1. QTL Analysis: Concept  Parents F1 F2 F2:3 × A B Generation Procedure
Alternatives: BC1, RIL, DHL
Field
PHT[cm]
210
190
203
159
206 .
171
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
QTL mapping is a multi step procedure that involves field and lab work as well as an elaborate statistical analysis.
In general, two homozygous lines that differ significantly for the trait under study are crossed. The F1 hybrid is selfed to produce a segregating F2 populations.
F2 individuals will be genotyped using molecular markers.
F2 will be selfed to produce F2:3 lines.  enough seed for repeated field trials.
QTL mapping idea (Lynch and Walsh)
By crossing two lines, linkage disequilibrium is created between loci that differ between the parental lines. This is creating associations between marker loci and linked segregating QTL.
Experimental designs
F2:3  in contrast to all other populations here three marker classes can be observed, therefore, dominance can be evaluated.
AIL  advanced intercross lines, Random mated populations, higher resolution, but decreased power of QTL detection.
RIL  homozygous genetic background, field trials can be repeated in multiple locations and years.
DHL BC
Marker information and phenotypic data is combined and statistical tools are used to map and characterize QTL.

2. QTL Analysis: Single Marker Analysis
240
Total
196
umc157 AA Aa aa
195
197
F = 0.48 ns
umc130 AA Aa aa
201
196
191
F = 6.47**
220
Plant height (cm)
200
180
160
A basic method to identify markers linked to QTL is the single marker analysis.
XMC (cm)

3. QTL Analysis: Single Marker Model (F2)
QQ Qq qq
MM (1-r) r(1-r) r μ(MM)
Mm r(1-r) (1-r)2+r2 r(1-r) μ(Mm)
mm r r(1-r) (1-r)2 μ(mm)
μ μ μ3 r M m Q q
Additive effect:
Dominance effect:
Expected QTL genotypic frequencies conditional on marker genotype.
The QTL mean for each marker genotype is equl to the frequency of each QTL type time the value of each QTL type, given the marker genotype.
Example:
uMM = u1 [(1-r)2] + u2 [2r(1-r)] +u3 [r2]
We have three equations but four parameters (u1 – u4, r). QTL effects and position of the QTL are confounded. We can only solve for the QTL effects if r is fixed.
F tests on the contrasts of marker classes test the following hypothesis:
a > 0 d > 0 r < 0.5
Schön, 2002

4. QTL Analysis: Single Marker Model (F2)
Example: Plant height, umc130
X(MM) = 201cm X(Mm) = 196cm X(mm) = 191cm
Case 1
Case 2
r = 0 M m Q q
r = 0.2 M m Q q
In single marker analysis, the only information we have are the means of each marker class. And based on this information it is possible to determine whether a marker is linked with a QTL. However, it is not possible to determine the effect of a QTL, because effect and QTL position are confounded.
PHT (cm) r = 0 r = r = 0.4
Add. Effect
X(QQ) X(Qq) X(qq)

5. 4. Association Analysis
Concepts

6. Dissecting A Quantitative Trait: Time Versus Resolution5
NILs
RI QTL
Mapping
Positional
Cloning
Research Time in Years
F2 QTL
Mapping
Associations 1 1
1x104
1x107
Resolution in bp

7. Resolution Versus Allelic Range
>40
Associations In
Diverse Germplasm
Pedigree
Alleles Evaluated
Associations In
Narrow Germplasm
F2 or RIL
Mapping
Positional
Cloning
NIL 1 1
1x104
1x107
Resolution in bp

8. Evaluate whether nucleotide polymorphisms associate with phenotype
Natural populations
Exploit extensive recombination
Association Tests T A G C
1.3m
1.5m
1.4m
1.8m
2.0m
Spend a lot of time on this slide

9. Association mapping Mainstay of human genetics Cystic fibrosis
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,

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

11. Complete Linkage Disequilibrium1 2
D’=1
r2=1 6
Locus 1
Locus 2
Same mutational history and no recombination.
No resolution
Adapted from Rafalski (2002) Curr
Opin Plant Biol 5:

12. Linkage Disequilibrium1 2
D’=1
r2=0.33 3 6
Locus 1
Locus 2
Different mutational history and no recombination.
Some resolution

13. Linkage Equilibrium D’=0 r2=0 1 2 3 Locus 1 Locus 2
Same mutational history with recombination.
Resolution

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

15. 5. QTL mapping analysis

16. QTL Analysis: Interval Mapping
Simple Interval Mapping
Composite 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)
This problem is solved by using interval mapping approaches.
PlabQTL

