Example 2:   Resource allocation for a rice breeding program using the GSY model

 

Cooper et al. (1999) conducted a resource allocation study for the Thai rainfed lowland rice breeding program in northern Thailand.  In this study over 1000 unselected breeding lines from 7 crosses were evaluated for 3 years at 8 sites.  

 

Variance components estimates were:

 

 

 

These estimates are of interest in themselves.  Their relative magnitudes yield important information about the nature of GE interaction in northern Thailand.  Inspection of these estimates leads to the following conclusions:

 

  1. σ2GS is very small relative to the other components, indicating that cultivars do not, on average, perform differently at different locations.  There is little evidence, therefore, that specific lines are adapted to specific locations within the TPE.

 

  1. σ2GYS is the largest component of GEI (a result found in many studies), indicating that cultivar ranks vary randomly from site to site and from year to year.

 

  1. σ2eis very large relative to other components of variance, indicating that within-trial field heterogeneity is great.  High levels of replication will be needed to achieve acceptable precision.  Improvements in field technique and the use of experimental designs that control within-block error should also be considered.

 

 

The predicted effect of site, year, and replicate number on the standard error of a line mean evaluated in northern Thailand is presented below:

 

The table below shows the effect of location, year and replicate number on the standard deviation of a cultivar mean: GLY model (variance component estimates from Cooper et al., 1999):   

 

Number of sites

Number of years

Number of replicates/ site

S.E. of cultivar mean

(t ha-1)

LSD.05 for the difference betw. cultivar means

(t ha-1)

1

1

1

.87

 

 

 

2

.73

 

 

 

3

.68

 

 

 

4

.65

 

 

 

 

 

 

 

2

1

.63

 

 

 

2

.54

 

 

 

3

.50

 

 

 

4

.49

 

 

 

 

 

 

5

1

1

.39

 

 

 

2

.33

 

 

 

3

.30

 

 

 

4

.29

 

 

 

 

 

 

 

2

1

.28

 

 

 

2

.24

 

 

 

3

.23

 

 

 

4

.22

 

 

 

 

 

 

10

1

1

.27

 

 

 

2

.23

 

 

 

3

.21

 

 

 

4

.21

 

 

 

 

 

 

 

2

1

.20

 

 

 

2

.17

 

 

 

3

.16

 

 

 

4

.15

 

 

Some conclusions:

 

  1. Testing in approximately 10 trials (5 sites x 2 years or 10 sites x 1 year) is needed to bring LSD values for the difference between 2 cultivars below 1 ton per ha (the LSD is approximately 3 times the standard error of a cultivar mean).

  2. Two replicate per trial are adequate if at least 5 trials are used to estimate means.

 

 

Estimates of the variance of cultivar means from single trials are biased downwards

 

It is important for breeders to recognize that the variance of cultivar means estimated from a single trials is severely biased downwards.  This is because in an analysis of a single trial, there is no way to separate σ2G  from σ2GY, σ2GS, and σ2GYS.

This is because G, GS, GY, and GYS effects are completely confounded (or inseparably mixed) in single trials.  In a single trial, only σ2e can be estimated separately from σ2G and used in the calculation of the variance of a cultivar mean.  

 

Thus, if the variance of a cultivar mean is estimated from a in a single trial,

 

whereas in a MET,

 

 

In a single trial, the values of y and s are 1, and the true variance of a cultivar mean is therefore:

 

 

rather than σ2e /r.  If the purpose of the trial is to predict future performance of the varieties under test, it is clear that  σ2Y’ severely underestimates σ2Y.  

The literature indicates that the true variance of a cultivar mean for purposes of prediction is at least twice as large as the variance estimated from a  single trial.  This is why breeders evaluate advanced lines at several sites.