedindividually. 19

PAGE 20

2{9 )whentheoverallmeanisassignedas1,andtheadditiveanddominanteectsassignedasa1=a2=a3=0:6andd12=d13=d14=d23=d24=d34=0:5.TheerrorvarianceisdeterminedaccordingtotheheritabilityofH2=0:1and0.4,respectively.ThemeansoftheMLEsofunknownparametersandtheirstandarderrorsbasedon1000simulationreplicatesareillustratedintable 3-1 ,table 3-2 ,table 3-3 andtable 3-4 .Ourmodelprovidesreasonableestimatesofallthemodelparameters.TheprecisionoftheMLEs,asassessedbythestandarderrors,increasesforalltheparameterswithincreasedsamplesize,increaseddegreeoflinkage,andincreasedheritability.Dierentdegreesofdoublereductioncanbepreciselyestimated. 20

PAGE 21

SampleSizen=100.EstimatesofDoubleReduction,RecombinationFraction,OverallMean,AdditiveEects,andDominantEectsfromFullyInformativeMarkers. 0:30:250:10.2950.3140.0470.1160.0372.2283.007-1.9532.375-2.661-2.107(SD)(SD)(0.047)(0.120)(2.339)(2.651)(2.496)(4.013)(4.237)(4.499)(4.349)(4.453)(4.407)0:30:250:40.3010.2510.5560.4960.5460.6770.6250.3130.4820.1810.138(SD)(SD)(0.048)(0.098)(0.986)(1.003)(1.133)(1.744)(1.861)(2.143)(1.947)(2.103)(1.931)0:30:050:10.2970.1420.6590.5800.5121.2161.130-0.0361.2860.119-0.084(SD)(SD)(0.041)(0.114)(1.330)(1.293)(1.303)(1.967)(2.208)(2.301)(2.129)(2.193)(2.102)0:30:050:40.2960.0570.6420.6430.5330.4450.5620.4280.6010.4880.594(SD)(SD)(0.045)(0.051)(0.461)(0.581)(0.497)(0.868)(0.787)(0.851)(0.973)(0.762)(0.687)0:150:250:10.1500.3050.2440.8210.9451.2321.3340.1670.660-0.150-0.373(SD)(SD)(0.034)(0.155)(1.800)(1.794)(1.965)(2.707)(2.645)(2.819)(2.820)(2.658)(2.614)0:150:250:40.1520.2390.5220.5480.5980.6450.4840.4490.4920.3820.230(SD)(SD)(0.031)(0.097)(0.777)(0.812)(0.794)(1.082)(1.166)(1.100)(1.203)(1.227)(1.238)0:150:050:10.1440.1680.4110.5400.9301.6161.2420.2711.033-0.037-0.313(SD)(SD)(0.035)(0.127)(2.103)(1.962)(1.635)(2.854)(2.698)(2.488)(2.452)(3.147)(2.700)0:150:050:40.1430.0570.3720.7360.5450.6850.9650.6210.6770.2820.453(SD)(SD)(0.035)(0.058)(0.877)(0.759)(0.775)(1.192)(1.148)(1.085)(1.085)(1.167)(1.147)0:050:250:10.0520.3710.3560.3000.4552.2392.178-0.6912.031-0.426-0.588(SD)(SD)(0.022)(0.180)(2.122)(2.576)(2.392)(3.425)(3.478)(3.104)(2.787)(2.998)(3.563)0:050:250:40.0510.2530.4400.4060.4581.2431.2020.5001.2240.5530.362(SD)(SD)(0.022)(0.111)(1.067)(1.003)(1.105)(1.522)(1.605)(1.341)(1.541)(1.483)(1.482)0:050:050:10.0520.1930.0561.0120.3621.5521.977-0.0651.068-1.077-0.438(SD)(SD)(0.025)(0.136)(2.119)(2.537)(2.121)(3.110)(2.718)(3.191)(3.427)(3.354)(3.391)0:050:050:40.0520.0640.5250.3610.3371.1191.1750.1931.2550.3030.351(SD)(SD)(0.024)(0.059)(1.005)(0.959)(1.076)(1.480)(1.482)(1.542)(1.636)(1.473)(1.285)

