blupf90은 ssGBLUP을 위하여 만든 프로그램이다. 그래서 gblup model을 다루기 위해서는 약간의 트릭이 필요하다. 그래서 renumf90으로 renumbering한 후 renumf90이 만들어낸 파라미터 파일을 이용하여 pregsf90을 실행하고 blupf90을 실행할 수 없다. pregsf90을 실행할 파라미터 파일을 직접 만들어 주어야 한다.
GBLUP과 ssGBLUP의 차이는 유전체 자료를 가지고 있지 않은 개체가 평가 모형에 포함되느냐 아니냐의 차이다. 유전체 자료(SNP data)를 이용해서 NRM과 비슷한 행렬을 만든다. 그것을 GRM(genomic relationship matrix)라고 한다. 이 GRM의 효율을 높이기 위하여 NRM을 약간 섞는데 NRM 1%, 5%, 10%정도 섞을 수 있다. 이상은 Mrode 책에 나오는 설명인데 예제에서는 정확하게 NRM을 몇 % 섞었는지 설명이 없다. 아래 예제에서는 NRM을 1% 섞는 것으로 한다. 또한 책에서는 주어진 혈통 그 이상을 알고 있어 계산한 NRM이 주어지는데 본 예제에서는 주어진 혈통 이외의 혈통을 알 수가 없으므로 책에 주어진 NRM과 같은 NRM을 구할 수가 없다. 결론적으로 책과 같은 해를 구할 수가 없다. 자세한 사항은 다음 글을 참고한다.
masuday.github.io/blupf90_tutorial/mrode_c11ex113_gblup.html
Numerical examples from Mrode (2014)
Numerical examples from Mrode (2014) Yutaka Masuda September 2019 Back to index.html. GBLUP Model The SNP marker model is equivalent to a model, so-called GBLUP, under some assumptions. The model includes a genomic relationship matrix, \(\mathbf{G}\). This
masuday.github.io
gblup_snpgenotype.txt
13 20110002120000000000000000000000000000000000000000
14 10000202100000000000000000000000000000000000000000
15 11211002120000000000000000000000000000000000000000
16 00210102210000000000000000000000000000000000000000
17 01120002120000000000000000000000000000000000000000
18 11010202210000000000000000000000000000000000000000
19 00110202200000000000000000000000000000000000000000
20 01100102200000000000000000000000000000000000000000
21 20000122120000000000000000000000000000000000000000
22 00011202000000000000000000000000000000000000000000
23 01100102210000000000000000000000000000000000000000
24 10001102000000000000000000000000000000000000000000
25 00011202100000000000000000000000000000000000000000
26 10110201000000000000000000000000000000000000000000
10개의 SNP 이외의 genotype이 있는데 pregsf90이 50개 미만의 SNP자료를 읽지를 못하여 부가적으로 붙인 것인다. 결과에 영향을 미치지 않는다.
gblup_snpgenotype_XrefID.txt
13 13
14 14
15 15
16 16
17 17
18 18
19 19
20 20
21 21
22 22
23 23
24 24
25 25
26 26
gblup_data.txt
13 0 0 1 558 9 0.001792115 1
14 0 0 1 722 13.4 0.001385042 2
15 13 4 1 300 12.7 0.003333333 3
16 15 2 1 73 15.4 0.01369863 4
17 15 5 1 52 5.9 0.019230769 5
18 14 6 1 87 7.7 0.011494253 6
19 14 9 1 64 10.2 0.015625 7
20 14 9 1 103 4.8 0.009708738 8
관측치는 6열이고 8열은 1열(개체 ID)의 새로운 ID이다.
