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11 Functions of variance components 17111.1 IntroductionF phenvar 1 + 2 # pheno varF genvar 1 * 4 # geno varH herit 4 3 # heritabilityASReml includes a post-analysis procedure tocalculate functions of variance components.Its intended use is when the variance componentsare either simple variances or are variancesand covariances in an unstructured matrix. The functions covered are linearcombinations of the variance components (for example, phenotypic variance), aratio of two components (for example, heritabilities) and the correlation basedon three components (for example, genetic correlation). The user must preparea .pin file. A simple sample .pin file is shown in the ASReml code box above.The .pin file specifies the functions to be calculated. The user re-runs ASRemlwith the -P command line option specifying the .pin file as the input file. AS-Reml reads the model information from the .asr and .vvp files and calculatesthe requested functions. These are reported in the .pvc file.11.2 SyntaxFunctions of the variance components are specified in the .pin file in lines of theformletter label coefficients• letter ( either F, H or R ) must occur in column 1– F is for linear combinations of variance components,– H is for forming the ratio of two components,– R is for forming the correlation based on three components,• label names the result,• coefficients is the list of coefficients for the linear function.Linear combinations of componentsFirst ASReml extracts the variance componentsfrom the .asr file and their variancematrix from the .vvp file. Each linear functionformed by an F line is added to the list ofF phenvar 1 + 2 # pheno varF genvar 1 * 4 # geno varH herit 4 3 # heritabilitycomponents. Thus, the number of coefficients increases by one each line. We seekto calculate k + c ′ v, cov (c ′ v, v) and var (c ′ v) where v is the vector of existingvariance components, c is the vector of coefficients for the linear function andk is an optional offset which is usually omitted but would be 1 to represent the