s_data_root <- "https://charlotte-ngs.github.io/lbgfs2024/data"
s_pgbv_p04 <- file.path(s_data_root, "aural_exam_pgbv_p04.csv")
tbl_pgbv_p04 <- readr::read_delim(s_pgbv_p04,
delim = ",",
show_col_types = FALSE)Prediction of Genomic Breeding Values
The following dataset is used to predict genomic breeding values. The column \(y\) contains the observations and columns S1 to S15 contain genotypes of 15 SNP marker loci.
In [1]:
The dataset shown as table
In [2]:
knitr::kable(tbl_pgbv_p04)| ID | sex | y | S1 | S2 | S3 | S4 | S5 | S6 | S7 | S8 | S9 | S10 | S11 | S12 | S13 | S14 | S15 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | M | 59.0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 2 | 1 | 1 |
| 2 | M | 33.5 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 |
| 3 | F | 75.1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 2 | 1 | 0 |
| 4 | F | 83.9 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 2 | 1 | 0 | 0 |
| 5 | F | 52.4 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 |
| 6 | M | 62.5 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 1 | 1 | 1 |
| 7 | F | 59.7 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |
| 8 | M | 81.1 | 1 | 0 | 2 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 2 |
| 9 | M | 54.4 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 2 | 1 | 0 | 0 |
| 10 | M | 29.0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 2 |
Use a marker effect model (MEM) to predict genomic breeding values for the animals given in the dataset shown above. Specify the marker effect model as a mathematical formula and list the meaning of all model components. Indicate the expected values and the variance-covariance matrices for all random effects in the model. You can assume \(\lambda = \sigma_e^2 / \sigma_q^2 = 1\).
Predict genomic breeding values using a breeding value based model (BVM) for all animals in the above given dataset. Specify the model as a mathematical formula and list the meaning of all model components. Indicate the expected values and the variance-covariance matrices for all random effects in the model. You can assume \(\lambda = \sigma_e^2 / \sigma_g^2 = 3\).