1. New Methods for Analyzing Complex Traits
Jun Zhu
Institute of Bioinformatics
Department of Agronomy
Zhejiang University

2. Phenotype Property of Complex Trait
y =  + E + G + GE + e
Genome
Genetic Effects
QTL Position & Effects G
Genetic Effect: A、D、I
GE: AE、DE、IE GE
Macro Env., Micro Env. E
Phenotype

3. Most Important Traits are Complex Trait
Complex traits:
Phenotypes controlled by multiple genes
Epistasis (gene-gene interaction)
Gene-environment interaction
Genetic heterogeneity
Low heritability
Limited statistical power

4. Genetic Definition of Gene Effects
y =  + E + G + GE + e
F1(i×j) Pi Pj Bi Bi Bj Bj Bi Bj  Ci Ci Cj Cj Cj Ci

5. P1 × P2 ? F1
Haploid DH
P1×F1
P2×F1
BC1
BC2   F2
连续自交 
IF2
RIL

6. Can Detect Position & Effect of QTL Between Markers Mi- & Mi+
Interval Mapping (Lander & Botstein,1989)
Genetic Model:
Advantages:
Can Detect Position & Effect of
QTL Between Markers Mi- & Mi+
Disadvantages：
Can Be Affected by Other QTLs

7. IM Method for Mapping QTL
Matrix form for QTL Mapping Model
Test H0: No QTLs vs H1: Having QTLs
by The Likelihood Ratio Statistic, LR
Test H0: No QTLs by The LOD Statistic
For df = 1, LR = × LOD, or LOD = × LR
Estimation of QTL Effects

8. Eliminate Inference of Other QTLs
Composite Interval Mapping (Zeng, 1994)
Genetic Model:
Mi– Qi
Mi+
Advantages:
Eliminate Inference of Other QTLs
Disadvantages：
QTL Effect Is Determined Also by Other Marker
Effects in the Model

9. CIM Method for Mapping QTL：
Matrix Form for QTL Mapping Model
Test H0: No QTLs by The Likelihood Ratio Statistic, LR
Estimation of QTL Effects (A+D)
Relationship Between Two Estimates

10. IM
CIM

11. Mixed-model Based Composite Interval Mapping （MCIM）（Zhu, 1998）
y =  + GQ + GM + 
CIM方法
y =  + GQ + GM + 

12. IM
CIM
MCIM

13. Genetic Model Construction
Mixed-model Based CIM for QTL Mapping (Wang et al. 1999, TAG, 99: )
Mapping QTL with A+AA and QE Interaction (DH, RIL) Ai
AAij Aj

14. MCIM Method (Zhu, 1998,1999) Test H0: No QTLs vs H1: Having QTLs
by The Likelihood Ratio Statistic, LR

15. Estimation of QTL Main Effects
Test of QTL Main Effects
df = n – rank(X)

16. Test of QE Interaction Effects
Prediction of QTL by Environment Interaction Effects
Test of QE Interaction Effects

17. Disadvantages for IM & CIM Methods:
⑴ All regression effects are fixed
⑵ Cannot including random effects E & QE
⑶ Cannot handling complex effects by
regression model
Advantages for MCIM Methods:
⑴ Mixed linear model having both fixed and
random effects
⑵ Fixed Q effects and random QE effects
estimated/predicted with no biase
⑶ Can handling complex effects

18. New Approache of Mapping QTL
Full Model:

19. Estimations of effects in mixed linear model can be given by Henderson’s Method

20. One-dimensional (1D) Search for QTLs with Single-locus Effects
Henderson Method III (Searle, 1971)
Partial Two-dimensional Search for QTLs with Episrasis Effects MCMC Method can be applied for making inference via Gibbs sampling.

21. QTLNetwork version 2.0

22. QTLNetwork 2.0

24. QTL位置和效应分析结果

25. Estimate [Parameter]

26. 无偏估算A,D,AA,AD,DA,DD
及AE,DE,AAE,ADE,DAE,DDE
IF2 群体

27. Summarized statistics of simulation study with 200 replicates for SLE QTL

28. Summarized statistics of simulation study with 200 replicates for epistasis

29. Mapping QTLs for Yield in Barley
Map & Data Files

30. QTL Detection by Two Methods
Mean of Yield =

31. Heritability Estimated by Two Methods

32. Predicting Total Genotype Value and Potential Breeding Merit
Mean of Yield =

33. Analyzing Q & QE Effects From Time 0t
Mapping Developmental QTL for Quantitative Traits
Time: 0 1 2  … t -1 t  t +1  …  f
Unconditional Model for Phenotypic Value at Time t
y(t) = (t) + GQ(t) + E(t) + GQE(t)
+ GM(t) + GME(t)+ (t)
Analyzing Q & QE Effects From Time 0t
Conditional Model for Phenotypic Value at Time t
y(t|t-1) = (t|t-1) + GQ(t|t-1) + E(t|t-1)
+ GQE(t|t-1) + GM(t|t-1) + GME(t|t-1)+ (t|t-1)
Analyzing Net Q & QE Effects From Time t -1  t

34. Table 2. Chromosomal regions and estimated genetic effects of QTLs for plant height (cm) at different stages in two environments.

35. Mapping QTL for Cause & Result Traits
Cause C  Result R
Unconditional Model for Phenotypic Value of Result Trait
y(R) = (R) + GQ(R) + E(R)
+ GQE(R) + GM(R) + GME(R)+ (R )
Conditional Model for Phenotypic Value of Result Trait Given Cause Trait
y(R|C) = (R|C) + GQ(R|C) + E(R|C)
+ GQE(R|C) + GM(R|C) + GME(R|C)+ (R|C )
Analyzing Net Q & QE Effects on Result Trait
When Influence of Cause Trait Is Excluded

36. Zhao et al, 2006, TAG, 113:33-38
8QTL
4+2+2
7QTL
2+0+5

37. Acknowledgments