PAGE 22

SampleSizen=200.EstimatesofDoubleReduction,RecombinationFraction,OverallMean,AdditiveEects,andDominantEectsfromFullyInformativeMarkers. 0:30:250:10.3020.3130.3970.2180.1262.3032.553-1.6492.272-1.471-1.268(SD)(SD)(0.031)(0.093)(1.708)(1.697)(1.443)(2.844)(3.144)(3.576)(3.048)(3.454)(3.526)0:30:250:40.3010.2340.5820.5530.6770.4930.3170.3400.6460.4590.262(SD)(SD)(0.034)(0.085)(0.781)(0.730)(0.727)(1.432)(1.402)(1.438)(1.416)(1.435)(1.362)0:30:050:10.3020.0930.5450.5510.6600.7390.7030.2060.9240.1140.089(SD)(SD)(0.032)(0.093)(0.789)(0.829)(0.753)(1.432)(1.561)(1.309)(1.355)(1.453)(1.486)0:30:050:40.2970.0470.5960.5850.5740.5220.5310.4640.5090.4200.530(SD)(SD)(0.032)(0.037)(0.362)(0.346)(0.342)(0.570)(0.645)(0.666)(0.611)(0.577)(0.569)0:150:250:10.1520.2770.6920.5630.5870.9530.968-0.2321.224-0.034-0.033(SD)(SD)(0.028)(0.117)(1.168)(1.225)(1.215)(1.866)(1.930)(1.862)(1.900)(1.780)(1.692)0:150:250:40.1470.2340.5810.6750.5800.4200.5510.5610.3860.4840.617(SD)(SD)(0.024)(0.078)(0.520)(0.471)(0.530)(0.838)(0.724)(0.775)(0.822)(0.745)(0.736)0:150:050:10.1490.1400.4750.5480.7231.2320.9850.2460.8630.048-0.325(SD)(SD)(0.024)(0.106)(1.251)(1.257)(1.479)(1.814)(1.719)(1.990)(1.968)(1.868)(1.824)0:150:050:40.1490.0550.6910.5730.5580.3940.3800.4780.5360.4850.523(SD)(SD)(0.026)(0.047)(0.558)(0.511)(0.585)(0.684)(0.799)(0.800)(0.862)(0.754)(0.745)0:050:250:10.0490.3260.7500.3250.5571.2351.190-0.4201.392-0.127-0.331(SD)(SD)(0.015)(0.143)(2.486)(2.232)(1.868)(2.857)(2.619)(3.332)(3.113)(3.023)(2.775)0:050:250:40.0480.2410.6190.3450.5280.8850.6580.2340.8790.4980.242(SD)(SD)(0.013)(0.075)(1.038)(1.037)(0.932)(1.365)(1.305)(1.282)(1.317)(1.190)(1.276)0:050:050:10.0500.1960.4900.2940.6121.7551.435-0.4871.713-0.146-0.379(SD)(SD)(0.015)(0.127)(1.941)(2.134)(2.157)(2.902)(2.792)(2.747)(2.872)(2.758)(2.855)0:050:050:40.0490.0590.6090.3510.6970.9520.6460.5480.9080.7370.412(SD)(SD)(0.017)(0.049)(0.978)(0.988)(0.967)(1.130)(1.527)(1.419)(1.285)(1.279)(1.001)

PAGE 23

SampleSizen=400.EstimatesofDoubleReduction,RecombinationFraction,OverallMean,AdditiveEects,andDominantEectsfromFullyInformativeMarkers. 0:30:250:10.3000.3000.1820.4350.2081.8002.002-1.2361.546-1.574-1.318(SD)(SD)(0.023)(0.082)(1.405)(1.400)(1.074)(2.357)(2.429)(2.829)(2.130)(2.744)(2.906)0:30:250:40.3010.2310.5850.5570.6030.5080.4510.3610.4940.4630.309(SD)(SD)(0.023)(0.078)(0.552)(0.497)(0.532)(1.050)(0.984)(0.977)(1.115)(1.060)(0.964)0:30:050:10.2980.0970.5770.6460.6290.7040.8180.2450.6890.2020.208(SD)(SD)(0.023)(0.077)(0.603)(0.637)(0.580)(1.067)(1.138)(1.206)(1.028)(1.120)(1.071)0:30:050:40.2990.0500.6260.5530.6390.5250.4420.4580.5070.5750.414(SD)(SD)(0.025)(0.027)(0.245)(0.253)(0.250)(0.388)(0.435)(0.405)(0.403)(0.388)(0.350)0:150:250:10.1500.2610.6410.4630.6110.9750.8600.1920.9950.2650.202(SD)(SD)(0.016)(0.135)(0.684)(0.904)(0.737)(1.372)(1.476)(1.423)(1.286)(1.458)(1.353)0:150:250:40.1500.2500.5840.6240.5650.4950.5520.4790.5160.4520.424(SD)(SD)(0.017)(0.060)(0.329)(0.358)(0.326)(0.511)(0.526)(0.510)(0.558)(0.478)(0.419)0:150:050:10.1500.1130.5830.5830.7060.7400.7050.2180.6670.1700.058(SD)(SD)(0.017)(0.095)(0.866)(0.846)(0.838)(1.341)(1.254)(1.322)(1.527)(1.272)(1.218)0:150:050:40.1500.0490.5260.6540.6070.5310.5720.5470.4060.4250.482(SD)(SD)(0.017)(0.034)(0.307)(0.382)(0.366)(0.557)(0.511)(0.551)(0.516)(0.506)(0.483)0:050:250:10.0500.3220.5160.7260.6291.2561.3270.1871.026-0.191-0.037(SD)(SD)(0.010)(0.113)(1.819)(1.626)(1.773)(2.170)(2.180)(2.155)(2.213)(2.437)(2.459)0:050:250:40.0500.2500.6100.6520.5510.4040.5620.4810.4800.4570.545(SD)(SD)(0.012)(0.057)(0.664)(0.680)(0.624)(0.873)(0.789)(0.867)(0.916)(0.909)(0.991)0:050:050:10.0500.1670.6560.3430.7231.1560.796-0.1641.1470.111-0.211(SD)(SD)(0.011)(0.109)(1.548)(1.553)(1.581)(2.032)(2.084)(2.157)(2.213)(1.997)(2.140)0:050:050:40.0510.0540.5910.6080.6350.5120.4590.5180.4690.4770.450(SD)(SD)(0.011)(0.037)(0.637)(0.624)(0.698)(0.771)(0.895)(0.894)(0.931)(0.800)(0.770)

