Single Marker Analysis and Interval Mapping Jiankang Wang, CIMMYT China and CAAS E-mail: jkwang@cgiar.org; wangjiankang@caas.cn Web: http://www.isbreeding.net 1
Comparison of Estimated Recombination Frequency in Bi- Parental Genetic Populations Sun Z., H. Li*, L. Zhang, J. Wang. 1. Estimation of recombination frequency in biparental genetic populations. Genetics Research 94: 163-177
Populations handled in QTL IciMapping Parent P1 Parent P Legends F1 1. P1BC1F1 7. F. PBC1F1 9. P1BCF1 13. P1BC1F 8. F3 14. PBC1F 1. PBCF1 15. P1BCF 16. PBCF Hybridization Selfing Repeated selfing Doubled haploids 11. P1BCRIL 5. P1BC1RIL 4. F1RIL 6. PBC1RIL 1. PBCRIL BC3F1, BC4F1 etc. P1BCF1 P1BC1F1 F1 PBC1F1 PBCF1 Marker-assisted selection 19. P1BCDH 17. P1BC1DH 3. F1DH 18. PBC1DH. PBCDH CSS lines or Introgression lines P1 CP P CP P3 CP Pn CP CP=common parent RIL family 1 RIL family RIL family 3 RIL family i RIL family n One NAM population
The genetic analysis can be very complicated even with biparental populations! F1-derived populations F, F3, DH, RIL: p=.5, q=.5 at each locus P1BC1-derived population F, F3, DH, RIL: p=.75, q=.5 at each locus PBC1-derived population F, F3, DH, RIL: p=.5, q=.75 at each locus P1BC-derived population F, F3, DH, RIL: p=.875, q=.15 at each locus PBC-derived population F, F3, DH, RIL: p=.15, q=.875 at each locus 4
Twenty biparental populations Allele frequencies can be different Genotypes and their frequencies are much different Are they equal good in estimating the recombination frequency between two linked loci? 5
LOD LOD LOD scores from different populations True r=.5 (Upper), True r=. (lower) 7 6 5 4 3 1 5 15 True r =.5 PopSize=5 PopSize=1 PopSize= F F3 F1DH F1RIL BC1F1 BC1F BC1DH BC1RIL BCF1 BCF BCDH BCRIL True r =. PopSize=5 PopSize=1 PopSize= 1 5 F F3 F1DH F1RIL BC1F1 BC1F BC1DH BC1RIL BCF1 BCF BCDH BCRIL 6
Standard error Deviation Deviations to the true value (upper) and standard errors (lower) of estimated recombination frequency.8.6.4. True r =.3 PopSize=5 PopSize=1 PopSize=.5..15.1 F F3 F1DH F1RIL BC1F1 BC1F BC1DH BC1RIL BCF1 BCF BCDH BCRIL True r =.3 PopSize=5 PopSize=1 PopSize=.5 F F3 F1DH F1RIL BC1F1 BC1F BC1DH BC1RIL BCF1 BCF BCDH BCRIL 7
Observations When two alleles at each locus have equal frequency of.5, we had a better estimation. When a population has more genotypes, we had a better estimation. For F and F3 to be efficient, we need codominant markers. 8
Minimum population size to have at least one recombinant Pop. r=.1 r=. r=.3 r=.5 r=.1 r=. r=.3 F (C, C) 15 75 5 3 15 8 5 F (C, D) 99 149 99 6 31 16 11 F (C, R) 99 149 99 6 31 16 11 F (D, D) 99 149 99 61 31 16 11 F (D, R) 149786 9956 13616 4754 1197 99 13 F (R, R) 99 149 99 61 31 16 11 DH 99 149 99 59 9 14 9 RIL 15 77 5 3 17 9 7 In the first column, C for co-dominant marker; D for dominant marker; R for recessive marker 9
Outlines Quantitative Traits and QTL Mapping Single Marker Analysis The Conventional (Simple) Interval Mapping 1
Quantitative Traits and QTL Mapping 11
Number of women Number of women Number of women Number of women Number of women Quantitative traits in 3 5 15 1 5 3 5 15 1 5 genetics Ear length (cm) of one maize inbred line (P1) 5 6 7 8 9 1 11 1 13 14 15 16 17 18 19 1 Midpoint group value Ear length (cm) of their F1 hybrids 5 6 7 8 9 1 11 1 13 14 15 16 17 18 19 1 Midpoint group value 3 5 15 1 5 16 14 1 1 8 6 4 16 14 1 1 8 6 4 Distribution of height (inches) among 4995 British women 54 56 58 6 6 64 66 68 7 7 74 Midpoint group value Ear length (cm) of aonther maize inbred line (P) 5 6 7 8 9 1 11 1 13 14 15 16 17 18 19 1 Midpoint group value Ear length (cm) of their F hybrids 5 6 7 8 9 1 11 1 13 14 15 16 17 18 19 1 Midpoint group value
Quantitative traits Continuous phenotypic variation Affected by many genes Affected by environment Epistasis Polygene (or multi-factorial ) hypothesis Classical quantitative genetics 13
