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Genetic Evaluation: Difference between revisions

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When the subject is genetic evaluation, one of the most common questions is “What is the main difference among ssGBLUP, BLUP, and genomic BLUP (GBLUP)?” In a nutshell, ssGBLUP uses phenotypes, pedigree, and genotypes for both genotyped and non-genotyped animals, whereas BLUP uses phenotypes and pedigree for all animals and GBLUP uses phenotypes and genotypes only for genotyped animals.  
When the subject is genetic evaluation, one of the most common questions is “What is the main difference among ssGBLUP, BLUP, and genomic BLUP (GBLUP)?” In a nutshell, ssGBLUP uses phenotypes, pedigree, and genotypes for both genotyped and non-genotyped animals, whereas BLUP uses phenotypes and pedigree for all animals and GBLUP uses phenotypes and genotypes only for genotyped animals.  


In the US, ssGBLUP has been used for genomic evaluation of beef and dairy cattle, pigs, chickens, and fish. For more information about ssGBLUP for beef cattle evaluation check Lourenco et al. (2015)<ref> Lourenco, D. A. L., S. Tsuruta, B. O. Fragomeni, Y. Masuda, I. Aguilar, A. Legarra, J. K. Bertrand, T. Amen, L. Wang, D. W. Moser, and I. Misztal. 2015. Genetic evaluation using single-step genomic best linear unbiased predictor in American Angus. Journal of Animal Science 93: 2653-2662.</ref>, Lourenco et al. (2017)<ref> Lourenco, D.A.L., J.K. Bertrand, H.L. Bradford, S. Miller, and I. Misztal. 2017. The promise of genomics for beef improvement. BIF Meeting (http://www.bifconference.com/bif2017/proceedings/01-lourenco.pdf) </ref>,  and Misztal & Lourenco (2018) <ref> Misztal, I. and D. Lourenco. 2018. Current research in unweighted and weighted ssGBLUP. In Proc. Beef Improvement Federation 11th genetic prediction workshop 11:6-13. </ref>.
In the US, ssGBLUP has been used for genomic evaluation of beef and dairy cattle, pigs, chickens, and fish. Regarding to beef cattle, Angus Genetics Inc. runs ssGBLUP evaluations for American Angus and Charolais, Canadian Angus, Red Angus, and Charolais, and Maine Anjou. Moreover, Livestock Genetic Services (A Neogen Company) runs ssGBLUP evaluations for Santa Gertrudis. For more information about ssGBLUP for beef cattle evaluation check Lourenco et al. (2015)<ref> Lourenco, D. A. L., S. Tsuruta, B. O. Fragomeni, Y. Masuda, I. Aguilar, A. Legarra, J. K. Bertrand, T. Amen, L. Wang, D. W. Moser, and I. Misztal. 2015. Genetic evaluation using single-step genomic best linear unbiased predictor in American Angus. Journal of Animal Science 93: 2653-2662.</ref>, Lourenco et al. (2017)<ref> Lourenco, D.A.L., J.K. Bertrand, H.L. Bradford, S. Miller, and I. Misztal. 2017. The promise of genomics for beef improvement. BIF Meeting (http://www.bifconference.com/bif2017/proceedings/01-lourenco.pdf) </ref>,  and Misztal & Lourenco (2018) <ref> Misztal, I. and D. Lourenco. 2018. Current research in unweighted and weighted ssGBLUP. In Proc. Beef Improvement Federation 11th genetic prediction workshop 11:6-13. </ref>.
 
<em>ssGBLUP for large genotyped populations</em> <p></p>
Running ssGBLUP evaluations for large genotyped populations can be a huge computational challenge. This is because the construction of ''H''<sup>''-1''</sup> requires the construction and inversion of ''G''. Matrix inversion has a cubic computational cost, requiring a large amount of memory. As an example, inverting ''G'' for 100,000 animals requires about 300Gb of memory and takes over 2 hours.
 
