rrBlupMethod6: rrBlupMethod6 - Re-parametrization of RR-BLUP to allow for a...

In rrBlupMethod6: Re-parametrization of RR-BLUP to allow for a fixed residual variance

Description

rrBlupMethod6 – Re-parametrization of the mixed model formulation of Kang et al. (2008), to allow for a fixed residual variance when using RR-BLUP for genomwide estimation of marker effects and linear transformation of the adjusted means proposed by Piepho et al.(2011).

Details

Package:	rrBlupMethod6
Type:	Package
Version:	1.3
Date:	2012-10-04
License:	GNU General Public License Version 2, June 1991
LazyLoad:	yes

Kang et al. (2008) describe an efficient mixed model formulation for the special case of only one random effect besides the error, which avoids any matrix computation in the REML estimation of variance components. Piepho et al. (2011) re-parametrize their formulation to allow for a fixed residual variance. This re-parametrization might be especially useful in a plant breeding context. Here, the phenotypes used for estimation of marker effects are commonly the adjusted (for all other random and fixed effects) entry means, obtained beforehand from a one- or two-step adjustment procedure, most likely a mixed-model analysis (Moehring and Piepho, 2009). From this analysis, good estimates of the residual variance are usually available, so that it is not necessary and even counterproductive to re-estimate this parameter in RR-BLUP (Moehring and Piepho, 2009). Please see Piepho et al. (2011) for details.

The method is restricted to the case where R = I sigma2, where R is the error variance-covariance matrix and sigma2 is the error variance. An independent estimate of R is often available from the analysis that yielded adjusted means. In case R does not meet this assumption, a linear transformation (rotation) can always be applied to ensure R = I sigma2 (Piepho et al., 2011, Schulz-Streeck et al., 2012), provided that R is known. Hence, we replace y by L_R y and Z by L_R Z, where y is the vector with the adjusted means, inv(R) = square(L_R) such that L_R is square and symmetric and Z is the matrix with marker information. L_R is easily obtained from a spectral decomposition of inv(R). With these replacements, analysis can proceed assuming that R = I sigma2 with sigma2 = 1.

The package rrBlupMethod6 implements the method denoted "Method 6" in Piepho et al. (2011). The original parametrization of Kang et al. (2008) was previously implemented in the R package rrBLUP (Endelman, 2011), available from CRAN under http://cran.r-project.org/web/packages/rrBLUP/index.html. We used parts of the code of an earlier version (1.1) of rrBLUP as a starting point for our implementation.

Author(s)

Torben Schulz-Streeck (1), Boubacar Estaghvirou (1), Frank Technow (2)

(1) University of Hohenheim, Institute of Crop Science, Stuttgart, Germany

(2) University of Hohenheim, Institute of Plant Breeding, Seed Science and Population Genetics, Stuttgart, Germany

Maintainer: Frank Technow [e-mail]

References

Piepho et al. (2012): Efficient computation of ridge-regression BLUP in genomic selection in plant breeding. Crop Science 52 (3), 1093-1104

Kang et al. (2008): Efficient control of population structure in model organism association mapping. Genetics 178:1709-1723

Moehring, J., Piepho, H. P. (2009): Comparison of weighting in two-stage analyses of series of experiments. Crop Science 49, 1977-1988

Piepho HP, Schulz-Streeck T, Ogutu JO (2011): A stage-wise approach for analysis of multi-environment trials. Biuletyn Oceny Odmian 33:7-20

Schulz-Streeck T, Ogutu JO, Piepho HP (2012) Comparisons of single-stage and two-stage approaches to genomic selection. Submitted

See Also

rrBlupM6, rrBlupRotation

rrBlupMethod6 documentation built on May 2, 2019, 7:38 a.m.