Quantitative trait does not have to be continuous Categorical traits: traits in which the phenotype corresponds to any one of a number of discrete categories Number of skin ridges forming the fingerprints Number of kernels on an ear of corn Number of puppies in a litter Threshold traits: traits that have only two, or a few, phenotypic classes, but their inheritance is determined by the effects of multiple genes acting together with the environment Liability to express the trait, which is not directly observable. When liability is high enough (above a threshold ), the trait will be expressed; Otherwise, the trait is not expressed. 14
What is QTL Mapping? The procedure to map individual genetic factors with small effects on the quantitative traits, to specific chromosomal segments in the genome The key questions in QTL mapping studies are: How many QTL are there? Where are they located in the marker map? How large an influence does each of them have on the trait of interest? Are they interacting with each other? Are they stably expressed across environments? 15
Dataset of QTL mapping Mapping population Marker data of each individual in the mapping population Linkage map Phenotypic data 16
Example: 1 RIL of Rice (linkage map of Chr. 5 ) Marker C63 R83 R3166 XNpb387 R569 R1553 C18 C14 XNpb81 C46 R953 C1447 Position (cm). 3.5 8.5 19.5 3. 66.6 74.1 78.6 81.8 91.9 9.7 96.8 RIL1.33 RIL 1.99 RIL3.4 RIL4 1.94 RIL5.76 RIL6.3 RIL7.3 RIL8.8 RIL9.4 RIL1.45 17 Grain width (mm)
Classification of mapping populations Bi-parental mapping populations (linkage mapping) Temporary population: F and BC Permanent population: RIL, DH, CSSL Secondary population Association mapping Natural populations: human and animals 18
Overview on QTL mapping methods Single marker analysis (Sax 193; Soller et al. 1976) The single marker analysis identifies QTLs based on the difference between the mean phenotypes for different marker groups, but cannot separate the estimates of recombination fraction and QTL effect. Interval mapping (IM) (Lander and Botstein 1989) IM is based on maximum likelihood parameter estimation and provides a likelihood ratio test for QTL position and effect. The major disadvantage of IM is that the estimates of locations and effects of QTLs may be biased when QTLs are linked. Regression interval mapping (RIM) (Haley and Knott 199; Martinez and Curnow 199 ) RIM was proposed to approximate maximum likelihood interval mapping to save computation time at one or multiple genomic positions. Composite interval mapping (CIM) (Zeng 1994) CIM combines IM with multiple marker regression analysis, which controls the effects of QTLs on other intervals or chromosomes onto the QTL that is being tested, and thus increases the precision of QTL detection. 19
Overview on QTL mapping methods Multiple interval mapping (MIM) (Kao et al. 1999) MIM is a state-of-the-art gene mapping procedure. But implementation of the multiple-qtl model is difficult, since the number of QTL defines the dimension of the model which is also an unknown parameter of interest. Bayesian model (Sillanpää and Corander ) In any Bayesian model, a prior distribution has to be considered. Based on the prior, Bayesian statistics derives the posterior, and then conduct inference based on the posterior distribution. However, Bayesian models have not been widely used in practice, partially due to the complexity of computation and the lack of user-friendly software. Inclusive Composite Interval Mapping (Li et al. 6) In the first step, stepwise regression was applied to identify the most significant regression variables in both cases but with different probability levels of entering and removing variables. In the second step, a onedimensional scanning or interval mapping was conducted for mapping additive and a two-dimensional scanning was conducted for mapping digenic epistasis.