The algorithm for proven and young (APY) was proposed by Misztal et al. (2014) <ref> Misztal, I., A. Legarra, and I. Aguilar. 2014. Using recursion to compute the inverse of the genomic relationship matrix. J. Dairy Sci. 97: 3943–3952. </ref> to overcome this computing limitation of ssGBLUP, and was based on Henderson’s algorithm to construct ''A''<sup>''-1''</sup> <ref> Henderson, C.R. 1976. A simple method for computing the inverse of a numerator relationship matrix used in the prediction of breeding values. Biometrics 32:69-83.</ref>. In APY, ''G''<sup>''-1''</sup> is constructed directly, avoiding the matrix inversion step. In this algorithm, genotyped animals are split into two groups: core and non-core. Breeding values of non-core animals are then calculated as functions of breeding values of core animals and the genomic relationships between core and non-core. If the number of genotyped animals surpasses 100,000, using APY ''G''<sup>''-1''</sup> in ssGBLUP is highly recommended. A simple graphic representation of APY ''G''<sup>''-1''</sup> is:
<center>
[[File:figure2_APY.jpg | 250px]]
</center>
 


<em>Marker effects in ssGBLUP</em><p></p>
<em>Marker effects in ssGBLUP</em><p></p>

Revision as of 18:47, 23 February 2019

EPD

Utility (compared to actual/adjusted phenotypes, ratios, disjoined marker scores, etc.) (Suggested writer: Megan Rolf)

Basic Models

BLUP

ssGBLUP (Suggested writer: Daniela Lourenco)

Single-step genomic BLUP (ssGBLUP) [1][2] is a method developed to enable the inclusion of marker genotypes into the well-known BLUP machinery. The idea of ssGBLUP came from the fact that only a small portion of the animals in the pedigree is genotyped. In this way, one approach to account for all animals (i.e., genotyped and non-genotyped) in the evaluation would be to combine pedigree and genomic relationships and use this as the covariance structure in the BLUP mixed model equations. Thus, ssGBLUP uses marker information to construct genomic relationships.

Legarra et al. (2009)[3] stated that genomic evaluations would be simpler if genomic relationships were available for all animals in the model. Then, their idea was to look at the pedigree relationship as a priori relationship and at the genomic relationship as the observed relationship. Based on that, they showed the genomic information could be extended (i.e., imputed) to non-genotyped animals. This means that in ssGBLUP pedigree relationships for non-genotyped animals are enhanced by the genomic information of their relatives. The relationship matrix that combines information for genotyped and non-genotyped animals is represented by H:

Where the subscripts 1 and 2 refer to non-genotyped and genotyped animals, respectively. A is the pedigree relationship matrix and G is the genomic relationship matrix computed based on markers. If M is a matrix of marker genotypes centered for allele frequency (p) and has the dimension of number of animals by number of SNP (n), G is computed as [4]:


Although H is very complicated, H-1 is quite simple [5]:

If we replace A^{-1} by H^{-1} in the BLUP mixed model equations, we have ssGBLUP[6]:

Where b and u are vectors of fixed effects and breeding values, respectively; X and Z are incidence matrices for the effects in b and u; y is a vector of phenotypes, and λ is the ratio of residual to additive genetic variance.

As a combined relationship is used in ssGBLUP, the output for each animal is automatically a genomic EBV, and the mixed model equations above can be simplistically represented as:

The genomic EPD is then calculated as:

When the subject is genetic evaluation, one of the most common questions is “What is the main difference among ssGBLUP, BLUP, and genomic BLUP (GBLUP)?” In a nutshell, ssGBLUP uses phenotypes, pedigree, and genotypes for both genotyped and non-genotyped animals, whereas BLUP uses phenotypes and pedigree for all animals and GBLUP uses phenotypes and genotypes only for genotyped animals.

In the US, ssGBLUP has been used for genomic evaluation of beef and dairy cattle, pigs, chickens, and fish. Regarding to beef cattle, Angus Genetics Inc. runs ssGBLUP evaluations for American Angus and Charolais, Canadian Angus, Red Angus, and Charolais, and Maine Anjou. Moreover, Livestock Genetic Services (A Neogen Company) runs ssGBLUP evaluations for Santa Gertrudis. For more information about ssGBLUP for beef cattle evaluation check Lourenco et al. (2015)[7], Lourenco et al. (2017)[8], and Misztal & Lourenco (2018) [9].

ssGBLUP for large genotyped populations

Running ssGBLUP evaluations for large genotyped populations can be a huge computational challenge. This is because the construction of H-1 requires the construction and inversion of G. Matrix inversion has a cubic computational cost, requiring a large amount of memory. As an example, inverting G for 100,000 animals requires about 300Gb of memory and takes over 2 hours.

