Single record animal model in ASReml-Standalone version
A single record animal model is the simplest mixed model used in animal breeding. This is called animal model because we estimate a breeding value for each animal defined in the pedigree. “Single record” refers to the fact that animals have only one observation available. For this example, there will be only fixed effects and additive genetic effects without other random effects to include such as maternal, dominance, and epistasis.
In the single record animal model, we often assume that the matrix of variance-covariance of errors, R, is equal to and the matrix of variance-covariance of additive effects, G, is equal to, and these are incorporated into the mixed model equation as shown below:
Note also that the matrices X and Z from above are the incidence matrices of fixed and random effects respectively that connect the data with the effects. The vectors of b̂ and û represent estimated fixed and predicted random effects,
In ASReml-Standalone we will have to specify:
There is no need to define variance structures more specifically because there is only one extra random effect besides the residual term. Here, we have put a scalar after the “animID” factor in the model statement to specify a starting value (optional).
A series of output files are produced with only “basename.as” of ASReml run. Running the example as above, the important output for the animal breeding area are written to the files with extensions: “asr”, “pvc”, “sln”, and “aif”.
The “basename.asr” file contains a summary of data, the iteration sequence, estimates of the variance parameters, and analysis of variance (ANOVA) table by Wald test and estimates of the fixed effects, among other things. In our dataset, additive genetic and residual variances for BW200d were estimated to be 53.56 and 137.32 kg2, respectively. Fixed effect tests for this trait show highly significant differences (P<0.01) for most factors, as shown in the green rectangle.
The operation of “vpredict! define” in basename.as file requests the additional estimation of the narrow-sense heritability and this is reported in the “basename.pvc” file. The heritability for BW200d, in this case, is: 0.28±0.03.
The estimates of all fixed (BLUE) and random (BLUP) effects are written to the file “basename.sln”. The figure below is an extract from this file containing fixed effect estimates on the left and estimated breeding values of animals (column 3) with standard errors (column 4) on the right.
The “basename.aif” file is another important one that reports estimates of each individual’s inbreeding coefficients. Because of the use of the !AIF qualifier, the diagonal elements of the relationship matrix are reported, which corresponds to the inbreeding coefficients (column 2), and the inverse of relationship matrix (column 3) reported in this file. A factor level of “Parent and Nonparent” (column 4) indicates that the individual status as a parent (with progeny in the pedigree) or a non-parent (with no progeny in the pedigree).