Single Marker Analysis 1
Evidence for marker and QTL association Three marker types MM, Mm, and mm at one marker locus When marker is linked with QTL, the three marker types will have un-equal means. Marker type mm Marker type Mm Marker type MM Marker type mm Marker type Mm Marker type MM
P1BC1F1 Backcrosses (P1BC1 and PBC1) of P1: MMQQ and P: mmqq Genotype Frequency Genotypic value PBC1F1 Genotype Frequency Genotypic value MMQQ (1-r)/ m+a MmQq (1-r)/ m+d MMQq r/ m+d Mmqq r/ m-a MmQQ r/ m+a mmqq r/ m+d MmQq (1-r)/ m+d mmqq (1-r)/ m-a 3
Difference between the two marker types (P1BC1 as example) Two marker types: MM 1 ) ( r r MMQQ MMQq (1 r)( m a) r( m d) m (1 r) a rd Mm rmmqq 1 r) ( MmQq r( m a) (1 r)( m d) m ra (1 r) d Difference in phenotype between the two types MM Mm (1 r)( a d) 4
Frequency Frequency A barley DH population Marker locus Act8A Marker locus Act8B.5 Type.5 Type.4 Type.4 Type.3.3...1.1. 36 38 4 4 44 46 48 5 Kernel weight. 36 38 4 4 44 46 48 5 Kernel weight 5
Significance test on phenotypic means of marker types Parameter Marker Act8A Marker Act8B Type Type Type Type Sample size 7 74 58 69 Degree of freedom 69 73 57 68 Mean 4.3 4.79 43.89 41.5 Variance 4.45 5.3 3.53.79 Standard error.11.31 1.88 1.67 Combined variance 4.9 3.13 T-test 1.51 (P=.134) 8.37 (P=1.E-13) 6
Frequency Frequency A soybean F population Marker locus *Satt339 Marker locus *Sat_33.7.6 Type Type 1.6.5 Type Type 1.5.4.3. Type.4.3. Type.1.1 1 3 4 5 1 3 4 5 Chlorophy II content Chlorophy II content
Significance test on phenotypic means of marker types Parameter Marker Act8A Marker Act8B Type Type 1 Type Type Type 1 Type Sample size 65 111 39 56 9 6 Mean 35.16 3.76 14. 3.7 3.47 9. Variance 47.71 4.4 65.5 9.13 97.4 133.8 Standard error 6.91 6.65 8.9 9.6 9.86 11.54 T-test of additive 15.6 (P=1.43E-33).8 (P=.464) T-test of dominance 8.47 (P=5.89E-13).35 (P=.77)
Problems with the Single Marker Analysis Cannot separate QTL effect and the marker-qtl distance Low detection power Does not take the advantage of genetic linkage map 9
Conventional Interval Mapping 3
Interval mapping (IM) (Lander and Botstein 1989; Milestone in QTL mapping methodology and applications ) Linear model (j=1,,,n ) y i b b b * represent QTL effect, x * j e variable ( or 1) for QTL genotype Likelihood profile * * x j Support interval: One-LOD interval j is the indicator 31
QTL genotypes under each marker type in P1BC1 (need to consider three loci simultaneously; double crossover not considered in this slide) P1: Mi Q Mi +1 P: mi q mi +1 Mi Q Mi +1 mi q mi +1 F1: Mi Q Mi +1 P1: Mi Q Mi +1 mi q mi +1 Mi Q Mi +1 Mi Q Mi +1 Mi Q Mi +1 Mi Q Mi +1 Mi Q Mi +1 Mi Q Mi +1 Mi Q mi +1 mi q M mi q Mi +1 Mi Q Mi +1 Mi Q Mi +1 mi q mi +1 Mi q mi +1 mi Q Mi +1 Marker class I Marker class II Marker class III Marker class IV 区间标记类型 1 区间标记类型 区间标记类型 3 区间标记类型 43