gblup_pedi.txt
1 0 0
2 0 0
3 0 0
4 0 0
5 0 0
6 0 0
7 0 0
8 0 0
9 0 0
10 0 0
11 0 0
12 0 0
13 0 0
14 0 0
15 13 4
16 15 2
17 15 5
18 14 6
19 14 9
20 14 9
21 1 3
22 14 8
23 14 11
24 14 10
25 14 7
26 14 12
pregsf90_gblup.par
# BLUPF90 parameter file created by RENUMF90
DATAFILE
gblup_data.txt
NUMBER_OF_TRAITS
1
NUMBER_OF_EFFECTS
2
OBSERVATION(S)
6
WEIGHT(S)
EFFECTS: POSITIONS_IN_DATAFILE NUMBER_OF_LEVELS TYPE_OF_EFFECT[EFFECT NESTED]
4 1 cross
1 26 cross
RANDOM_RESIDUAL VALUES
245.00
RANDOM_GROUP
2
RANDOM_TYPE
add_animal
FILE
gblup_pedi.txt
(CO)VARIANCES
35.250
OPTION SNP_file gblup_snpgenotype.txt gblup_snpgenotype_XrefID.txt
OPTION no_quality_control
OPTION AlphaBeta 0.99 0.01
OPTION tunedG 0
OPTION saveAscii
OPTION saveG
OPTION saveGInverse
OPTION createGimA22i 0
pregsf90 실행 화면
pregsf90 실행 로그
pregsf90_gblup.par
preGSf90 ver. 1.19
Parameter file: pregsf90_gblup.par
Data file: gblup_data.txt
Number of Traits 1
Number of Effects 2
Position of Observations 6
Position of Weight (1) 0
Value of Missing Trait/Observation 0
EFFECTS
# type position (2) levels [positions for nested]
1 cross-classified 4 1
2 cross-classified 1 26
Residual (co)variance Matrix
245.00
Random Effect(s) 2
Type of Random Effect: additive animal
Pedigree File: gblup_pedi.txt
trait effect (CO)VARIANCES
1 2 35.25
REMARKS
(1) Weight position 0 means no weights utilized
(2) Effect positions of 0 for some effects and traits means that such
effects are missing for specified traits
Options read from parameter file for genomic
* SNP format: BLUPF90 standard (text)
* SNP file: gblup_snpgenotype.txt
* SNP Xref file: gblup_snpgenotype_XrefID.txt
* NOT CreateGimA22i (default=.false.)
* Save G Matrix (default=.false.)
* Save G Inverse matrix (default=.false.)
* No Quality Control Checks !!!!! (default .false.): T
* Create a tuned G (default = 2): 0
* AlphaBeta defaults alpha=0.95, beta=0.05) : 0.99 0.01
* Matrix in Ascii format(default=binary)
*--------------------------------------------------------------*
* Genomic Library: Dist Version 1.281 *
* *
* Optimized OpenMP Version - 6 threads *
* *
* Modified relationship matrix (H) created for effect: 2 *
*--------------------------------------------------------------*
Read 26 animals from pedigree file: "D:\users\bhpark\2020\job\공부하기\07_Linear Models for the Prediction of Animal Breeding Values_3rd_Mrode\20_gblup for computing SNP effects_blupf90\gblup_pedi.txt"
Number of Genotyped Animals: 14
Creating A22
Extracting subset of: 26 pedigrees from: 26 ...elapsed time: 0.0000
Calculating A22 Matrix by Colleau OpenMP...elapsed time: .0004
Numbers of threads=1 6
Reading SNP file
Column position in file for the first marker: 4
Format to read SNP file: (3x,400000i1)
Number of SNPs: 50
Format: integer genotypes (0 to 5) to double-precision array
Number of Genotyped animals: 14
Reading SNP file elapsed time: .00
Statistics of alleles frequencies in the current population
N: 50
Mean: 0.079
Min: 0.000
Max: 0.964
Var: 0.038
Quality Control - Monomorphic SNPs Exist - NOT REMOVED: 40
Genotypes missings (%): 0.000
Calculating G Matrix
Dgemm MKL #threads= 1 6 Elapsed omp_get_time: 0.0005
Scale by Sum(2pq). Average: 3.53826530612245
Detecting samples with similar genotypes
elapsed time= 0.0
Blend G as alpha*G + beta*A22: (alpha,beta) 0.990 0.010
Frequency - Diagonal of G
N: 14
Mean: 1.131
Min: 0.668
Max: 2.267
Range: 0.080
Class: 20
#Class Class Count
1 0.6681 1
2 0.7480 5
3 0.8280 1
4 0.9079 0
5 0.9879 0
6 1.068 2
7 1.148 1
8 1.228 0
9 1.308 0
10 1.388 0
11 1.468 1
12 1.547 1
13 1.627 1
14 1.707 0
15 1.787 0
16 1.867 0
17 1.947 0
18 2.027 0
19 2.107 0
20 2.187 1
21 2.267 0
Check for diagonal of genomic relationship matrix
** High Diagonal of genotype 3 1.63 Not Removed
** High Diagonal of genotype 9 2.27 Not Removed
** Low Diagonal of genotype 11 0.67 Not Removed
Check for diagonal of genomic relationship matrix, genotypes not removed: 3
------------------------------
Final Pedigree-Based Matrix
------------------------------
Statistic of Rel. Matrix A22
N Mean Min Max Var
Diagonal 14 1.000 1.000 1.000 0.000
Off-diagonal 182 0.148 0.000 0.500 0.032
----------------------
Final Genomic Matrix
----------------------
Statistic of Genomic Matrix
N Mean Min Max Var
Diagonal 14 1.131 0.668 2.267 0.210
Off-diagonal 182 -0.085 -0.941 1.043 0.203
Correlation of Genomic Inbreeding and Pedigree Inbreeding
Variance of Y is Zero !!
