planning rice breeding programs for impact heritability in multi-location trials and response to...

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


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


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)


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


Phenotypic variance for GE model

σ2P = σ2

G + σ2GE/e + σ2

e/re

Where:

e = number of trials

r = number of reps per trial


σ2G

σ2G + (σ2

GE /e) + (σ2e /re)

=H


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


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


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


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


σ2G

’

σ2P

=H

σ2G + σ2

GE

σ2G + σ2

GE + (σ2e /r)

=

Broad-sense heritability for single trial


σ2G

σ2G + (σ2

GE /e) + (σ2e /re)

=H

H for 2-way model


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


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


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


σ2G

σ2G + (σ2

GY /y) + (σ2GS /s) + (σ2

GSY /ys) + (σ2e /rsy)

=H


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


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


The relationship between H and selection response (R)

R = k H σG

Where:

k = selection differential in standard deviation units


y0 ys

K = ys – y0

σP

Standardized selection differential (k)


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):


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


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)


Can anyone briefly summarize:

• relationship between H and the correlation across locations?

• relationship between H and selection response?


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

planning rice breeding programs for impact heritability in multi-location trials and response to...

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