## 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

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*

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

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

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

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

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

**Importance of SCA**

If , then the impact of SCA can be ignored (Longin, 2013)

**Inbreeding depression**

**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, 2013Topic: Crop Science, Plant breeding Tags: None