Correlation: 0.0000
Diagonal elements
Estimating Regression Coefficients G = b0 11' + b1 A + e
Regression coefficients b0 b1 = NaN NaN
Correlation diagonal elements G & A NaN
All elements - Diagonal / Off-Diagonal
Estimating Regression Coefficients G = b0 11' + b1 A + e
Regression coefficients b0 b1 = -0.300 1.443
Correlation all elements G & A 0.733
Off-Diagonal
Using 84 elements from A22 >= .02000
Estimating Regression Coefficients G = b0 11' + b1 A + e
Regression coefficients b0 b1 = -0.215 1.226
Correlation Off-Diagonal elements G & A 0.361
***********************************************************************
* CORRELATION FOR OFF-DIAGONALS G & A22 IS LOW THAN 0.50 !!!!! *
* MISIDENTIFIED GENOMIC SAMPLES OR POOR QUALITY GENOMIC DATA *
***********************************************************************
Saving G in file: "G"
elapsed time= 0.0
Creating A22-inverse
Inverse LAPACK MKL dpotrf/i #threads= 1 6 Elapsed omp_get_time: 0.0019
----------------------
Final A22 Inv Matrix
----------------------
Statistic of Inv. Rel. Matrix A22
N Mean Min Max Var
Diagonal 14 1.536 1.000 3.500 0.364
Off-diagonal 182 -0.082 -0.667 0.000 0.046
Creating G-inverse
Inverse LAPACK MKL dpotrf/i #threads= 1 6 Elapsed omp_get_time: 0.0000
--------------------------
Final Genomic Inv Matrix
--------------------------
Statistic of Inv. Genomic Matrix
N Mean Min Max Var
Diagonal 14 41.948 3.572 88.271 687.247
Off-diagonal 182 -0.425 -44.402 39.443 305.004
Saving G-inverse in file: "Gi"
elapsed time= 0.0
*--------------------------------------------------*
* Setup Genomic Done !!!, elapsed time: 0.043 *
*--------------------------------------------------*
자세한 설명은 생략. 실제 자료가 아니라 문제가 막 튀어 나오는데 QC를 하지 않으므로 그냥 PASS
pregsf90 실행 결과로 생긴 파일
freqdata.count : allele frequency
1 0.321429
2 0.178571
3 0.357143
4 0.357143
5 0.142857
6 0.607143
7 0.071429
8 0.964286
9 0.571429
10 0.392857
11 0.000000
12 0.000000
13 0.000000
14 0.000000
15 0.000000
16 0.000000
17 0.000000
18 0.000000
19 0.000000
20 0.000000
21 0.000000
22 0.000000
23 0.000000
24 0.000000
25 0.000000
26 0.000000
27 0.000000
28 0.000000
29 0.000000
30 0.000000
31 0.000000
32 0.000000
33 0.000000
34 0.000000
35 0.000000
36 0.000000
37 0.000000
38 0.000000
39 0.000000
40 0.000000
41 0.000000
42 0.000000
43 0.000000
44 0.000000
45 0.000000
46 0.000000
47 0.000000
48 0.000000
49 0.000000
50 0.000000
sum2pq
3.53826530612245
NRM을 1% 섞은 Genomic Relationship Matrix
1 1 1.467519840782
1 2 -.441110314271
2 2 .748038939835
1 3 .982865906929
2 3 -.920764248235
3 3 1.627404485436
1 4 .061029200220
2 4 -.441110314271
3 4 .423269650637
4 4 .907923584490
1 5 .680582198257
2 5 -.940749828817
3 5 1.042822648674
4 5 .400784070111
5 5 1.587433324273
1 6 -.161312186125
2 6 .183442683655
3 6 -.361167991943
4 6 -.161312186125
5 6 -.101355444379
6 6 .748038939835
1 7 -.700922861835
