Post on 19-Jan-2016
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Planning rice breeding programs for impact
Heritability in multi-location trials and response to selection
IRRI: Planning breeding Programs for Impact
Learning objectives
• To define H for 2-way and 3-way MET models
• To understand the relationship between H and the correlation across locations
• To understand the relationship between H and selection response
IRRI: Planning breeding Programs for Impact
Introduction
• H integrates information on genetic variation and environmental “noise” into a measure of repeatability
• H is closely related to selection response (R)
• H can be used to model effect of changes to breeding program organization on R
IRRI: Planning breeding Programs for Impact
Question: What does H tell us?
• Proportion of phenotypic variation in genotype means that is due to genotypic differences
• Repeatability (the expected correlation between means from independent sets of trials conducted within the TPE)
IRRI: Planning breeding Programs for Impact
Estimating H for GE model
Source Mean Square EMS
Environments (E)
Replicates within E
Genotypes (G) MSGσ2
e + rσ2GE + reσ2
G
G x E MSGEσ2
e + rσ2GE
Error
(Plot Residuals)MSe
σ2e
IRRI: Planning breeding Programs for Impact
Phenotypic variance for GE model
σ2P = σ2
G + σ2GE/e + σ2
e/re
Where:
e = number of trials
r = number of reps per trial
IRRI: Planning breeding Programs for Impact
σ2G
σ2G + (σ2
GE /e) + (σ2e /re)
=H
IRRI: Planning breeding Programs for Impact
Example: RL variety trials in southern/central Laos
σ2e = MSE = 153102
σ2GE = (MSGE – MSe)/r = 201340
σ2G = (MSG – MSGE)/re = 111520
Source Mean Square EMS
Environments (E)
(e=6)
Replicates within E
(r=4)
Genotypes (G) 3644950 σ2e + rσ2
GE + reσ2G
G x E 958462 σ2e + rσ2
GE
Plot Residuals 153102 σ2e
IRRI: Planning breeding Programs for Impact
Trials Replicates per trial H
1 1 0.24
2 0.29
4 0.32
3 1 0.49
2 0.55
4 0.58
5 1 0.61
2 0.67
4 0.70
Example: modeling H for a MET program: GE model
IRRI: Planning breeding Programs for Impact
Conclusions for 2-way model
1. H increases with replication within and across sites
2. In METs, site number has a greater effect than within-sit replication
3. For large METs, even 2 reps per site may give enough repeatability
IRRI: Planning breeding Programs for Impact
H estimates for a single trial are biased upwards, because G effects from single trial = G + GE in MET:
Ysingle = M + G + e
YMET = M + E + G + GE + e
Note
IRRI: Planning breeding Programs for Impact
σ2G
’
σ2P
=H
σ2G + σ2
GE
σ2G + σ2
GE + (σ2e /r)
=
Broad-sense heritability for single trial
IRRI: Planning breeding Programs for Impact
σ2G
σ2G + (σ2
GE /e) + (σ2e /re)
=H
H for 2-way model
IRRI: Planning breeding Programs for Impact
σ2G
’
σ2P
=H
σ2G + σ2
GE
σ2G + σ2
GE + (σ2e /r)
=
111520 + 201340
111520 +201340 + (153102/4)
= =
Extent of bias in IRRI upland trial example: Approximate H estimate from single-trial data
0.89
IRRI: Planning breeding Programs for Impact
σ2G
σ2P
=H
σ2G
σ2G + σ2
GE + (σ2e /r)
=
111520
111520 +201340 + (153102/4)
= =
Extent of bias in Lao Ws 2004 example: approximate H estimate from MET data
0.32
IRRI: Planning breeding Programs for Impact
A more realistic MET model subdivides the “environment” factor into “years” and “sites”:
Yijkl = M + Ei + R(E)j(i) + Gk + GEik + eijkl
Yijklm = M + Yi + Sj + YSij + R(YS)k(ij)+ Gl + GYil + GSjl + GYSijl + eijklm
σ2Y = σ2
GY/y + σ2GS/s + σ2
GYS/ys + σ2e/rys
The genotype x site x year model
IRRI: Planning breeding Programs for Impact
σ2G
σ2G + (σ2
GY /y) + (σ2GS /s) + (σ2
GSY /ys) + (σ2e /rsy)
=H
IRRI: Planning breeding Programs for Impact
Example: modeling H for the Thai RL breeding program
1070 lines
3 years x 8 sites x 2 reps
σ2G = 0.060 ± 0.006
σ2GS = 0.003 ± 0.006
σ2GY = 0.049 ± 0.006
σ2GYS = 0.259 ± 0.009
σ2e = 0.440 ± 0.006
IRRI: Planning breeding Programs for Impact
Number of sitesNumber of
yearsNumber of
replicates/site H
1 1 1 .07
2 .10
4 .12
2 1 .14
2 .18
4 .22
5 1 1 .24
2 .29
4 .33
2 1 .35
2 .39
4 .49
Example: modeling H for a MET program using the GSY model
IRRI: Planning breeding Programs for Impact
The relationship between H and selection response (R)
R = k H σG
Where:
k = selection differential in standard deviation units
IRRI: Planning breeding Programs for Impact
y0 ys
K = ys – y0
σP
Standardized selection differential (k)
IRRI: Planning breeding Programs for Impact
p k
.01 2.67
.02 2.42
.05 2.06
.10 1.76
.15 1.55
.20 1.40
.25 1.27
.30 1.16
The relationship between k (# of standard deviations above the mean) and the proportion of the population selected (p):
IRRI: Planning breeding Programs for Impact
Effect of changes in H on RWhen comparing 2 testing methods, 1 and 2:
• R1 = k1 H1 σG1
• R2 = k2 H2 σG2
If k1 = k2 and σG1 = σG2
R1/R2 = H1 / H2
IRRI: Planning breeding Programs for Impact
Example:Predicting effect of increased replication over sites on R for Thai RL program
Protocol 1: testing over 4 reps at 1 site
Protocol 2: testing over 1 rep at 5 sites
H1 = .12
H2 = .24
R2/R1 = H2 / H1
= 1.41
Which selection strategy gives greater response?
• Evaluation of 50 varieties in 4-rep trials at 6 sites, selecting 10 for further testing
OR
• Evaluation of 100 varieties in 2-rep trials at 6 sites
P =10/50 = 0.2; k = 1.4P = 10/100 = 0.1; k = 1.76
H = H =
σ2G = 0.060 σ2
G = 0.060
R= R=
50 varieties x 2 reps 100 lines x 2 reps
The equation for R allows to look at effects of increasing nr of lines tested and reducing replication: (Example using Thai RL variance components)
IRRI: Planning breeding Programs for Impact
Can anyone briefly summarize:
• relationship between H and the correlation across locations?
• relationship between H and selection response?
IRRI: Planning breeding Programs for Impact
Summary• H measures the repeatability of yield trials
• If trials replicated over sites & years, within-site replication can be reduced with little effect on H
• Estimates of H are severely inflated when derived from a single trial
• H is the expected value of the correlation between sets of means derived in different trials
• Selection response is proportional to both √H and k Sometimes better to have fewer reps but test more lines