Quick tour of BLUPF90

Yutaka Masuda

September 2019

Trivial analyses for single-step GBLUP

In ssGBLUP, the program requires 5 files: parameter, data, pedigree, marker, and cross-reference files. The first 3 files are the same as a regular animal model so you need additional 2 files for ssGBLUP. In this section, first, we describe the relationship matrices needed in the analysis. Then we introduce the 2 additional files and run the program.

Single-step GBLUP

Model and relationship matrices

To demonstrate ssGBLUP, we will use the same animal model introduced in the previous section \[ y_{ijk} = A_i + S_j + \beta x_k + u_k + e_{ijk} \] where \(u_k\) is the additive genetic effect for an animal \(k\). We treat \(S_j\) as a fixed effect. Following is the mixed model equations. \[ \left[ \begin{array}{ll} \mathbf{X}'\mathbf{R}^{-1}\mathbf{X} & \mathbf{X}'\mathbf{R}^{-1}\mathbf{Z} \\ \mathbf{Z}'\mathbf{R}^{-1}\mathbf{X} & \mathbf{Z}'\mathbf{R}^{-1}\mathbf{Z} + \mathbf{A}^{-1}/\sigma_u^2 \end{array} \right] \left[ \begin{array}{c} \mathbf{\hat{b}}\\ \mathbf{\hat{u}} \end{array} \right] = \left[ \begin{array}{l} \mathbf{X}'\mathbf{R}^{-1}\mathbf{y} \\ \mathbf{Z}'\mathbf{R}^{-1}\mathbf{y} \end{array} \right] \] In ssGBLUP, \(\mathbf{A}^{-1}\) is replaced with \(\mathbf{H}^{-1}\) which has the following structure: \[ \mathbf{H}^{-1} = \mathbf{A}^{-1} + \left[ \begin{array}{cc} \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{G}^{-1}-\mathbf{A}_{22}^{-1} \end{array} \right] \] where \(\mathbf{G}\) is the genomic relationship matrix for genotyped animals and \(\mathbf{A}_{22}\) is the subset of the numerator relationship matrix for genotyped animals. So this method can combine both genotyped and non-genotyped animals in the same equations.

BLUPF90 prepares \(\mathbf{G}^{-1}\) and \(\mathbf{A}_{22}^{-1}\) before the program solves the equations. The program also checks SNP markers and reports errors if found.

Files

We can use exactly the same data and pedigree files used in the previous animal model. We, nevertheless, put different file names to data and pedigree to avoid the confusion.

  3.0  1  1  1.0   6
  2.0  1  2  1.0   9
  4.0  1  1  2.0  12
  6.0  2  2  2.0   7
  3.0  2  1  1.0  10
  6.0  2  2  2.0  13
  6.0  3  1  2.0   8
  6.0  3  2  1.0  11
  8.0  3  1  1.0  14
  4.0  3  2  2.0  15

The following is the pedigree file.

The parameter file is also the same except for an option to read a marker file.

DATAFILE
data4.txt
NUMBER_OF_TRAITS
1
NUMBER_OF_EFFECTS
4
OBSERVATION(S)
1
WEIGHT(S)

EFFECTS:
2  3 cross
3  2 cross
4  1 cov
5 15 cross
RANDOM_RESIDUAL VALUES
2.0
RANDOM_GROUP
4
RANDOM_TYPE
add_animal
FILE
pedigree4.txt
(CO)VARIANCES
0.5
OPTION SNP_file snp4.txt snp4index.txt

The last line specifies the name of the marker file. The option SNP file makes BLUPF90 read the marker file snp4.txt and the cross-reference file snp4index.txt, and invoke the genomic computations. You can omit the second argument (the name of cross-reference file) if its name is the name of marker file + _XrefID. In this case, if the cross-reference file is snp4.txt_XrefID, you can omit the second argument in that option.

We assume only 8 animals are genotyped (2, 4, 6, 10, 11, 12, 13, and 15). We also assume each genotyped animal has the original name and the marker file contains the names (ID002, ID004, ID006, ID010, ID011, ID012, ID013, and ID015, respectively). The following is the marker file.

ID002 1212020111001211212000102001202022201112000110020102011001012212110122100001210101112200210
ID004 2222020200110122210121001100022221102111000010011202020002002222000222000020120000020200200
ID006 2122020101100221121111212100112111112212000101012211111001201211112022100201220110022200220
ID010 2111121101111210121211112210202021211211000110021211111001101211101122100111221000022200120
ID011 2211121200121111220211011210112121111201000120011202020002002222000222000021221000021200110
ID012 2222020200110122210121001100022221102111000010011202020002002222000222000020120000020200200
ID013 2122020101210121121222101200112122102212000010012211111001101211101122100110220000021200210
ID015 2122020101210121121222101200112122102212000010012211111001101211101122100110220000021200210

BLUPF90 accepts only a marker file prepared with the following rules.