PAGE 24

Samplesizen=400.EstimatesofDoubleReduction,RecombinationFraction,OverallMean,AdditiveEects,andDominantEectswithPartiallyInformativemarkers. 0:30:250:10.30.2180.8860.450.450.2550.2550.2590.880.7740.774(SD)(SD)(0.038)(0.097)(0.677)(0.49)(0.49)(0.763)(0.763)(1.094)(1.394)(0.852)(0.852)0:30:250:40.30.2380.5620.5780.5780.3460.3460.5190.1820.3040.304(SD)(SD)(0.035)(0.111)(0.434)(0.296)(0.296)(0.47)(0.47)(0.588)(0.816)(0.503)(0.503)0:30:050:10.2970.0980.9211.2431.2430.550.550.8380.8781.4991.499(SD)(SD)(0.039)(0.089)(0.608)(0.673)(0.673)(1.03)(1.03)(1.2)(2.467)(1.124)(1.124)0:30:050:40.2990.070.6110.5540.5540.6230.6230.4840.5950.5770.577(SD)(SD)(0.04)(0.081)(0.298)(0.27)(0.27)(0.402)(0.402)(0.57)(0.97)(0.625)(0.625)0:150:250:10.1460.250.5610.6420.6420.5420.5420.5430.3680.520.52(SD)(SD)(0.032)(0.111)(0.547)(0.508)(0.508)(0.64)(0.64)(1.02)(1.395)(0.805)(0.805)0:150:250:40.150.2590.5940.5540.5540.5720.5720.5190.3860.4010.401(SD)(SD)(0.031)(0.099)(0.401)(0.325)(0.325)(0.446)(0.446)(0.7)(1.054)(0.651)(0.651)0:150:050:10.1540.0880.6350.6450.6450.5590.5590.6490.320.6020.602(SD)(SD)(0.03)(0.093)(0.479)(0.363)(0.363)(0.474)(0.474)(0.768)(1.204)(0.753)(0.753)0:150:050:40.1510.0810.6130.4570.4570.650.650.4280.550.3950.395(SD)(SD)(0.031)(0.092)(0.341)(0.327)(0.327)(0.372)(0.372)(0.711)(0.955)(0.516)(0.516)0:050:250:10.0540.2831.2581.4731.4730.4860.4861.8680.9232.5342.534(SD)(SD)(0.019)(0.197)(1.722)(1.423)(1.423)(1.963)(1.963)(2.848)(3.577)(2.291)(2.291)0:050:250:40.0510.2510.7130.7060.7060.4840.4840.8350.3530.9490.949(SD)(SD)(0.021)(0.13)(0.874)(0.655)(0.655)(0.707)(0.707)(1.357)(1.813)(1.098)(1.098)0:050:050:10.0530.1531.21.6591.6590.3270.3272.2270.0652.2842.284(SD)(SD)(0.017)(0.141)(1.359)(1.042)(1.042)(1.533)(1.533)(2.147)(3.063)(2.018)(2.018)0:050:050:40.0520.0810.7150.5680.5680.5850.5850.570.5750.6470.647(SD)(SD)(0.018)(0.088)(0.662)(0.531)(0.531)(0.741)(0.741)(1.057)(1.374)(0.829)(0.829)

PAGE 25

2001b )( 2004 )itisimportanttoincorporatedoublereductionintoaQTLmappingframework.OurmodelprovideapowerfultoolforQTLmappingandunderstandingthegeneticcontrolofaquantitativetraitinanautotetraploid.Ourmodelmadeuseof11dierentclassicationsoftwo-locusgameteformations,derivedbyFisher,( 1947 )duringtetraploidmeiosisandhasproventobepowerfulforsimultaneousestimationofthefrequenciesofdoublereductionandtherecombinationfractionbetweendierentloci.Wewillbeinabetterpositiontounderstandthegeneticdierentiationamongpolyploidgenomesandcharacterizethegeneticarchitectureofquantitativelyinheritedtraitsforthisuniquegroupofspecies. 25

PAGE 26

26

PAGE 27

27

PAGE 28

MynameisJiahanLi.IwasborninLuoyang,China.AftergraduatingfromShanghaiJiaotongUniversity,IcametoDepartmentofStatistics,UniversityofFlorida. 28