2 7 .203428264237
3 7 -.620980539508
4 7 .418269650749
5 7 -.361167991943
6 7 .200928264293
7 7 .788010100999
1 8 -.541038217180
2 8 .083514780746
3 8 -.181297766707
4 8 .298356167258
5 8 -.201283347289
6 8 .081014780801
7 8 .383298489473
8 8 .827981262162
1 9 .877938004131
2 9 .098500361439
3 9 .118485942021
4 9 -.521052636598
5 9 -.181297766707
6 9 .098500361439
7 9 -.720908442417
8 9 -.561023797762
9 9 2.266943064056
1 10 -.780865184162
2 10 .403284070055
3 10 -.700922861835
4 10 -.501067056016
5 10 -.441110314271
6 10 -.158812186181
7 10 .140971522547
8 10 -.258740089090
9 10 -.521052636598
10 10 1.187721712636
1 11 -.201283347289
2 11 -.136326605655
3 11 .158457103185
4 11 .358312909003
5 11 .138471522603
6 11 .140971522547
7 11 .160957103129
8 11 .600639875930
9 11 -.221268927871
10 11 -.478581475490
11 11 .668096617507
1 12 -.141326605543
2 12 .483226392383
3 12 -.341182411362
4 12 -.700922861835
5 12 -.640966120089
6 12 -.358667991999
7 12 -.338682411417
8 12 -.178797766763
9 12 .118485942021
10 12 .700567778839
11 12 -.398639153163
12 12 1.067808229145
1 13 -.820836345326
2 13 .363312908891
3 13 -.740894022999
4 13 -.261240089034
5 13 -.481081475435
6 13 .081014780801
7 13 .380798489529
8 13 -.018913122108
9 13 -.561023797762
10 13 .860452423494
11 13 -.238754508508
12 13 .380798489529
13 13 .827981262162
1 14 -.261240089034
2 14 .363312908891
3 14 -.461095894853
4 14 -.261240089034
5 14 -.481081475435
6 14 -.198783347345
7 14 .101000361383
8 14 -.298711250254
9 14 -.281225669616
10 14 .580654295348
11 14 -.518552636654
12 14 .380798489529
13 14 .260885006038
14 14 1.107779390308
NRM을 구성할 때 혈통을 이용
NRM을 1% 섞은 GRM의 inverse
1 1 36.374112147756
1 2 -27.980861774302
2 2 88.270926666259
1 3 -8.255548353247
2 3 31.300275470378
3 3 17.520566628931
1 4 -7.273154470752
2 4 -7.935058588596
3 4 -13.839579561710
4 4 59.029844228979
1 5 -16.994409615350
2 5 26.742040202839
3 5 10.825563830254
4 5 1.183435492773
5 5 16.559517365607
1 6 1.865090988759
2 6 -30.838117848755
3 6 -13.961143487346
4 6 35.035830728961
5 6 -3.740681212886
6 6 33.908530891321
1 7 1.034309816800
2 7 -16.074769262009
3 7 10.966959887452
4 7 -44.042226922475
5 7 6.054790042008
6 7 -9.402982983010
7 7 76.598931919425
1 8 23.579731230504
2 8 -3.254062300818
3 8 -4.373575563548
4 8 13.642319923702
5 8 -10.355941361690
6 8 4.610816099161
7 8 -30.643656293298
8 8 38.819147341585
1 9 2.957758933413
2 9 -1.421961970816
3 9 1.150380418263
4 9 4.069157034358
5 9 1.660646618910
6 9 4.195695275841
7 9 2.332803703845
8 9 3.865774059947
9 9 3.571863763864
1 10 39.442736583671
2 10 -44.401612414027
3 10 -15.360569585413
4 10 8.964674694062
5 10 -23.795163924540
6 10 17.932250568059
7 10 -4.681081006798
8 10 31.070735197126
9 10 4.523044730378
10 10 65.241156282393
1 11 15.759887763419
2 11 -27.861655984766
3 11 -3.670240835263
4 11 -16.848814124536