A marker file is a text file with a fixed-width format including 2 columns.
The first column contains an animal’s ID. You don’t have to use the common ID to data and pedigree. So you can put the animal’s original ID here. (BLUPF90 actually skip this column so you can put any information here.)
The second column contains an animal’s genotypes. It has 4 possible value: 0 (homozygote), 1 (heterozygote), 2 (alternative homozygote) and 5 (missing or unknown).
All the second column must start with a fixed position in a line. In the above example, the second column always starts the 9th character.
Each genotyped animals must have the same number of markers.
You must not insert a space between 2 adjacent genotypes.
You don’t have to sort the marker file by ID.

The program will immediately stop if it finds the inconsistent data in the file.

We need one more file to run BLUPF90. The last file is a cross-reference file that relates the integer code used in BLUPF90 to the ID in the marker file. This is a text file with 2 columns separated with spaces.

2 ID002
4 ID004
6 ID006
10 ID010
11 ID011
12 ID012
13 ID013
15 ID015

The order of animals must be the same as the marker file. The first column contains the integer value (common to pedigree file) and the second line has the original ID found in the marker file. This file can be automatically prepared by RENUMF90.

Why do we consider such a tricky example? Because the original-ID-in-the-marker-file situation actually happens in real life. A farm animal usually has a unique (original) ID and phenotypes. Pedigrees and genotypes are recorded with the original ID whereas BLUPF90 accepts only an integer value as an animal’s ID. So we usually use RENUMF90 to replace the original ID with integer values and create renumbered files. However, the marker file is really huge and it is very inefficient to replace the original ID with an integer code. The RENUMF90 does not rewrite the marker file. Instead, RENUMF90 generates the cross-reference file to make the correspondence between the ID in markers and the ID in pedigree.

Running the program

We can now run BLUPF90 program with the 5 files. You can see a very long output from the genomic routine on the screen. We briefly explain what happens in this process.

Read the pedigrees for genotyped animals and compute \(\mathbf{A}_{22}\).
Read SNP markers and perform quality control on the data (possibly remove unqualified markers).
Compute \(\mathbf{G}\) and compare it with \(\mathbf{A}_{22}\).
Compute \(\mathbf{A}_{22}^{-1}\) and \(\mathbf{G}^{-1}\).
Finally compute \(\mathbf{G}^{-1}-\mathbf{A}_{22}^{-1}\) as a gingle matrix, and store them into a file.
After the process, BLUPF90 starts building the system of the mixed model equations with \(\mathbf{G}^{-1} - \mathbf{A}_{22}^{-1}\), and the program solve it.

There are many options to precisely control the genomic routine. Each option has the default value. The user should know the default behavior of the program. This explanation is out of the scope of this introductory chapter. We will see the details in the later chapters.

After running the program, we can find the solutions file.

trait/effect level  solution
   1   1         1      0.23340767
   1   1         2      2.19314788
   1   1         3      3.16386924
   1   2         1      2.28753998
   1   2         2      1.69948874
   1   3         1      0.52196308
   1   4         1      0.00700521
   1   4         2      0.08747780
   1   4         3     -0.01954304
   1   4         4      0.02639925
   1   4         5      0.07679027
   1   4         6     -0.18438116
   1   4         7      0.15271384
   1   4         8     -0.09012753
   1   4         9      0.01442435
   1   4        10     -0.23558188
   1   4        11      0.22278505
   1   4        12      0.10730577
   1   4        13      0.20708267
   1   4        14      0.32362808
   1   4        15     -0.21760840

Single-step GBLUP directly provides GEBV (estimated breeding values enhanced with genomic information). The above solutions for animals are GEBV. The values are very different from the previous animal-model analysis. This is due to the model difference as well as the small data.

Remarks

If your marker data is relatively large, you should consider a more efficient way. Each relationship matrix created in the genomic routine is fully stored in memory i.e., dense matrix consuming a lot of memory. The required memory is 8\(n^2\) /\(1024^3\) GB (gigabytes) for each relationship matrix with \(n\) genotyped animals. Computing time will be longer with many genotyped animals. To determine appropriate options to obtain stable GEBV, you should run the program many times. You can save a relationship matrix to a file and reuse the file.

The PREGSF90 performs the genomic computations only. It can do the same computation as BLUPF90 does (except for the solution of mixed model equations). The best practice is to run PREGSF90 to check and clean up the markers, to compute the relationship matrices, and to save the matrices to files before you run BLUPF90. BLUPF90 can read the files generated with PREGSF90, and you can save your time.

Summary

BLUPF90 can perform a single-step GBLUP (ssGBLUP) analysis.
With ssGBLUP, a marker file and cross-reference file are needed in addition to data, pedigree, and parameter files needed in a regular animal model analysis.
An option in a parameter file is needed.
There are many options to control genomic computations. See the manual.
The marker file is a fixed-length text file with an animal’s ID and genotypes.
Cross-reference (XrefID) file relates the animal’s ID in marker file to integer code in the pedigree file. This file is generated by RENUMF90.
GEBV is directly obtained as a solution.
PREGSF90 is useful to save a relationship matrix to a file if you run the program several times using the same pedigree and genomic information. BLUPF90 reads the file so you can save time.

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