Marker types and QTL types in DH populations (double crossover is considered in this slide) 1 ( r R 1 rl )(1 ) 1 ( 1 rl 1 rr ) ( 1 rl ) rr 1 rl rr No crossover One crossover between left marker and QTL 1 r )(1 r ) 1 r ) ( L R L( R One crossover between QTL and right marker r ( 1 r ) r L R Two crossovers between the two markers r L r R
QTL types under each marker class ( 1 rl )(1 R ) 1 r 1 ( 1 rl ) rr 1 ( rl 1 r R ) 1 rl rr 1 rl rr 1 r 1 r L ( R ) 1 1 rl ) 1 ( r 1 r )(1 r ) R ( L R Marker class I Marker class II Marker class III Marker class IV
Probablity density Probablity density Probablity density Probablity density Two QTL genotypes in 4 marker classes in DH population Proportion of QTL genotypes depends on QTL position and the marker interval.4.3 AABB QQ qq.4.3 AAbb QQ qq...1.1 1 3 4 5 6 7 8 1 3 4 5 6 7 8 Quantitative trait Quantitative trait.4.3 aabb QQ qq.4.3 aabb QQ qq...1.1 1 3 4 5 6 7 8 Quantitative trait 1 3 4 5 6 7 8 Quantitative trait 35
Probability density Probability density Probability density Probability density Probability density Probability density Probability density Probability density Probability density Three QTL genotypes in 9 marker classes in F population Proportion of QTL genotypes depends on QTL position and the marker interval.4.3 AABB QQ Qq qq.4.3 AABb QQ Qq qq.4.3 AAbb QQ Qq qq....1.1.1 1 3 4 5 6 7 8 Quantitative trait 1 3 4 5 6 7 8 Quantitative trait 1 3 4 5 6 7 8 Quantitative trait.4.3 AaBB QQ Qq qq.4.3 AaBb QQ Qq qq.4.3 Aabb QQ Qq qq....1.1.1.4.3 1 3 4 5 6 7 8 aabb QQ Qq qq Quantitative trait.4.3 1 3 4 5 6 7 8 aabb QQ Qq qq Quantitative trait.4.3 1 3 4 5 6 7 8 aabb QQ Qq qq Quantitative trait....1.1.1 1 3 4 5 6 7 8 Quantitative trait 1 3 4 5 6 7 8 Quantitative trait 1 3 4 5 6 7 8 Quantitative trait 36
Frequency of QTL genotypes in each marker class in DH population ( 1 rl )(1 R ) 1 r 1 ( 1 rl ) rr 1 ( rl 1 r R ) 1 rl rr 1 rl rr 1 r 1 r L ( R ) Marker interval Sample Frequency QTL genotype Left Right size QQ qq AA BB n 1 ½ (1-r) ½ (1-r L -r R +r L r R ) ½r L r R AA bb n ½r ½ (1-r L )r R ½r L (1-r R ) aa BB n 3 ½r ½r L (1-r R ) ½ (1-r L )r R aa bb n 4 ½ (1-r) ½r L r R ½ (1-r L -r R +r L r R ) r r r r r 37 L R L 1 1 rl ) R R 1 ( r 1 r )(1 r ) ( L R
MLEs of means of QTL genotypes 38 k q k ik Y ij N, 1, ), ( ~ q k k ij ik n j m i q y f L i, 1,, 1, ;, 1, 1 ), ( ln ),,, ( ln y Y
EM algorithm for calculating MLE The Expectation step, given initial values w ijk ik f ( ik' k ' 1,, q y ij f ( y ij () k, () k ', () ) () ) w ijk measures the probability of QTL genotypes of each DH line given the marker class 39