The algorithm for proven and young (APY) was proposed by Misztal et al. (2014) [10] to overcome this computing limitation of ssGBLUP, and was based on Henderson’s algorithm to construct A-1 [11]. In APY, G-1 is constructed directly, avoiding the matrix inversion step. In this algorithm, genotyped animals are split into two groups: core and non-core. Breeding values of non-core animals are then calculated as functions of breeding values of core animals and the genomic relationships between core and non-core. If the number of genotyped animals surpasses 100,000, using APY G-1 in ssGBLUP is highly recommended. A simple graphic representation of APY G-1 is:


Marker effects in ssGBLUP

Although the marker information in ssGBLUP is used to construct genomic relationships, it is possible to calculate SNP effects once we obtain genomic EBV (Wang et al., 2012[12], Lourenco et al., 2015[13]). Marker effects can be then used to calculate predictions based only on marker genotypes for young genotyped animals that are not yet or will never make into an official evaluation.

Single-step Hybrid Marker Effects Models (Suggested writer: Bruce Golden)

Interim Calculations

Bias

(in)complete reporting / contemporary groups / preferential treatment (Suggested writer: Bob Weaber

Accuracy (Suggested writer: Matt Spangler)

meaning of accuracy

what impacts accuracy

different definitions of accuracy (true, BIF, reliability)

Variance components (Suggested writer: Steve Kachman)

Impact on EPD, accuracy, genetic gain (Suggested writer: Steve Kachman)

Heterogeneous variance

Connectivity (Suggested writer: Ron Lewis)

Measures of (Suggested writer: Ron Lewis)

==Impact on GE== (Suggested Writer: Ron Lewis)

Current GE

How each breed (organization) is modeling each trait (Suggested writers: Steve Miller, Lauren Hyde, AHA)

  1. Legarra, A., I. Aguilar, and I. Misztal. 2009. A relationship matrix including full pedigree and genomic information. J. Dairy Sci. 92:4656-4663.
  2. Aguilar, I., I. Misztal, D. L. Johnson, A. Legarra, S. Tsuruta, and T. J. Lawlor. 2010. Hot topic: A unified approach to utilize phenotypic, full pedigree, and genomic information for genetic evaluation of Holstein final score. Journal of Dairy Science 93: 743-752.
  3. Legarra, A., I. Aguilar, and I. Misztal. 2009. A relationship matrix including full pedigree and genomic information. J. Dairy Sci. 92:4656-4663.
  4. VanRaden, P. M. 2008. Efficient methods to compute genomic predictions. J. Dairy Sci. 91:4414-4423.
  5. Aguilar, I., I. Misztal, D. L. Johnson, A. Legarra, S. Tsuruta, and T. J. Lawlor. 2010. Hot topic: A unified approach to utilize phenotypic, full pedigree, and genomic information for genetic evaluation of Holstein final score. Journal of Dairy Science 93: 743-752.
  6. Aguilar, I., I. Misztal, D. L. Johnson, A. Legarra, S. Tsuruta, and T. J. Lawlor. 2010. Hot topic: A unified approach to utilize phenotypic, full pedigree, and genomic information for genetic evaluation of Holstein final score. Journal of Dairy Science 93: 743-752.
  7. Lourenco, D. A. L., S. Tsuruta, B. O. Fragomeni, Y. Masuda, I. Aguilar, A. Legarra, J. K. Bertrand, T. Amen, L. Wang, D. W. Moser, and I. Misztal. 2015. Genetic evaluation using single-step genomic best linear unbiased predictor in American Angus. Journal of Animal Science 93: 2653-2662.
  8. Lourenco, D.A.L., J.K. Bertrand, H.L. Bradford, S. Miller, and I. Misztal. 2017. The promise of genomics for beef improvement. BIF Meeting (http://www.bifconference.com/bif2017/proceedings/01-lourenco.pdf)
  9. Misztal, I. and D. Lourenco. 2018. Current research in unweighted and weighted ssGBLUP. In Proc. Beef Improvement Federation 11th genetic prediction workshop 11:6-13.
  10. Misztal, I., A. Legarra, and I. Aguilar. 2014. Using recursion to compute the inverse of the genomic relationship matrix. J. Dairy Sci. 97: 3943–3952.
  11. Henderson, C.R. 1976. A simple method for computing the inverse of a numerator relationship matrix used in the prediction of breeding values. Biometrics 32:69-83.
  12. Wang, H., I. Misztal, I. Aguilar, A. Legarra, and W. M. Muir. 2012. Genome-wide association mapping including phenotypes from relatives without genotypes. Genet. Res. 94(2):73-83.
  13. Lourenco, D. A. L., S. Tsuruta, B. O. Fragomeni, Y. Masuda, I. Aguilar, A. Legarra, J. K. Bertrand, T. Amen, L. Wang, D. W. Moser, and I. Misztal. 2015. Genetic evaluation using single-step genomic best linear unbiased predictor in American Angus. Journal of Animal Science 93: 2653-2662.