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Planning rice breeding programs for impact. Multi-environment trials: design and analysis . SO. Introduction: P roblem of individual trials?. Multi-environment trials (METs) used to predict performance in farmers fields. Its predictive power = low. SO.

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planning rice breeding programs for impact

Planning rice breeding programs for impact

Multi-environment trials:

design and analysis

introduction p roblem of individual trials

SO

Introduction:Problem of individual trials?

Multi-environment trials (METs) used to predict performance in farmers fields

Its predictive power = low

IRRI: Planning breeding Programs for Impact

introduction p roblem of mets

SO

IntroductionProblem of METs?

Must be planned carefully to ensure they are predictive and efficient

very expensive and require much coordination and time

IRRI: Planning breeding Programs for Impact

learning objectives
Learning objectives
  • To clarify the purpose of variety trials
  • To introduce linear models for multi-environment trials (MET’s)
  • To describe the structure of the analysis of variance for MET’s
  • To model the variance of a cultivar mean estimated from a MET
  • To examine the effect of replication within and across sites and years on measures of precision

IRRI: Planning breeding Programs for Impact

purpose of met s

WS 2002

WS 2003 +

Purpose of MET’s

 To predict performance:

  • Off-station
  • In the future

IRRI: Planning breeding Programs for Impact

met s reduce sem for cultivars
MET’s reduce SEM for cultivars

Single trial

0

6

Yield (t/ha)

Mean of 3 trials

0

6

Yield (t/ha)

IRRI: Planning breeding Programs for Impact

the genotype x environment model
The genotype x environment model

Simplest MET model considers trials “environments”

Where:

  • M = mean of all plots
  • Ei = effect of trial i
  • R(E)j(i) = effect of rep j in trial I
  • Gk = effect of genotype k
  • GEik = interation of genotype k and trial i
  • eijkl = plot residual

Yijkl = M + Ei + R(E)j(i) + Gk + GEik + eijkl [7.1]

IRRI: Planning breeding Programs for Impact

the genotype x environment model8
The genotype x environment model

Trials and reps are random factors

They sample the TPE

We do not select varieties for specific trials or reps

Genotypes are fixed factors

We are interested in the performance of the specific lines in the trial

IRRI: Planning breeding Programs for Impact

the genotype x environment model9
The genotype x environment model

The GE interaction is a random factor

Interactions of fixed and random factors are always random

Random interactions with genotypes are part of the error variance for genotype means

IRRI: Planning breeding Programs for Impact

relationship between ge model and single trial model

Single trial: Yijk = μ + Rj + Gi + ek(j)

GE model: Yijkl = M + Ei + R(E)j(i) + Gk + GEik + eijkl

Relationship between GE model and single-trial model:

IRRI: Planning breeding Programs for Impact

anova for gly model
ANOVA for GLY model

IRRI: Planning breeding Programs for Impact

variance of a cultivar mean

σ2Y = σ2GE/e + σ2e/re[7.2]

Variance of a cultivar mean

Where:

  • e = number of trials
  • r = number of reps per trial

IRRI: Planning breeding Programs for Impact

estimating g ge and e
Estimating σ²G, σ²GE and σ²e

σ2e = MSerror

σ2GE = (MSGE – Mserror)/r

σ2G = (MSG – MSGE)/re

IRRI: Planning breeding Programs for Impact

example modeling the lsd for a met program using ge model

Hypothetical values:

σ2e = .45 (t/ha)2

σ2GE = 0.30 (t/ha)2

σ2Y = σ2GE/e + σ2e/re[7.2]

Example: modeling the LSD for a MET program using GE model

IRRI: Planning breeding Programs for Impact

example modeling the lsd for a met program using ge model15

Number of sites

Nr of reps/site

SEM t/ha

LSD

1

1

.87

2.61

2

.72

2.16

4

.64

1.92 

2

1

.61

1.83

2

.51

1.53

4

.45

1.35

5

1

.39

1.08

2

.32

0.96 

4

.29

0.87

10

1

.27

0.81

0.69

2

.23

4

.20

0.60

Example: modeling the LSD for a MET program using GE model

Table 1. The effect of trial and replicate number on the standard deviation of a cultivar mean: genotype x environment model

slide16

The “real” SEM (with GE component estimated separately) for a single trial is:

  • SEM = (σ2GE/e + σ2e/re)0.5
    • = ((0.3/1) + (0.45/4)) 0.5
    • = 0.64 t/ha
  • The “apparent” SEM (with GE and G components confounded) for a single trial is:
    • SEM = (σ2e/r)0.5
    • = (0.45/4) 0.5
    • = 0.35

IRRI: Planning breeding Programs for Impact

the genotype x site x year model

Yijkl = M + Ei + R(E)j(i) + Gk + GEik + eijkl

The genotype x site x year model

A more realistic MET model subdivides the “environment” factor into “years” and “sites”:

Yijklm = M + Yi + Sj + YSij + R(YS)k(ij)+ Gl + GYil + GSjl + GYSijl + eijklm

σ2Y = σ2GY/y + σ2GS/s +σ2GYS/ys + σ2e/rys

IRRI: Planning breeding Programs for Impact

anova for gsy model

Source

Mean square

EMS

Years (Y)

