Planning rice breeding programs for impact

1. Planning rice breeding programs for impact Models, means, variances, LSD’s and Heritability

2. Learning objectives • Review the linear model for plot measurements in variety trials and nurseries, and the derived statistics • Understand the purpose of replication in breeding programs • Model the relationship between replication, the standard error of a cultivar mean (SEM), and the least significant difference (LSD) between the means of 2 cultivars   IRRI: Planning breeding Programs for Impact

3. Introduction • Measurements made on field plots contain both genotypic effects (G) and plot residuals (e) • Purpose of experimental design and statistical analysis is to separate genotypic “signal” from “noise” of plot residuals. IRRI: Planning breeding Programs for Impact

4. 2.0 2.3 1.9 2.2 0.8 1.1 2.0 2.5 2.6 2.3 2.8 3.2 3.5 3.8 2.5 2.6 2.3 2.4 1.0 0.6 1.8 3.1 3.2 2.9 3.3 3.5 3.9 4.1 2.7 2.8 2.4 2.6 2.7 1.3 0.5 3.1 3.4 3.5 3.3 3.7 4.0 4.4 IRRI: Planning breeding Programs for Impact

5. Yij = μ + Gi + ej [4.1] Linear model for plot measurements For a completely randomized design (CRD): Where: • Yij = a plot measurement • μ = the mean of all plots • Gi = the effect of the ith genotype • ej = the “residual” effect of the jth plot G’s and e’s sum to 0 IRRI: Planning breeding Programs for Impact

6. Yi. = μ + Gi + e [4.2] • As r increases, e approaches 0, Y approaches μ + Gi • Breeders replicate to reduce effect of e! • But even if r is 3 or 4, e’s have big effect on estimates of G • E(e) =0 IRRI: Planning breeding Programs for Impact

7. Yi. = μ + Gi + ej [4.1] • Thus, for measurements on a single plot, G and e are confounded • Because of the confounding, Y is an unreliable estimator of G • In replicated trials, the mean of Y over several plots is a better estimator of G, because e’s tend to cancel each other out IRRI: Planning breeding Programs for Impact

8. Variance of a mean • The variance of a genotype mean is an important measure of the precision of a trial: • σ2Y = σ2e/r[4.3] • σ2e is the error mean square from the ANOVA • Standard error of a mean (SEM) • SEM = σ2Y Variances, standard errors and LSD’s IRRI: Planning breeding Programs for Impact

9. Variance of a difference between 2 means σ2D = 2σ2e/r[4.4] Standard error of a difference (SED) SED = √(2σ2e/r) [4.5] IRRI: Planning breeding Programs for Impact

10. Least significant difference (LSD) LSD = tα/2,edf x SED = tα/2,edf x √(2 σ2e /r) [4.6] tα/2,edf roughly equals 2, so LSD = 3 SEM SEM, SED, and LSD are important measures of the precision of a trial Precision is determined mainly by replication IRRI: Planning breeding Programs for Impact

11. Repeatability • 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

12. Yi. = m + Gi + Σeij The phenotypic variance: single trial model Cultivar mean: Variance AMONG cultivar means: σ2P = σ2G + (σ2e /r) IRRI: Planning breeding Programs for Impact

13. σ2G = σ2P σ2G = σ2G +(σ2e /r) Broad-sense heritability for single trial H IRRI: Planning breeding Programs for Impact

14. What does H tell us, and what is it useful for? • Proportion of phenotypic variation in genotype means that is due to genotypic differences (“signal:noise” ratio) • Repeatability of a trial, or the expected correlation between 2 identical variety trials conducted in the same field • It tells us how reliable the results of an experiment are • It can be used to examine the effect of increasing or decreasing replicate number on repeatability of the experiment IRRI: Planning breeding Programs for Impact

15. What does H NOTtell us? • Mendelian transmissability • Anything about genetic control of a trait • Note that H is not a constant! It is affected by the level of replication of the selection unit IRRI: Planning breeding Programs for Impact

16. Estimating H for the single-trial model Variance components (including σ²G) are estimated from ANOVA table (for balanced trials) or REML software IRRI: Planning breeding Programs for Impact

17. Example: a 40-entry micro plot trial 40 upland varieties were evaluated in single-row micro plots at IRRI IRRI: Planning breeding Programs for Impact

18. σ2G = (6891 – 1544) / 3 = 1782 Table 8.3. Predicted Hfor yield in micro plots with 1- 4 replicates σ2G / [σ2G + (σ2e /r)] = 1782/[1782 + (1544/1)] = 0.54 σ2G / [σ2G + (σ2e /r)] = 1782/[1782 + (1544/2)] = 0.70 σ2G / [σ2G + (σ2e /r)] = 1782/[1782 + (1544/3)] = 0.78 σ2G / [σ2G + (σ2e /r)] = 1782/[1782 + (1544/4)] = 0.82 IRRI: Planning breeding Programs for Impact

19. H for the single trial model • H is not a constant; it approaches 1.0 with increased r • Single-trial H estimates are biased upward by GEI • Estimates apply only to TPE and genetic population from which they were derived IRRI: Planning breeding Programs for Impact

20. Can anyone briefly explain: • the purpose of replications? • heritability? IRRI: Planning breeding Programs for Impact

21. Conclusion 1 • In field trials & nurseries, genotype & plot effects are confounded • Purpose of replication in breeding programs = reduce this confounding, increasing our ability to identify superior genotypes • Error mean square from representative experiments = used to predict LSD value we obtain from given level of replication IRRI: Planning breeding Programs for Impact

22. Conclusion 2 • H = a measure of repeatability of variety trials • Genotype and error variances estimated from replicated trials used to model H • Gains in precision and repeatability from increasing replication diminish quickly for trials with > 4 reps IRRI: Planning breeding Programs for Impact