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Multiple Trait Evaluation: Difference between revisions
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[[Category: Genetic Evaluation]] | |||
Multiple-trait genetic evaluation differs from a single-trait evaluation in that several phenotypic traits are evaluated at the same time. Reasons for doing a multiple-trait genetic evaluation include greater prediction [[Accuracy| accuracy]] and reduced [[Prediction Bias |prediction bias]]. | |||
As with single trait genetic evaluation most traits use [[BLUP]] to obtain [[Expected Progeny Difference| EPD]] by solving the mixed model equations. For single | As with single-trait genetic evaluation most traits use [[Best Linear Unbiased Prediction | BLUP]] to obtain [[Expected Progeny Difference| EPD]] by solving the mixed-model equations. For single traits with breeding values as the only random effect the mixed-model equations take the form | ||
<center> | <center> | ||
<math> | <math> | ||
\begin{pmatrix} | \begin{pmatrix} | ||
\mathbf{X}'\mathbf{X}&\mathbf{X}'\mathbf{Z}\\ | \mathbf{X}'\mathbf{X}&\mathbf{X}'\mathbf{Z}\\ | ||
\mathbf{Z}'\mathbf{X}&\mathbf{Z}'\mathbf{Z}+\mathbf{ | \mathbf{Z}'\mathbf{X}&\mathbf{Z}'\mathbf{Z}+\mathbf{K}^{-1}\lambda | ||
\end{pmatrix} | \end{pmatrix} | ||
\begin{pmatrix} | \begin{pmatrix} | ||
| Line 18: | Line 19: | ||
</math> | </math> | ||
</center> | </center> | ||
where <math>\mathbf{X}</math> and <math>\mathbf{Z}</math> are the incidence matrices for the fixed and random effects, <math>\mathbf{ | where <math>\mathbf{X}</math> and <math>\mathbf{Z}</math> are the incidence matrices for the fixed and random effects, <math>\mathbf{K}</math> is a relationship matrix, <math>\hat\boldsymbol{\beta}</math> are estimated fixed effects, <math>\hat\mathbf{u}</math> the predicted breeding values, <math>\mathbf{y}</math> the vector of observed phenotypes, and <math>\lambda=\sigma^2_e/\sigma^2_g</math> is the ratio of the environmental variance <math>\sigma^2_e</math> and the additive genetic variance <math>\sigma^2_g</math>. | ||
In a multiple trait genetic evaluation we have covariances in | In a multiple-trait genetic evaluation we have covariances in addition to variances associated with the random effects<ref> Henderson, C. R., and R. L. Quaas. 1976. Multiple trait evaluation using relatives' records, J. Anim. Sci. 43:1188–1197.</ref><ref>Mrode, R. A. 2005. Best linear unbiased prediction of breeding value: multivariate models. In: Linear models for the prediction of animal breeding values 2nd ed. CAB Int., Wallingford, Oxfordshire, UK. p. 83-119. </ref>. In addition, different animals could have observed phenotypes for different subsets of traits. In the case where we have two traits and with breeding values as the only random effects, the mixed-model equations take the form | ||
<center> | <center> | ||
<math> | <math> | ||
| Line 37: | Line 38: | ||
</math> | </math> | ||
</center> | </center> | ||
where <math>G</math> is the genetic covariance matrix and is a function of | where <math>\mathbf{G}</math> is the genetic covariance matrix and is a function of a relationship matrix <math>\mathbf{K}</math> and genetic variances of the two traits and the genetic covariance between the two traits, and <math>\mathbf{R}</math> is the environmental covariance matrix and is a function of the environmental variances of the two traits and the environmental covariance between the two traits. | ||
==References== | |||
<references /> | |||
Latest revision as of 09:59, 6 April 2022
Multiple-trait genetic evaluation differs from a single-trait evaluation in that several phenotypic traits are evaluated at the same time. Reasons for doing a multiple-trait genetic evaluation include greater prediction accuracy and reduced prediction bias.
As with single-trait genetic evaluation most traits use BLUP to obtain EPD by solving the mixed-model equations. For single traits with breeding values as the only random effect the mixed-model equations take the form
where and are the incidence matrices for the fixed and random effects, is a relationship matrix, are estimated fixed effects, the predicted breeding values, the vector of observed phenotypes, and is the ratio of the environmental variance and the additive genetic variance .
In a multiple-trait genetic evaluation we have covariances in addition to variances associated with the random effects[1][2]. In addition, different animals could have observed phenotypes for different subsets of traits. In the case where we have two traits and with breeding values as the only random effects, the mixed-model equations take the form
where is the genetic covariance matrix and is a function of a relationship matrix and genetic variances of the two traits and the genetic covariance between the two traits, and is the environmental covariance matrix and is a function of the environmental variances of the two traits and the environmental covariance between the two traits.
References
- ↑ Henderson, C. R., and R. L. Quaas. 1976. Multiple trait evaluation using relatives' records, J. Anim. Sci. 43:1188–1197.
- ↑ Mrode, R. A. 2005. Best linear unbiased prediction of breeding value: multivariate models. In: Linear models for the prediction of animal breeding values 2nd ed. CAB Int., Wallingford, Oxfordshire, UK. p. 83-119.
