The use of complex populations in breeding with markers
SBC “Breeding with molecular markers”
David Francis
Contact: [email protected]
breeding programs tend to have complex population structures consisting of many independent crosses
Genetic studies tend to focus on bi-parental crosses with defined structure.
Jargon:QTL
LD
SNP Structure
Mixed Model Analysis of
Variance
Iden
tity
by d
esce
nt
Please stop me and ask when a definition will help clarify
Objectives
Understand the diversity of populations that are being used to test marker-trait associations (linkage).
Understand the difference between the discovery of linkage and use of markers for selection.
Use this information to facilitate interaction with colleagues from other disciplines (field, marker support, analysis, etc…).
Use information to design and implement discovery and selection projects.
Background
Introduction to Populations
Case study
Discovery Populations
Selection Populations
Association Mapping
Single Marker analysis of variance
Changes to the model used for analysis:
Account for population structure
Haplotypes to gain information
Standard populations for inbred species (line crosses)
F2
RIL (recombinant inbred lines)BC (back cross)AB (Advanced Back Cross) *IBC (Inbred Back cross) *
Emerging populations for association mapping
Natural populationsUnstructured populationsFamily-based *Nested Association Mapping (NAM; a variation of RIL)
Standard populations for inbred species (line crosses)
F2 Few meiosis, population not fixedRIL Few meiosis, population fixed (can replicate)BC Few meiosis, population not fixedAB Few meiosis, population not fixedIBC Few meiosis, population fixed
Emerging populations for association mapping
Nat. pop. Samples all meiosis in history of species, pop. often fixed.
Unst. pop. Samples all meiosis since pop. establishedFamily-based Samples all meiosis in pedigreeNAM See RIL. Meiosis increased due to size of pop/
and multiple crosses.
Populations• Early generation (F2, BC1)
– Strong theoretical basis– Balanced designs– Tools for interval mapping (point of analysis)– Most breeding programs do not collect extensive data on early
generation populations– Retain too much “donor” Parent
• AB and IBC populations– Reduce donor parent, isolate genetic factors, allow detection– Unbalanced design may limit power
• Unstructured (natural populations)– More like populations that breeders use
Frequency of heterozygotes (Cc) and homozygotes (CC+cc) in each generation of selfing a hybrid (F1).
00.10.20.30.40.50.60.70.80.9
1
F1 F2 F3 F4 F5 F6 F¥
Generation
Fre
qu
ency
Cc
CC+cc
Freq CC = p2 + pqF Freq Cc = 2pq (1-F)
Freq cc = q2 + pqF
Review: affect of inbreeding
Advanced Backcross and Inbred Backcross Populations
Parent 1 x Parent 2 (Donor)
F1 x ‘Parent 1
BC1 (n lines)
BC1-1 x Parent 1 BC2-1S0 ⊗ . . . BC2-1S5
BC1-2 x Parent 1 BC2-2S0 ⊗ . . . BC2-2S5
.
.BC1-n x Parent 1 BC2-nS0 ⊗ . . . BC2-nS5
AB IBC
Statistical considerations with AB, IBC, and association populations
0
2
4
6
8
10
0
Genotypic classT
rait
va
lue
Unequal sample size/unbalanced dataDonor class is under representedNeed to adjust Df for F-testproper F-test {Mj/Gk(Mj)}These considerations affect power and whether significance level is accurately estimated
Take home messages:
A) Genotyping throughput and reagent packaging favors working with very large populations (~480)
B) Measuring traits (Phenotyping) is the limiting factor
C) For elite polpulations, marker number and the ability to distinguish descent (IBD) from state (IBS) are limitations (this is a function of linkage phase and LD)
D) Incorporating pedigree data or population structure data into analysis improves detection of trait associations (QTL) and the efficiency of MAS (defined as relative efficiency of selection).
E) We can detect some known QTL, but not all known QTL in complex populations. Power goes up with population size and marker number.
F) Phenotypic selection is effective.
Case study: mapping and selection of bacterial spot resistance in tomato
populations.
David Francis, Sung-Chur Sim, Hui Wang, Matt Robbins, Wencai Yang.
Bacterial Spot is a disease complex caused by ~4 species of Xanthomonas bacteria. There are physiological races.
Sources of resistance are mostly close relatives of cultivated tomato Solanum lycopersicum or Solanum pimpinellifolium.
