Problem 1: Predicted Traditional Breeding Values For Progeny
According to the results from Exercise 4, animals 6 and 9 are mated to each other. The result of this mating are two male and two female offspring. From the two brothers and the two sisters the better male offspring and the better female offspring should be selected. Figure @ref(fig:pedigreemating) shows the pedigree of the described matings.
Your Tasks
- Compute the predicted breeding values for all offspring from mating animals 6 and 9, assuming that the offspring do not have any observations.
- Is it possible to find the better male and female offspring based on the predicted
Hints
- The breeding values of the offspring can either be derived using an argument from quantiative genetics about the relationship of predicted breeding values of parents and progeny or it can be computed by extending the mixed model equation from Problem 1 in Exercise 4.
Your Solution
In a first step, the predicted breeding values of the four offsprings are computed from the predicted breeding values of their parents. We have to remember that we do not have genomic information available and that the predicted breeding values of the parents are the result of a BLUP animal model.
In the second step, we want to verify the result by extending the traditional BLUP animal model by the four offspring. To do that, we have to set up the mixed model equations for the extended pedigree. The mixed model equations, require the vector \(y\) and matrices \(X\), \(Z\) and \(A^{-1}\)
# vector y
# matrix X
# matrix Z
# inverse matrix of A can be computed with pedigreemm
# set up mixed model equations as coefficient matrix and right-hand side
# solve mixed model equations
Problem 2: Genomic Breeding Values For Progeny
The four offsprings of parents 6 and 9 also have genotype data. The complete genomic data for all animals can be read from
https://charlotte-ngs.github.io/gelasmss2021/data/data_ex05_p02_gen.csv
Your Tasks
- Predict genomic breeding values as in Problem 2 of Exercise 4 using a GBLUP approach. But this time the four offsprings of parents 6 and 9 are also included in the analysis.
- Try to rank the four offpsring according to their genomic breeding value.
Hints
- Use the same phenotypic information as in Problem 1.
- Use the same procedure to make the genomic relationship matrix \(G\) invertible as shown in Problem 2 of Exercise 4.
- Use the same model as in Problem 2 of Exercise 4.
Your Solution
We are predicting breeding values using Genomic BLUP (GBLUP). This means, we have to set up the mixed model equations, but instead of the numerator relationship matrix \(A\), we are using the genomic relationship matrix \(G\). The steps to the solution are the same, but we have to adapt the matrices that are required.
# vector y
# matrix X
# matrix Z
# inverse matrix G
# mixed model equations
# solve mixed model equations
Latest Changes: 2021-03-26 09:54:38 (pvr)
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bWF0cmljZXMgdGhhdCBhcmUgcmVxdWlyZWQuIAoKYGBge3J9CiMgdmVjdG9yIHkKCiMgbWF0cml4IFgKCiMgbWF0cml4IFoKCiMgaW52ZXJzZSBtYXRyaXggRwoKIyBtaXhlZCBtb2RlbCBlcXVhdGlvbnMKCiMgc29sdmUgbWl4ZWQgbW9kZWwgZXF1YXRpb25zCgpgYGAKCgogCgoKYGBge3IsIGVjaG89RkFMU0UsIHJlc3VsdHM9J2FzaXMnfQpjYXQoJ1xuLS0tXG5cbiBfTGF0ZXN0IENoYW5nZXM6ICcsIGZvcm1hdChTeXMudGltZSgpLCAnJVktJW0tJWQgJUg6JU06JVMnKSwgJyAoJywgU3lzLmluZm8oKVsndXNlciddLCAnKV9cbicsIHNlcCA9ICcnKQpgYGAK