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Table 1 List of abbreviations used in alphabetical order

From: An analytical framework to derive the expected precision of genomic selection

Abbreviation Full meaning
\({\mathbf{a}}\) Vector of economic weights in \(\gamma\)
\(\alpha\) Lower bound of the distribution of minor allele frequencies
\(A_{k}\) and \(B_{k}\) Alleles at SNP \(k\)
\(\beta_{k}\) Effect of SNP \(k\)
\(\hat{{\beta}}_{k}\) Prediction of the effect of SNP \(k\)
\({\varvec{\upbeta}}_{j}\) Vector of SNP effects for trait \(j\)
\({\varvec{\upbeta}}\) Vector of SNP effects
\({\mathbf{B}}\) Covariance matrix \(v\left( {\varvec{\upbeta}} \right)\)
\({\tilde{{\boldsymbol{\beta}}}}\) Estimates of fixed effects
\(\gamma\) Selection objective
\(\hat{\gamma }\) BLUP of \(\gamma\)
\({\mathbf{D}}\) Expectation of \({\mathbf{X^{\prime}X}} + {\varvec{\Lambda}}\)
\(\delta_{k}\) \(k^{th}\) diagonal term of \({\mathbf{D}}\)
\({\mathbf{E}}\) Deviation of \({\mathbf{X^{\prime}X}} + {\varvec{\Lambda}}\) from \({\mathbf{D}}\)
\({\mathbf{e}}\) Vector of residuals
\(f_{min}\) Minimum minor allele frequency
\(f_{k}\) Frequency of \({\text{allele }}B_{k}\)
\({\mathbf{F}}\) Matrix of SNP genotypes
\(g\) Genetic value of the candidate
\(\hat{g}\) GEBV of the candidate
\({\mathbf{g}}\) Vector of genetic values
\({\hat{\mathbf{g}}}\) BLUP of \({\mathbf{g}}\)
\(h_{0}^{2}\) Heritability
\({\varvec{\Lambda}}\) Diagonal matrix with elements \(\lambda_{k}\)
\(\lambda\) Ratio \(\sigma_{e}^{2} /\sigma_{{{\boldsymbol{g}}_{k} }}^{2}\)
\(\lambda_{k}\) Ratio \(\sigma_{e}^{2} /\sigma_{{{\boldsymbol{\beta}}_{k} }}^{2}\)
\(M_{e}\) Effective number of loci
\(M\) Number of SNPs
\(N_{e}\) Effective population size
\(N\) Size of the reference population
\({\mathbf{P}}\) Working matrix (\({\mathbf{D}}^{ - 1} {\mathbf{ED}}^{ - 1} {\mathbf{E}}\))
\({\mathbf{R}}\) Covariance matrix \(v\left( {\mathbf{e}} \right)\)
\(\widetilde{{r^{2} }}\) Estimate of the precision of GEBV based on [17]
\(\hat{r}^{2}\) Approximation of \(r^{2}\) proposed here
\(r^{2} \left( {{\mathbf{X}},{\mathbf{w}}} \right)\) Expected precision of GEBV, given \(\varvec{X}\) and \(\varvec{w}\)
\(r^{2}\) Marginal expected precision of GEBV
\(\sigma_{{{\boldsymbol{\beta}}_{k} }}^{2}\) Variance of the effects \(\beta_{k}\)
\(\sigma_{k}^{2}\) Variance of the number of \(B_{k}\) alleles
\(\sigma_{g}^{2}\) Genetic variance
\(\sigma_{e}^{2}\) Environmental variance
\(\sigma_{Y}^{2}\) Phenotypic variance
\({\mathbf{w}}\) Vector of SNP genotypes
\({\mathbf{X}}\) Genotype matrix
\({\mathbf{y}}\) Vector of the phenotypes of the reference population