Hawaii 7998 (T1)
Hawaii 7981 (T3)
PI128216 (T3)
PI 114490 (T1, T2, T3, T4)
Field rating based on Horsfall-Barratt scale quantitative scale (1-12)en.wikipedia/org/wiki/Horsfall-Barratt_scale
Distribution approaches normal (ANOVA, regression, mixed models)
GH rating based on HRScored 0 or 1 (non-parametric)
Bacterial spot QTL discovery in IBC Populations Ohio, T2 & T1
(2000-2004)
FL, T3 and T4(2002-2004)
Brasil
T3 2002-2004
SSR111
LEGTOM5c
CosOH51
SSR601
SSR320
TOM59
TOM196
TOM144
SSR637a
SSR637b
SSR637c
SSR637d
SSR637e
CosOH57
I2B
GEN 3 3 3 3 3 3 11 11 11 11 11 11 11 11 11
PI114490 1.5 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1Fla7600 6 2 2 2 2 2 1 1 2 0 1 0 1 0 2 2OH9242 7 3 2 2 2 2 2 2 3 1 0 0 0 1 2 1
6142 3 3 1 2 2 2 2 1 2 0 1 0 1 0 1 16148 4 3 1 1 1 2 2 12 23 1 1 0 1 1 2 -6149 4.5 13 2 1 2 2 12 1 2 0 1 0 1 0 2 26027 5 1 1 2 2 2 2 1 2 0 1 0 1 0 2 26053 5 1 1 1 2 2 2 12 23 1 0 0 0 1 2 16082 5 3 2 2 2 2 2 1 2 0 1 0 1 0 2 26110 5 3 2 2 2 2 2 1 1 0 0 1 0 0 2 1
OH5949 5 1 2 1 2 2 1 1 2 0 1 0 1 0 2 2OH5882 5 3 2 2 2 2 2 1 2 0 1 0 1 0 2 2OH6027 5 1 1 1 2 2 2 1 2 0 1 0 1 0 2 2
6021 5.5 3 2 1 2 2 2 1 2 0 1 0 1 0 2 1
6076 8 3 2 2 2 2 2 2 3 1 0 0 0 1 2 16088 8 3 2 2 2 2 2 2 3 1 0 0 0 1 2 16118 8 3 2 2 2 2 2 2 3 1 0 0 0 1 2 16120 8 2 2 2 2 2 1 2 3 1 0 0 0 1 2 16125 8 3 2 2 2 2 2 2 3 1 0 0 0 1 2 16127 8 3 2 2 2 2 2 2 3 1 0 0 0 1 2 16133 8 3 2 2 2 2 2 2 3 1 0 0 0 1 12 16135 8 3 2 2 2 2 2 2 3 1 0 0 0 1 2 16158 8 3 2 - 2 2 2 2 3 1 0 0 0 1 2 16161 8 3 2 2 2 2 2 2 3 1 0 0 0 1 2 1
Results of discovery studies:
Three IBC populations [[OH88119 x Ha7998]x(OH88119)] x(OH88119)[[OH88119 x PI128216]x(OH88119)] x(OH88119)[FL7600 x PI114490]x(OH9242)]x(OH9242)
Multiple F2 populationsIBC x elite parentOH7870 x Ha7981
Results:
Hawaii 7998 (T1) Rx-1, Rx-2, Rx-3, Chr11 QTL
Hawaii 7981 (T3) R-Xv3
PI128216 (T3) Rx-4, Chr11
PI 114490 (T1, T2, T3, T4) QTL Chr 11, Chr3, Chr4
X X
We have IBC lines and IBC x elite derived lines that “look good” and we want to integrate them with the elite breeding program. Strategy:
1) Develop populations to combine loci for resistance to multiple races
2) Validate Marker-QTL associations in order to assess feasibility of MAS
3) Conduct simultaneousphenotypic and MAS.
OH75 FL82 K64 OH86 OH74 MR13
Genes
Parents
OH75 FL82 K64 OH74 MR13OH75 F1-1 F1-2 F1-3 F1-4FL82 F1-5 F1-6 K64 F1-7 F1-8OH74 F1-9
Rx-3 (5) Rx-4(11) QTL11 QTL11 ? ?
F1-1 F1-2 F1-3 F1-4 F1-5 F1-6 F1-7F1-1 X X XF1-2 X X X X F1-3 X X X X
“Population” consisting of 11 independent crosses, progeny segregate
First segregating generation: grow ~100 plants in the field (total populations size 1,100) and select plants from each extreme (n = 110)
0
2
4
6
8
10
12
Following year: Evaluate plots
RCB, two replicates, rating based on a plot (not single plant), scale 1-12.