Sites (S)

Y x S

Replicates within Y x S

Genotypes (G)

MSG

σ2e + rσ2GYS + rsσ2GY+ ryσ2GS+ rysσ2G

G x S

MSGS

σ2e + rσ2GYS + ryσ2GS

G x Y

MSGY

σ2e + rσ2GYS + rsσ2GY

G x Y x S

MSGYS

σ2e + rσ2GYS

Plot residuals

MSe

σ2e

ANOVA for GSY model
estimating 2 gy 2 gs 2 gy s and 2 e
Estimating σ2GY , σ2GS , σ2GY S, and σ2e

σ2e = MSerror

σ2GYS = (MSGYS – MSerror)/r

σ2GY = (MSGY – MSGYS)/rs

σ2GS = (MSGS – MSGYS)/ry

σ2G = (2MSG - MSGS – MSGY)/2rsy

IRRI: Planning breeding Programs for Impact

example modeling the lsd for a met program using the gsy model
Example: Modeling the LSD for a MET program using the GSY model

For NE Thailand OYT:

σ2e = 0.440 (t/ha)2

σ2GS = 0.003 (t/ha)2

σ2GY = 0.049 (t/ha)2

σ2GYS = 0.259 (t/ha)2

(Cooper et al., 1999)

IRRI: Planning breeding Programs for Impact

example modeling the lsd for a met program using the gsy model21

Number of sites

Number of years

Number of replicates/site

LSD (t ha-1)

1

1

1

2.45

2

2.06

4

1.85

2

1

1.79

2

1.52

4

1.37

5

1

1

1.10

2

0.93

4

0.83

2

1

0.81

2

0.69

4

0.62

Example: Modeling the LSD for a MET program using the GSY model

IRRI: Planning breeding Programs for Impact

conclusions from error modeling exercise
Conclusions from error modeling exercise?
  • σ2GS was very small in this case

 little evidence of specific adaptation to sites

  • σ2GSY was very large in this case

 much random variation in cultivar performance from site to site and year to year

  • σ2e very large, methods to reduce plot error are needed
  • σ2GYS was very large compared to σ2GY and σ2GS

 sites and years are equivalent for testing

IRRI: Planning breeding Programs for Impact

deciding whether to divide a tpe
Deciding whether to divide a TPE
  • If TPE = large and diverse, it may be worthwhile to divide it into sets of more homogeneous sites
  • If no pre-existing hypothesis about how to group environments, use cluster, AMMI, or pattern analysis
  • If there is a hypothesis that can be formed based on geography, soil type, management system, etc, group trials according to this fixed factor

IRRI: Planning breeding Programs for Impact

the genotype x subregion model
The genotype x subregion model

Environments can be grouped into subregions:

Yijkl = M + Ei + R(E)j(i) + Gk + GEik + eijkl

Yijklm = M + Si + Ej(Si) + R(E(S))k(ij)+ Gl + GSil + GE(S)lij + eijklm

  • Subregions are fixed
  • Trials within subregions are random
  • If GS interaction term is not significant, subdivision is unnecessary, and could be harmful

IRRI: Planning breeding Programs for Impact

slide25
Expected mean squares for ANOVA of the genotype x subregion model for testing fixed groupings of sites

IRRI: Planning breeding Programs for Impact

example are central and southern laos separate breeding targets
Example: Are central and southern Laos separate breeding targets?

Should breeders and agronomists in Laos consider central and southern regions as separate TPE for RL rice?

22 traditional varieties tested in 4-rep trials at

3 sites in central region, 3 in south in WS 2004

IRRI: Planning breeding Programs for Impact

anova testing hypothesis c entral southern regions of laos separate rl breeding targets
ANOVA testing hypothesis: central & southern regions of Laos = separate RL breeding targets

22 TVs tested in WS 2004

are central and southern laos separate breeding targets
Are central and southern Laos separate breeding targets?

Genotype x subregion interaction is not significant when tested against variation among locations within subregions

 Subdivision is therefore not needed

 Subdivision might even be harmful, because it would reduce replication within each subregion

IRRI: Planning breeding Programs for Impact

can anyone briefly clarify the purpose of variety trials
Can anyone briefly clarify the purpose of variety trials?

When should you divide a TPE?

IRRI: Planning breeding Programs for Impact

summary 1
Summary 1
  • Purpose of a variety trial is to predict future performance in the TPE
  • Random GEI interaction is large, and reduces precision with which cultivar means can be estimated
  • Variance component estimates for the GLY model can be used to study resource allocation in testing programs
  • Within homogeneous TPE, the GSY variance usually the largest. If so, strategies that emphasize testing over several sites or several years likely equally successful

IRRI: Planning breeding Programs for Impact

summary 2
Summary 2
  • Little benefit from including more than 3 replicates (and often more than 2) in a MET
  • Standard errors and LSD’s estimated from single sites are unrealistically low because they do not take into account random GEI
  • Fixed-subregion hypotheses allow a hypothesis about the existence of genotype x subregion interaction to be tested against genotype x trial within subregion interaction

IRRI: Planning breeding Programs for Impact