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--- how_to_run_pure_gblup [2019/06/07 00:39] – yutaka
+++ how_to_run_pure_gblup [2019/07/30 18:41] – [Procedure to run GBLUP] dani
@@ Line 15: / Line 15: @@
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-where $\mathbf{y}$ is a vector of observations, $\mathbf{b}$ is a vector of fixed effects (typically a single $\mu$), $\mathbf{u}$ is a vector of additive genetic effects, $\mathbf{e}$ is a vector of residual effects. We assume $\mathrm{var}(\mathbf{y})=\mathrm{var}(\mathbf{u})+\mathrm{var}(\mathbf{e})=\mathbf{G}\sigma_{u}^{2}+\mathbf{R}\sigma_{e}^{2}$ where $\mathbf{G}$ is the genomic relationship matrix, $\mathbf{R}$ is a diagonal matrix (typically $\mathbf{I}$), $\sigma_{u}^{2}$ is the additive genetic variance, and $\sigma_{e}^{2}$ is the residual variance. The system of mixed model equations (MME) is shown as follows.
+where $\mathbf{y}$ is a vector of observations, $\mathbf{X}$ is a design matrix relating the fixed effects to the observations (typically $\mathbf{1}$), $\mathbf{b}$ is a vector of fixed effects (typically a single $\mu$), $\mathbf{u}$ is a vector of additive genetic effects, $\mathbf{e}$ is a vector of residual effects. We assume $\mathrm{var}(\mathbf{y})=\mathrm{var}(\mathbf{u})+\mathrm{var}(\mathbf{e})=\mathbf{G}\sigma_{u}^{2}+\mathbf{R}\sigma_{e}^{2}$ where $\mathbf{G}$ is the genomic relationship matrix, $\mathbf{R}$ is a diagonal matrix (typically $\mathbf{I}$), $\sigma_{u}^{2}$ is the additive genetic variance, and $\sigma_{e}^{2}$ is the residual variance. The system of mixed model equations (MME) is shown as follows.
 $$
@@ Line 38: / Line 38: @@
 \right]
 $$
-Note that $\mathbf{R}^{-1}=\mathbf{I}/\sigma_{e}^{2}$.
+Note that $\mathbf{R}^{-1}=\mathbf{I}/\sigma_{e}^{2}$ in the typical case.
 ===== A way to build MME in blupf90 =====
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 The blupf90 program is designed to solve the animal model that has the inverse of the numerator relationship matrix ($\mathbf{A}^{-1}$). Also, this program is extended to perform the single-step GBLUP analysis including the inverse of a subset pedigree matrix for genotyped animals ($\mathbf{A}_{22}^{-1}$) as well as $\mathbf{G}^{-1}$.
-Regardless of the above GBLUP model, the program literally creates the following MME.
+Regardless of whether you need the pedigree relationships, the program literally creates the following MME.
 $$
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 .00
 OPTION AlphaBeta  1 0
-OPTION GammaDelta 0 0
 OPTION tunedG 0
 </file>
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 We call this adjustment //tuning// to obtain the final matrix.
 $$
-\mathbf{G}_{\mathrm{final}} = a\mathbf{G}_{\mathrm{updated}} + b\mathbf{J}
+\mathbf{G}_{\mathrm{final}} \leftarrow a\mathbf{G}_{\mathrm{updated}} + b\mathbf{J}
 $$
 The constants $a$ and $b$ are tuning parameters. It is critical for genomic prediction when the genotyped animals are from only the last generation but you have the historical pedigree (i.e. incompatible $\mathbf{G}$ and $\mathbf{A}_{22}$).