EM algorithm for calculating MLE The Maximization step, given QTL genotypes are known from w ijk in E-step ln L( () () 1,, q, X x) wijk ln f ( yij k, ) i1,, m; k 1,, q j1,, n i (1) k w ijk i1,, m; j1,, n i w ijk i1,, m; j1,, n i y ij (1) w ijk i1,, m; j1,, n i ( y ij w ijk i1,, m; j1,, n i (1) k ) 4
Test the existence of QTL H H A : 1 : 1,, q are not equal q Likelihood under H : L(, Y y) f ( y ij, ) i1,, m; j1,, n i Likelihood ratio test: LRT ln max max L( H ) ~ ( df q 1) L( H ) A Likelihood of odd (LOD): LOD log 1 max max L( H L( H A ) ) 41
Estimation of genetic effects DH populations: 1 for QQ, for qq 1 a a 1 ( ˆ ˆ 1 ) a ( ˆ ˆ ) ˆ 1 ˆ 1 F populations, 1 for QQ, for Qq, 3 for qq 1 a d 3 a 1 ( ˆ ˆ ) 1 a ( ) ˆ 1 3 ˆ ˆ1 ˆ3 dˆ ( ˆ ˆ 1 1 3 )
Contribution of a QTL No distortion PVE V V G P 1% V G(DH) â V G(F) 1 aˆ 1 4 dˆ With distortion V G(DH) 4 fqq fqqa V G(F) fqq fqq ( fqq fqq) ] a fqq ( fqq fqq) ad ( fqq fqq ) [ d
PVE (%) Additive effect LOD score Interval mapping in a barley DH population 14 1 1 8 6 4 1.5 -.5-1 -1.5 4 3 1 11111111333333334444444455555555555566666666777777777 One dimensional scanning on the seven barley chromosomes, step=1cm 11111111333333334444444455555555555566666666777777777 One dimensional scanning on the seven barley chromosomes, step=1cm 11111111333333334444444455555555555566666666777777777 One dimensional scanning on the seven barley chromosomes, step=1cm
QTL identified in the barley DH population Chromo. Position (cm) Left marker Right marker LOD PVE (%) Additive 5 3 ABA36B Act88 13.15 34.55-1.31 7 drpg1 ipgd1a.55 7.79 -.6 7 98 VAtp57A MWG571D 5.36 15.77 -.89
LOD Genetic effect Interval mapping in a soybean F population 4 3 15 1 5 Additive Dominance 1-5 -1 4 6 8 1 1 14 16 4 6 8 1 1 14 16 Scanning on one chromosome -15 Scanning on one chromosome
QTL identified in the soybean F population Position (cm) Left marker Right marker LOD PVE (%) Additive Dominance 39 *Satt85 *Sat_39 7.89 73. -1.96 9.48 78 *Sat_39 *Satt55 36. 68.49-11.9 9.39 91 *Satt55 *Satt339 38.3 58.1-1.66 8.9 131 *Satt51 *Sat_33 18.4 69.56-11.7 9.68
4 6 8 1 4 6 8 1 4 6 8 1 4 6 8 1 4 6 8 1 4 6 8 1 LOD Problems with Simple Interval Mapping Multiple peaks when QTLs are unlinked 1 8 6 4 Scanning on 6 chromosomes, each of 1cM. Step = 1cM 48
4 6 8 1 4 6 8 1 4 6 8 1 4 6 8 1 4 6 8 1 4 6 8 1 LOD Problems with Simple Interval Mapping Ghost QTL when two QTLs are linked 15 Ghost QTL 1 5 Scanning on 6 chromosomes, each of 1cM. Step = 1cM 49
4 6 8 1 4 6 8 1 4 6 8 1 4 6 8 1 4 6 8 1 4 6 8 1 Additive effect Problems with Simple Interval Mapping Biased estimation of QTL effects 1.5 1.5 -.5 Scanning on 6 chromosomes, each of 1cM. Step = 1cM 5
实习 5 QTL IciMapping 软件 (I) ( 上周 ) 连锁图谱构建功能 (MAP) Grouping: 分群 设定 Anchor 信息 Ordering: 标记排序 Rippling: 图谱调整 连锁图绘制 输入和输出 多个图谱的整合功能 (CMP) 两个位点间重组率的估计工具 (pointrec) 方差分析工具 (ANOVA)
实习 5 QTL IciMapping 软件 (II) 双亲群体 QTL 作图 (BIP 功能 ) 选择作图方法 设定作图参数 结果分析 QTL 作图功效分析 (BIP 功能 ) 设定遗传模型 功效分析