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QTL Analysis: Concept Parents F1 F2 F2:3 × AB Generation Procedure Alternatives: BC1, RIL, DHL Field PHT[cm] Marker # M 1 B B H H A.. A 2 H A H A A.. H 3 B B H H H.. A 4 H H B B B.. H 5 H B H H A.. B.... N A H H H A.. A Laboratory Chromosome 1 LOD score PHT Office

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QTL Analysis: Single Marker Analysis Plant height (cm) X MC (cm) Total 196 umc130 AAAaaa F = 6.47** umc157 AAAaaa F = 0.48 ns

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QTL Analysis: Single Marker Model (F2) r M m Q q Additive effect: Dominance effect: F tests on the contrasts of marker classes test the following hypothesis: a > 0 d > 0 r < 0.5 QQ Qq qq MM (1-r) 2 2r(1-r) r 2 μ(MM) Mm r(1-r) (1-r) 2 +r 2 r(1-r) μ(Mm) mm r 2 2r(1-r) (1-r) 2 μ(mm) μ1 μ2 μ3 Schön, 2002

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QTL Analysis: Single Marker Model (F2) r = 0 M m Q q r = 0.2 M m Q q Example: Plant height, umc130 Case 1Case 2 X(MM) = 201cm X(Mm) = 196cm X(mm) = 191cm PHT (cm) r = 0 r = 0.2 r = 0.4 Add. Effect X(QQ) X(Qq) X(qq)

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4. Association Analysis Concepts

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Dissecting A Quantitative Trait: Time Versus Resolution Resolution in bp 1x Research Time in Years 5 1 Associations 1x10 4 F2 QTL Mapping F2 QTL Mapping NILs Positional Cloning Positional Cloning RI QTL Mapping RI QTL Mapping

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Resolution Versus Allelic Range Resolution in bp 1x Alleles Evaluated >40 1 Associations In Diverse Germplasm Associations In Diverse Germplasm 1x10 4 NIL Pedigree F2 or RIL Mapping F2 or RIL Mapping Positional Cloning Positional Cloning Associations In Narrow Germplasm Associations In Narrow Germplasm

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Association Tests Evaluate whether nucleotide polymorphisms associate with phenotype Natural populations Exploit extensive recombination 1.3m 1.5m 1.4m 1.8m 2.0m TA GA A CG GA A CG TA A TA TC G TG TA G TG GA G

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Association mapping Mainstay of human genetics –One of a few possible approaches –Reproducibility was an issue Cystic fibrosis –Kerem, et al. (1989). Science 245, Alzheimer's disease –Corder et al. (1994). Nature Genet. 7,

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Associations may result from at least three causes 2. The locus is in linkage disequilibrium with the cause of the phenotype Linked and highly correlated 1. The locus is the cause of the phenotype

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12 Complete Linkage Disequilibrium Adapted from Rafalski (2002) Curr Opin Plant Biol 5: D =1 r 2 =1 6 6 Locus 1 Locus 2 Same mutational history and no recombination. No resolution

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12 Linkage Disequilibrium D =1 r 2 = Locus 1 Locus 2 Different mutational history and no recombination. Some resolution 3

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12 Linkage Equilibrium D =0 r 2 =0 3 3 Locus 1 Locus 2 Same mutational history with recombination. Resolution 3 3

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Andes U.S. 3. Population structure can produce associations GTGGGGTTTGTT P=0.04 GT P<<0.001 T G These non-functional associations can be accounted for by estimating the population structure using random markers.

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5. QTL mapping analysis

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QTL Analysis: Interval Mapping PLOT Peak at 96 LOD = === ===== I === === I == === I == I = == I ==== I I ==== ===========********** ****** *************** 0.0 M M MC -- M M C M M cM ( 0.47) r1 M1 m1 Q q M2 m2 r2 r Simple Interval Mapping Composite Interval Mapping PlabQTL

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QTL Analysis: Power of QTL detection Power:Probability of finding a QTL Heritability: Utz and Melchinger, 1994

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QTL Analysis: Conclusions There are a number of QTL, in analysis the largest ones easiest to detect BUT Makes detection of others difficult Models can adjust for this – detect others

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QTL Analysis: Conclusions QTL mapping combines qualitative linkage analysis with quantitative genetic analysis. – Association between marker genotypes and phenotypic trait values. Single marker analysis is easy to perform but QTL effect and position are confounded. This results in low power of QTL detection. Interval mapping approaches increase power of QTL detection and allow the estimation of QTL effects and position.

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QTL Analysis: Conclusions Estimates of QTL effects and the proportion of the genotypic variance explained by QTL are biased due to genotypic and environmental sampling. Estimates of QTL position show low precision. With large populations a large number of QTL is found for complex traits. When conducting a QTL study you may wish to use a large population size.