Phenotypic evaluation (Focus on T1). Selection conducted in 2007 was predictive of plot performance in 2008 based on both nonparametric analysis and analysis of variance (p < 0.0001).
Heritability estimated from the parent-offspring regression suggests a narrow sense heritability of 0.32.
Plants rated as resistant in 2007 produced plots with an average disease rating of 4.02 in 2008; plants rated as susceptible produced plots with an average disease rating of 5.16 in 2008 (LSD 0.39).
Realized gain under selection ~13% decrease in disease
OH75 rated 3.5; OH88119 rated 9.0
Y = μ REPy + Qw + Markerα + Zv + Error
Sequence variation linked to traits
Marker analysis using The Unified Mixed Model
Buckler Lab, TASSEL
%macro Mol(mark);proc mixed data = three;class &mark gen rep;model T1 = &mark / solution;random gen rep;%mend;
%Mol(TOM144); %Mol(CT10737I); %Mol(CT20244I); %Mol(pto); %Mol(SL10526);
%Mol(rx3);
Markerα
0.00
1.002.00
3.00
4.00
5.006.00
7.00
8.00
30 40 50 60 70 80 90
single-point analysis
Rx-3
Y = μ REPy + Qw + Markerα + Zv + Error
Adding matrix of population structure can correct for background effects and can add insight to which crosses, pedigrees, subpopulations have highest breeding value
0.80 0.90 1.000.40 0.50 0.60 0.700.00 0.10 0.20 0.30
r 2 value
Ch
rom
som
e
P v
alu
e
>0.05
<0.05
<0.01
<0.001
<0.0001
Combined
12
1
10
11
41
2
3
4
5
6
7
8
9
2 3 11 127 8 9 105 6
Qw
Pedigree information
Proportion of genome from a parent (pedigree)
Designation of cross (0/1)
Q – Matrix from Structuregen subpop1 subpop2 subpop3 subpop4 subpop5 subpop66111R1 0.129 0.128 0.016 0.696 0.016 0.0156111R2 0.671 0.088 0.016 0.184 0.015 0.0266111R3 0.934 0.013 0.011 0.015 0.007 0.0196111S1 0.88 0.051 0.009 0.019 0.009 0.0326111S2 0.456 0.213 0.048 0.22 0.014 0.0496115S3 0.077 0.018 0.53 0.027 0.008 0.3416115S4 0.018 0.016 0.908 0.024 0.008 0.0266117R1 0.86 0.01 0.012 0.1 0.006 0.0126117R2 0.392 0.011 0.264 0.055 0.011 0.2676117S1 0.205 0.016 0.481 0.227 0.008 0.0636117S2 0.156 0.035 0.193 0.426 0.011 0.1796117S3 0.016 0.009 0.922 0.029 0.014 0.0116117S4 0.227 0.015 0.317 0.28 0.009 0.1526124R1 0.015 0.079 0.766 0.063 0.008 0.0696124R2 0.016 0.033 0.526 0.4 0.01 0.014
%macro Mol(mark);proc mixed data = three;class &mark gen rep;model T1 = OH75 FL82 K64 OH86 OH74 &mark / solution;random gen rep;%mend;
%Mol(TOM144); %Mol(CT10737I); %Mol(CT20244I); %Mol(pto); %Mol(SL10526);
%Mol(rx3);
MarkerαQw
0.00
1.002.00
3.00
4.00
5.006.00
7.00
8.00
30 40 50 60 70 80 90
single-point analysis
single-point analysis corrected for population structure
Rx-3
M1 M2Rx-3
rx-3
OH75: 1, R, 1
OH86: 0, S, 1
FL82 1, S, 0
M1 M2
M1 M2rx-3
OH75 x OH86, M1 can be used for selection, M2 cannot
OH75 x FL82, M2 can be used for selection, M2 cannot
What happens when the breeding material is a combination of progeny from both crosses?
M1 M2
M1 M2Rx-3
rx-3
OH75: 1, R, 1
OH86: 0, S, 1
FL82 1, S, 0
M1 M2
M1 M2rx-3
Reality check: Markers are identical by state but not by descent (presumably because of LD decay). Potential solution is to use haplotypes.
M1 M2
proc mixed data = three;class mark1 mark2 gen rep;model T1 = mark1*mark2 OH75 FL82 K64 OH86 OH74 / solution;random gen rep;
M1 M2 M3 M4 M5 M6
M1*M2, M2*M3, M3*M4, M5*M6
Interactions term defines haplotypes
0.00
1.002.00
3.00
4.00
5.006.00
7.00
8.00
30 40 50 60 70 80 90
single-point analysis
single-point analysis corrected for population structure
indicates haplotype analysis
haplotype analysis corrected for population structure.
