# cropscience.ch

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## Estimation of general combining ability (GCA) and prediction of hybrid performance

1.      Field design

If you want to use the block effect for adjustment, be sure that hybrids with the same female are not grown in the same block, otherwise you will correct for the effect of the females. As such the randomization has to be done for the females. For example in each block 14 females could be randomized + 2 checks.

2.      Geostatistic adjustment within a partially replicated trial

library(nlme)

lme(GY ~ hybrid, random= (1|column), correlation=corAR1())

The alternative to the autoregressive model corAR1 is the moving average model corARMA(q=2).

The alternative to the library nlme is the library asreml. To use asreml you need a licence.

library(asreml)

asreml(GY ~1, random =~ hybrid + Block, rcov=ar1(Column) : ar1(Row), data=dta)

if the hybrid effect is fixed the checks are used to estimate the error term. Like this you do not confound the g and gxe effect.

3.      Estimation of mean hybrid performance and GCA

library(lme4)

lmer(GY ~ 1 + (1|trial) + (1|female) + (1|male) + (1|hybrid) + (1|female:trial) + (1|male:trial)

the alternative to the two step analysis is a one-step analysis

lmer(GY ~ 1 + (1|trial) +(1|Column) +  (1|female) + (1|male) + (1|hybrid) + (1|female:trial) + (1|male:trial) + (1|hybrid:trial)

the GCA of the female and male parental lines can be estimated as follows

fGCA<-data.frame(ranef(model)$female) mGCA<-data.frame(ranef(model)$male)

the heritability of the trait can be estimated as follows

$h^2=\frac{\sigma_{m}^{2}+\sigma_{f}^{2}+\sigma_{h}^{2}}{(\sigma_{m}^{2}+\sigma_{f}^{2}+\sigma_{h}^{2})+\sigma_{mt}^{2}/T+\sigma_{ft}^{2}/T+\sigma_{ht}^{2}/T}$ where T is the number of trials (Gowda et al., 2012).

Mating designs

There are different mating designs for creating hybrids. see other post

Prediction of hybrid performance

prediction of the cross A x B

$\bar{x}_{AB}=\mu + gca_{A}+ gca_{B}+ sca_{AB}$

———————————

prediction of the cross (A x B) x R

$\frac{\bar{x}_{AR}+\bar{x}_{BR}}{2}=\mu + \frac{gca_{A}+ gca_{B}}{2}+ gca_{R}$

In this case SCA of A, B, and R are supposed to be 0

———————————

prediction of the cross (A x B) x (R x S)

$\frac{\bar{x}_{AR}+\bar{x}_{AS}+\bar{x}_{BR}+\bar{x}_{BS}}{4}=\mu + \frac{gca_{A}+ gca_{B}}{2}+ \frac{gca_{R}+ gca_{S}}{2}$

The correlation between the actual performance and the predicted performance based on GCA estimates can be predicted using the following formula

$r(Y,GCA)=\frac{\sigma_{GCA}}{\sqrt{\sigma_{GCA}^2+\sigma_{SCA}^2}}$

Evaluate as well the correlation between per se or mid-parent performance and hybrid performance

Importance of SCA

If  $\frac{\sigma_{SCA_{AB}}^2}{\sigma_{GCA_{A}}^2+\sigma_{GCA_{B}}^2}<0.5$, then the impact of SCA can be ignored (Longin, 2013)

Inbreeding depression

$\frac{F_{1}-F_{2}}{F_{1}}*100$

References

Gowda, M., C.F.H. Longin, V. Lein, and J.C. Reif. 2012. Relevance of Specific versus General Combining Ability in Winter Wheat. Crop Sci. 52(6): 2494.

Longin, F. 2013. Hybrid wheat : Quantitative genetic parameters and consequences for the design of breeding programs. TAG.

December 11th, 2013
Topic: Crop Science, Plant breeding Tags: None