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6. Candidate Genes

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Functional Genomics Using Diversity Forward Genetics Trait Positionally clone gene Reverse Genetics Trait Candidate gene QTL Candidate Polymorpism

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Association Analysis Identification of More Favorable Alleles Enhanced Marker Assisted Breeding

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7. Linkage Disequilibrium Analysis

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25 Properties of LD A a P AB = p A p B + D AB P Ab = p A p b - D AB P aB = p a p B - D AB P ab = p a p b + D AB Bb pApA papa pBpB pbpb 1 The basic measure of LD is: D AB = P AB - p A p B ( D AB = D Ab = D aB = D ab )

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Linkage Disequilibrium versus Generations Since its Creation

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Other Measures of LD Can divide D AB by the maximum value it can obtain: D AB = D AB / [max(-p A p B, -p a p b )]if D AB < 0 D AB / [min (p A p b, p a p B )] if D AB > 0 The sampling properties of D AB are not well understood. r 2 AB = D 2 AB p A p B p a p b E(r 2 )= 1 / (1 – 4Nc)

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LD generally decays rapidly with distance r2r2 Remington, D. L., et al PNAS-USA 98: & unpublished

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InvestigatorPopulation Studied Extent of LD GautLandraces<1000 bp BucklerDiverse Inbreds2000 bp RafalskiElite Lines100 kb? (6 kb euchromatin?) Population Effect on Linkage Disequilibrium in Maize Reviewed in Flint-Garcia, S. A. et al Annual Review of Plant Biology 54:

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8. Association Analysis

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Allele Case-Control Test n 1|aff n 2|aff n 1|unaff n 2|unaff Affected Unaffected allele 1 allele 2 2 n aff 2 n unaff n1n1 n2n2 2 N individuals X 2 = i (n i|aff - n i|unaff ) 2 n i|aff + n i|unaff ~ 2 (k-1) marker if n aff = n unaff (k alleles)

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Population Stratification: American Indian and Diabetes Knowler 1988 Am J Hum Genet 43,

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Use SSR Markers to Estimate Population Structure 8 Stiff Stalk 38 Non-Stiff Stalk 30 Sub-Tropical Method: Pritchard, J. K., M. Stephens, and P. Donnelly Inference of population structure using multilocus genotype data. Genetics 155: Example: Remington, D. L., et al Proc Natl Acad Sci U S A 98:

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Logistic Regression Ratio Test For Association Adapted from Pritchard case-control approach Where: – C = candidate polymorphism distribution – T = trait value – Q = matrix of population membership Evaluated by logistic regression Significance evaluated by permutation based on haplotype distribution in populations Pritchard, J. K., M. Stephens, N. A. Rosenberg, and P. Donnelly Am J Hum Genet 67:

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Population Structure Estimates Greatly Reduce Estimated Type I Error Rates Flowering TimeHeight Fields

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Su1 Sugary1 is an isoamylase, a starch debranching enzyme Sequenced fully from 32 diverse lines Sampled 2 small parts of gene from 102 lines 11100bp Whitt, S. R., et al PNAS-USA 99:

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su1 Promoter & 1 st Exon Two distinct alleles Sweet phenotype not associated

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su1 Coding Region Two distinct alleles Sweet phenotype associated with W578R

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Su1 578:W R Based on survey of 12kbp from lines.

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Dwarf8 functional variation 2 Amino Acid Deletion SH2 Domain When controlling for population structure, associates with flowering time & plant height across 12 environments. Thornsberry et al Nat. Genet. MITE Indel Days to Silking relative to B73

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9. Type I and Type II Error

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Statistics - Hypothesis Test Null Hypoth TrueNull Hypoth False Reject Null Hypothesis Type I Error α Correct Fail to Reject Null Hypothesis Correct Type II Error β Power = 1- β P-value = α

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Experimentwise P value Each statistical test has a Type I error rate –Test 20 independent SNPs, one will be significant at P<0.05 Bonferroni correction essentially divides the P by number of tests –Often too conservative (no power), as markers are correlated Churchill and Doerge permutation help estimate experimentwise P, –Permutes the entire genotype relative to the phenotypes

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Power of approaches Sample size –100 to 1000 are typical Heritability of trait –H 2 = 10% - 90% –Depends on ability to measure trait –Interactions with environment Depends on statistical properties of test

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Association Approaches Complement QTL Linkage Mapping Linkage (RILs)Association 10,000,000 bp2000 bpResolution High PowerLittle PowerGenome Scan HighLow Statistical Power per Allele Low (1 or 2)High (10s)Allelic Range

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