5 11 -5.409628976497
6 11 1.618086379708
7 11 31.963192006762
8 11 -11.691869904844
9 11 2.296427605333
10 11 12.420172214465
11 11 33.289780498461
1 12 -17.655277777373
2 12 -31.453869451043
3 12 -9.610207612292
4 12 24.984206447650
5 12 8.978713862467
6 12 33.085527157687
7 12 24.524531681789
8 12 -26.201393052725
9 12 3.932687423384
10 12 -9.861323926268
11 12 12.723588395898
12 12 65.529756384831
1 13 .709886622910
2 13 38.437384536377
3 13 12.371399723371
4 13 -3.932589146850
5 13 8.462389615927
6 13 -19.286778706349
7 13 -23.250880956380
8 13 11.745624274467
9 13 1.096598339716
10 13 -22.528242543689
11 13 -8.688864312408
12 13 -29.485256595986
13 13 46.430966020324
1 14 5.177116824003
2 14 -6.092801764317
3 14 -1.151050225076
4 14 4.327310182797
5 14 .465043915303
6 14 5.157724634274
7 14 .443047275678
8 14 3.079022874246
9 14 2.906885066300
10 14 2.733882533018
11 14 6.555679888597
12 14 5.120296531692
13 14 4.504947248223
14 14 6.133181220876
blupf90 실행 화면
blupf90 실행 로그
blupf90_gblup.par
BLUPF90 ver. 1.68
Parameter file: blupf90_gblup.par
Data file: gblup_data.txt
Number of Traits 1
Number of Effects 2
Position of Observations 6
Position of Weight (1) 0
Value of Missing Trait/Observation 0
EFFECTS
# type position (2) levels [positions for nested]
1 cross-classified 4 1
2 cross-classified 8 14
Residual (co)variance Matrix
245.00
Random Effect(s) 2
Type of Random Effect: user defined from file
User File: Gi
trait effect (CO)VARIANCES
1 2 35.25
REMARKS
(1) Weight position 0 means no weights utilized
(2) Effect positions of 0 for some effects and traits means that such
effects are missing for specified traits
* The limited number of OpenMP threads = 4
* solving method (default=PCG):FSPAK
Data record length = 8
# equations = 15
G
35.250
read 8 records in 0.1562500 s, 17
nonzeroes
g_usr_inv: read 105 elements
largest row, column, diagonal: 14 14 14
user defined matrix
36.3741 -27.9809 -8.2555 -7.2732 -16.9944 1.8651 1.0343 23.5797 2.9578 39.4427 15.7599 -17.6553 0.7099 5.1771
-27.9809 88.2709 31.3003 -7.9351 26.7420 -30.8381 -16.0748 -3.2541 -1.4220 -44.4016 -27.8617 -31.4539 38.4374 -6.0928
-8.2555 31.3003 17.5206 -13.8396 10.8256 -13.9611 10.9670 -4.3736 1.1504 -15.3606 -3.6702 -9.6102 12.3714 -1.1511
-7.2732 -7.9351 -13.8396 59.0298 1.1834 35.0358 -44.0422 13.6423 4.0692 8.9647 -16.8488 24.9842 -3.9326 4.3273
-16.9944 26.7420 10.8256 1.1834 16.5595 -3.7407 6.0548 -10.3559 1.6606 -23.7952 -5.4096 8.9787 8.4624 0.4650
1.8651 -30.8381 -13.9611 35.0358 -3.7407 33.9085 -9.4030 4.6108 4.1957 17.9323 1.6181 33.0855 -19.2868 5.1577
1.0343 -16.0748 10.9670 -44.0422 6.0548 -9.4030 76.5989 -30.6437 2.3328 -4.6811 31.9632 24.5245 -23.2509 0.4430
23.5797 -3.2541 -4.3736 13.6423 -10.3559 4.6108 -30.6437 38.8191 3.8658 31.0707 -11.6919 -26.2014 11.7456 3.0790
2.9578 -1.4220 1.1504 4.0692 1.6606 4.1957 2.3328 3.8658 3.5719 4.5230 2.2964 3.9327 1.0966 2.9069