17. QTL Analysis: Power of QTL detection10 20 30 40 50 60 70 80 90
100
Heritability
0.4
0.5
0.6
0.7
0.8
0.9
1.0
N = 600
N = 300
N = 100
Power: Probability of finding a QTL
Heritability:
Simulation Model
Additive genetic model
F2 or F3 lines
Maize genetic model, marker interval 20cM
16500 F2 F3 individuals that were partitioned into the different population
Utz, H.F., and A.E. Melchinger Comparison of different approaches to interval mapping of quantitative trait loci. pp ed. J.W. van Ooijen, and J. Jansen. Biometrics in Plant Breeding Applications of Molecular Markers. Proceedings of the Ninth Meeting of the EUCARPIA section Biometrics in Plant Breeding. Wageningen. CPRO-DLO, Wageningen, the Netherlands.ns.
Utz and Melchinger, 1994

18. 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

19. 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.

20. 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.

21. 6. Candidate Genes

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

23. Association Analysis
Identification of More Favorable Alleles
Enhanced Marker Assisted Breeding

24. 7. Linkage Disequilibrium
Analysis

25. Properties of LD The basic measure of LD is: DAB = PAB - pA pB A a
( DAB = -DAb = -DaB = Dab ) A a
PAB =
pApB + DAB
PAb =
pApb - DAB
PaB =
papB - DAB
Pab =
papb + DAB B b pA pa pB pb 1 25

26. Linkage Disequilibrium versus Generations Since its Creation
100
200
300
400
500
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1
c = 0.1
c = 0.02
c = 0.01
c = 0.005
c = 0.001
Disequilibrium,rAB
Generation, g
rAB  (1-c)g
Recomb. Rate (c)

27. Other Measures of LD E(r2)= 1 / (1 – 4Nc)
Can divide DAB by the maximum value it can obtain:
D’AB = DAB / [max(-pApB, -papb)] if DAB < 0
DAB / [min (pApb, papB)] if DAB > 0
The sampling properties of D’AB are not well understood.
r2AB =
D2AB
pA pB pa pb
E(r2)= 1 / (1 – 4Nc)

28. LD generally decays rapidly with distance
Remington, D. L., et al PNAS-USA 98: & unpublished r2

29. Population Effect on Linkage Disequilibrium in Maize
Investigator
Population Studied
Extent of LD
Gaut
Landraces
<1000 bp
Buckler
Diverse Inbreds
2000 bp
Rafalski
Elite Lines
100 kb?
(6 kb euchromatin?)
Reviewed in Flint-Garcia, S. A. et al Annual Review of Plant Biology 54:

30. 8. Association Analysis

31. Allele Case-Control Test
marker
allele 1
allele 2
Affected
n1|aff
n2|aff
2 naff
Unaffected
n1|unaff
n2|unaff
2 nunaff n1 n2
2 N individuals
if naff = nunaff
(ni|aff - ni|unaff)2
~ c2(k-1)
X2 = Si
ni|aff + ni|unaff
(k alleles)

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

33. Use SSR Markers to Estimate Population Structure
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:
8 Stiff Stalk
38 Non-Stiff Stalk
30 Sub-Tropical

34. 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:

35. Population Structure Estimates Greatly Reduce Estimated Type I Error Rates
Fields
Flowering Time
Height

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

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

38. su1 Coding Region Two distinct alleles
Sweet phenotype associated with W578R

39. Su1 5 7 8 : W R
Based on survey of 12kbp from lines.

40. Dwarf8 functional variation
2 Amino Acid
Deletion
MITE
Indel
SH2 Domain
Days to Silking relative to B73
When controlling for population structure, associates with flowering time & plant height across 12 environments.
Thornsberry et al. 2001
Nat. Genet.

41. 9. Type I and Type II Error

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

43. 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

44. Power of approaches Sample size Heritability of trait
100 to 1000 are typical
Heritability of trait
H2 = 10% - 90%
Depends on ability to measure trait
Interactions with environment
Depends on statistical properties of test

45. Association Approaches Complement QTL Linkage Mapping
Linkage (RILs)
Association
10,000,000 bp
2000 bp
Resolution
High Power
Little Power
Genome Scan
Low (1 or 2)
High (10s)
Allelic Range
High
Low
Statistical Power per Allele