Planning rice breeding programs for impact

1. Planning rice breeding programs for impact Multi-environment trials: design and analysis

2. 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

3. 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

4. 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

5. WS 2002 WS 2003 + Purpose of MET’s  To predict performance: • Off-station • In the future IRRI: Planning breeding Programs for Impact

6. 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

7. 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

8. 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

9. 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

10. 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

11. ANOVA for GLY model IRRI: Planning breeding Programs for Impact

12. 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

13. Estimating σ²G, σ²GE and σ²e σ2e = MSerror σ2GE = (MSGE – Mserror)/r σ2G = (MSG – MSGE)/re IRRI: Planning breeding Programs for Impact

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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

25. Expected mean squares for ANOVA of the genotype x subregion model for testing fixed groupings of sites IRRI: Planning breeding Programs for Impact

26. 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

27. ANOVA testing hypothesis: central & southern regions of Laos = separate RL breeding targets 22 TVs tested in WS 2004

28. 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

29. Can anyone briefly clarify the purpose of variety trials? When should you divide a TPE? IRRI: Planning breeding Programs for Impact

30. 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

31. 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