39.4427 -44.4016 -15.3606 8.9647 -23.7952 17.9323 -4.6811 31.0707 4.5230 65.2412 12.4202 -9.8613 -22.5282 2.7339
15.7599 -27.8617 -3.6702 -16.8488 -5.4096 1.6181 31.9632 -11.6919 2.2964 12.4202 33.2898 12.7236 -8.6889 6.5557
-17.6553 -31.4539 -9.6102 24.9842 8.9787 33.0855 24.5245 -26.2014 3.9327 -9.8613 12.7236 65.5298 -29.4853 5.1203
0.7099 38.4374 12.3714 -3.9326 8.4624 -19.2868 -23.2509 11.7456 1.0966 -22.5282 -8.6889 -29.4853 46.4310 4.5049
5.1771 -6.0928 -1.1511 4.3273 0.4650 5.1577 0.4430 3.0790 2.9069 2.7339 6.5557 5.1203 4.5049 6.1332
finished peds in 0.1562500 s, 114 nonzeroes
left hand side
0.0327 0.0041 0.0041 0.0041 0.0041 0.0041 0.0041 0.0041 0.0041 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0041 1.0360 -0.7938 -0.2342 -0.2063 -0.4821 0.0529 0.0293 0.6689 0.0839 1.1189 0.4471 -0.5009 0.0201 0.1469
0.0041 -0.7938 2.5082 0.8880 -0.2251 0.7586 -0.8748 -0.4560 -0.0923 -0.0403 -1.2596 -0.7904 -0.8923 1.0904 -0.1728
0.0041 -0.2342 0.8880 0.5011 -0.3926 0.3071 -0.3961 0.3111 -0.1241 0.0326 -0.4358 -0.1041 -0.2726 0.3510 -0.0327
0.0041 -0.2063 -0.2251 -0.3926 1.6787 0.0336 0.9939 -1.2494 0.3870 0.1154 0.2543 -0.4780 0.7088 -0.1116 0.1228
0.0041 -0.4821 0.7586 0.3071 0.0336 0.4739 -0.1061 0.1718 -0.2938 0.0471 -0.6750 -0.1535 0.2547 0.2401 0.0132
0.0041 0.0529 -0.8748 -0.3961 0.9939 -0.1061 0.9660 -0.2668 0.1308 0.1190 0.5087 0.0459 0.9386 -0.5471 0.1463
0.0041 0.0293 -0.4560 0.3111 -1.2494 0.1718 -0.2668 2.1771 -0.8693 0.0662 -0.1328 0.9068 0.6957 -0.6596 0.0126
0.0041 0.6689 -0.0923 -0.1241 0.3870 -0.2938 0.1308 -0.8693 1.1053 0.1097 0.8814 -0.3317 -0.7433 0.3332 0.0873
0.0000 0.0839 -0.0403 0.0326 0.1154 0.0471 0.1190 0.0662 0.1097 0.1013 0.1283 0.0651 0.1116 0.0311 0.0825
0.0000 1.1189 -1.2596 -0.4358 0.2543 -0.6750 0.5087 -0.1328 0.8814 0.1283 1.8508 0.3523 -0.2798 -0.6391 0.0776
0.0000 0.4471 -0.7904 -0.1041 -0.4780 -0.1535 0.0459 0.9068 -0.3317 0.0651 0.3523 0.9444 0.3610 -0.2465 0.1860
0.0000 -0.5009 -0.8923 -0.2726 0.7088 0.2547 0.9386 0.6957 -0.7433 0.1116 -0.2798 0.3610 1.8590 -0.8365 0.1453
0.0000 0.0201 1.0904 0.3510 -0.1116 0.2401 -0.5471 -0.6596 0.3332 0.0311 -0.6391 -0.2465 -0.8365 1.3172 0.1278
0.0000 0.1469 -0.1728 -0.0327 0.1228 0.0132 0.1463 0.0126 0.0873 0.0825 0.0776 0.1860 0.1453 0.1278 0.1740
right hand side:
0.32 0.04 0.05 0.05 0.06 0.02 0.03 0.04 0.02 0.00
0.00 0.00 0.00 0.00 0.00
solution:
9.94 0.07 0.11 0.05 0.26 -0.49 -0.36 0.14 -0.23 0.03
0.11 -0.24 0.14 0.05 0.35
solutions stored in file: "solutions"
blupf90 실행 결과 : solutions
trait/effect level solution
1 1 1 9.94327493
1 2 1 0.06981142
1 2 2 0.11059485
1 2 3 0.04780743
1 2 4 0.25776306
1 2 5 -0.49280367
1 2 6 -0.35505536
1 2 7 0.14266450
1 2 8 -0.22698269
1 2 9 0.02673761
1 2 10 0.11379233
1 2 11 -0.23776246
1 2 12 0.14174468
1 2 13 0.05374991
1 2 14 0.35057024