Planning rice breeding programs for impact

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Planning rice breeding programs
for impact

• Models, means, variances, LSDs and Heritability

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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  

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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.

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2.0
2.3
1.9
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2.6
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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
• Gs and es sum to 0

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E(e) 0
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• 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 es
  tend to cancel each other out

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Variances, standard errors and LSDs
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Least significant difference (LSD) LSD
ta/2,edf x SED ta/2,edf x v(2 s2e
/r) 4.6   ta/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
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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

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The phenotypic variance single trial model
Cultivar mean
Variance AMONG cultivar means
s2P s2G (s2e /r)
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Broad-sense heritability for single trial
H
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What does H tell us, and what is it useful for?

• Proportion of phenotypic variation in genotype
  means that is due to genotypic differences
  (signalnoise 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

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What does H NOT tell 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

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Estimating H for the single-trial model

• Variance components (including s²G) are estimated
  from ANOVA table (for balanced trials) or REML
  software

Source MS EMS
Genotypic MSG s2e rs2G
Plot residuals MSe s2e
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Example a 40-entry micro plot trial

• ?40 upland varieties were evaluated in single-row
  micro plots at IRRI

Source Mean square (g/plot)² EMS
Replicates
Genotypes (G) 6891 s2e rs2G
Plot residuals 1544 s2e
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s2G (6891 1544) / 3 1782
Table 8.3. Predicted H for yield in micro plots
with 1- 4 replicates
Replicates H
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2
3
4
s2G / s2G (s2e /r) 1782/1782 (1544/1)
0.54
s2G / s2G (s2e /r) 1782/1782 (1544/2)
0.70
s2G / s2G (s2e /r) 1782/1782 (1544/3)
0.78
s2G / s2G (s2e /r) 1782/1782 (1544/4)
0.82
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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

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Can anyone briefly explain

• the purpose of replications?
• heritability?

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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

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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 gt 4 reps