Rx-3
Interval P to S L 10526 E s timate S D DF t value P r > |t|Pto*SL10526 0 0 3.76 0.531 96 7.09 <.0001Pto*SL10526 0 2 3.99 0.624 96 6.41 <.0001Pto*SL10526 2 0 3.22 0.375 96 8.59 <.0001Pto*SL10526 2 2 6.14 0.501 96 12.26 <.0001Pto*SL10526 1 0 4.35 0.395 96 11.01 <.0001Pto*SL10526 1 2 5.48 0.470 96 11.65 <.0001Pto*SL10526 1 1 7.39 0.975 96 7.59 <.0001
C hr. Marker F value P r > F1 S L10945 2.48 0.08942 S L10649 0.03 0.9742 SL10771 0.14 0.8693 SL10910 0.37 0.69083 SL10736 1.33 0.25153 SL10494 0.22 0.63853 SL10425 1.17 0.31613 SSR601 0.05 0.8284 SL10322 6.03 0.00344 SL10888 1.29 0.28036 SL10401 0.18 0.83626 SL10187 0.11 0.89357 SL20017 0.62 0.53779 SL10024 1.02 0.36519 LEOH8.4 0.25 0.779
Genome-Wide Scan
We can detect resistance conferred by the Rx-3 locus on chromosome 5
We can detect resistance conferred by Rx-4 on chromosome 11
We cannot detect QTL on chromosome 11
We can detect a strong interaction between loci on 11 and 5 (data not shown)
What needs to happen to improve prospects for “whole genome” discovery and/or selection?
More markers
Larger populations
F = Gen/Error (non-replicated)
F = Gen/Gen(Marker) (replicated)
Worst (genetic pop)
Worst (breeding pop)
Best
Population sizes
• F-test – Marker/Gen(Marker)– Larger F from greater marker effect (strength of
locus or closely linked to the causal gene)– Larger F by decreasing error– For maker studies it will nearly always be more
powerful to increase the number of genotypes rather than increasing replicates of genotypes
Sample size power estimates
=0.05
=0.10
=0.01
=0.05
N for r2=0.10
101 171
N for r2=0.05
206 349
N for r2=0.01
1047 1774
False +False -
Proportion σ2P
0
1
2
3
4
5
6
7
1 2 3 4 5 6 7 8 9 10 11 12
0
1
2
3
4
5
6
7
1 2 3 4 5 6 7 8 9 10 11 12
Discovery populations:
Magnitude of difference between R and S is large
Gen(Marker) variation moderate
Breeding populations
Difference between R and S is moderate
Gen(Marker) variation is moderate
Detecting significant marker trait associations is more difficult when magnitude of difference between genotypic classes is reduced
Population sizes can be increased by decreasing plot replication.
“Augmented designs” with a few checks highly replicated
Checks provide “error” to assess significance of differences between un-replicated genotypes
Checks can be used to normalize data (nearest check, flanking checks, etc…)
Take home messages:A) Genotyping throughput and reagent packaging favors working
with very large populations (~480) (effective MAS implementation will require larger populations)
B) Measuring traits (Phenotyping) is the limiting factor. (scoring larger populations will minimize Gen(Marker) error)
C) For elite polpulations, marker number and the ability to distinguish descent (IBD) from state (IBS) are limitations (this is a function of linkage phase and LD) (haplotypes)
D) Incorporating pedigree data or population structure data into analysis improves detection of trait associations (QTL) and the efficiency of MAS (defined as relative efficiency of selection). (corrects for structure; avoids false positives)
E) We can detect some known QTL, but not all known QTL in complex populations. Power goes up with population size and marker number. (Marker analysis is still more descriptive than predictive)
F) Phenotypic selection is effective.
AcknowledgmentsFrancis GroupMatt Robbins
Sung-Chur SimTroy Aldrich
Collaborators, OSUEsther van der Knaap
Bert BishopTea MeuliaSally Miller
Melanie Lewis Ivey
Collaborators, UCDAllen Van Deynze
Kevin StoffelAlex Kozic
FundingUSDA/AFRIOARDC RECGP matching funds grant; MAFPA
Collaborators, CAUHui Wang
Wencai Yang
Collaborators, UFLJay Scott
Sam Hutton