The function ltcmt conducts Line x Tester analysis for multiple traits when the data contains only crosses. The experimental design may be RCBD or Alpha lattice design.
# Load the package
library(gpbStat)
#Load the dataset
data("alphaltcmt")
# View the structure of dataframe.
str(alphaltcmt)
#> Classes 'tbl_df', 'tbl' and 'data.frame': 60 obs. of 7 variables:
#> $ replication: num 1 1 1 1 1 1 1 1 1 1 ...
#> $ block : num 1 1 1 2 2 2 3 3 3 4 ...
#> $ line : chr "l5" "l1" "l2" "l2" ...
#> $ tester : chr "t1" "t3" "t3" "t1" ...
#> $ hsw : num 26.7 22.1 26.2 25.7 18 ...
#> $ sh : num 82.2 83.6 83.8 81.7 81.6 ...
#> $ gy : num 61.3 30.7 48.1 25.9 29.1 ...
# Conduct Line x Tester analysis
result = ltcmt(alphaltcmt, replication, line, tester, alphaltcmt[,5:7], block)
#>
#> Analysis of Line x Tester for Multiple traits
#> Warning in sqrt(x): NaNs produced
#> Warning in sqrt(x): NaNs produced
#> Warning in sqrt(x): NaNs produced
#> Warning in sqrt(x): NaNs produced
#> Warning in sqrt(x): NaNs produced
#> Warning in sqrt(x): NaNs produced
# View the output
result
#> $Mean
#> $Mean$hsw
#> Tester
#> Line 1 2 3
#> 1 24.28100 24.38975 26.43250
#> 2 24.75150 23.17850 23.85100
#> 3 22.12950 25.09375 25.46600
#> 4 25.36125 26.52300 26.32225
#> 5 24.40525 23.86375 22.90450
#>
#> $Mean$sh
#> Tester
#> Line 1 2 3
#> 1 82.93436 83.87124 84.20399
#> 2 83.89508 84.62547 83.77366
#> 3 83.61044 84.45869 83.04424
#> 4 84.27547 84.32636 81.81483
#> 5 83.04301 82.58873 84.83067
#>
#> $Mean$gy
#> Tester
#> Line 1 2 3
#> 1 54.26683 48.86251 44.75305
#> 2 44.95867 45.31223 47.39452
#> 3 46.06275 54.77228 55.05693
#> 4 60.56487 52.13965 53.79695
#> 5 58.26799 53.53054 53.55139
#>
#>
#> $ANOVA
#> $ANOVA$hsw
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 123.547315 41.182438 5.2008347 0.006007617
#> Blocks within Replication 16 159.485732 9.967858 1.2588177 0.292524662
#> Crosses 14 95.615586 6.829685 0.8625051 0.603263868
#> Lines 4 44.431866 11.107966 1.0223891 0.406049177
#> Testers 2 6.558666 3.279333 0.3018333 0.740946613
#> Lines X Testers 8 44.625055 5.578132 0.5134172 0.839950285
#> Error 26 205.879143 7.918429 NA NA
#> Total 59 584.527775 NA NA NA
#>
#> $ANOVA$sh
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 47.865214 15.9550714 5.5805022 0.004306487
#> Blocks within Replication 16 61.859599 3.8662250 1.3522645 0.240056532
#> Crosses 14 40.010784 2.8579131 0.9995938 0.481506718
#> Lines 4 3.066186 0.7665466 0.1874088 0.943757507
#> Testers 2 2.486129 1.2430645 0.3039100 0.739429879
#> Lines X Testers 8 34.458468 4.3073085 1.0530702 0.412196780
#> Error 26 74.335936 2.8590745 NA NA
#> Total 59 224.071534 NA NA NA
#>
#> $ANOVA$gy
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 3170.89296 1056.96432 7.6637547 0.0007890292
#> Blocks within Replication 16 2338.16012 146.13501 1.0595843 0.4350901435
#> Crosses 14 1411.76346 100.84025 0.7311646 0.7260111510
#> Lines 4 787.68515 196.92129 0.9743323 0.4310135285
#> Testers 2 48.50139 24.25070 0.1199882 0.8872136703
#> Lines X Testers 8 575.57692 71.94711 0.3559818 0.9379857942
#> Error 26 3585.84969 137.91730 NA NA
#> Total 59 10506.66623 NA NA NA
#>
#>
#> $GCA.Line
#> Trait 1 Trait 2 Trait 3
#> Line 1 0.4375167 -0.01655394 -2.258613
#> Line 2 -0.6699000 0.41165231 -5.664270
#> Line 3 -0.3671500 0.01804113 0.411244
#> Line 4 1.4719333 -0.21419481 3.947743
#> Line 5 -0.8724000 -0.19894469 3.563895
#>
#> $GCA.Tester
#> Trait 1 Trait 2 Trait 3
#> Tester 1 -0.41120 -0.1347434 1.2714786
#> Tester 2 0.01285 0.2876815 -0.6293023
#> Tester 3 0.39835 -0.1529380 -0.6421764
#>
#> $SCA
#> $SCA$`Trait 1`
#> Tester
#> Line 1 2 3
#> 1 -0.3422167 -0.6575167 0.9997333
#> 2 1.2357000 -0.7613500 -0.4743500
#> 3 -1.6890500 0.8511500 0.8379000
#> 4 -0.2963833 0.4413167 -0.1449333
#> 5 1.0919500 0.1264000 -1.2183500
#>
#> $SCA$`Trait 2`
#> Tester
#> Line 1 2 3
#> 1 -0.60075619 -0.08630744 0.6870636
#> 2 -0.06824822 0.23971724 -0.1714690
#> 3 0.04072451 0.46655392 -0.5072784
#> 4 0.93799581 0.56645558 -1.5044514
#> 5 -0.30971591 -1.18641930 1.4961352
#>
#> $SCA$`Trait 3`
#> Tester
#> Line 1 2 3
#> 1 3.701222 0.19768507 -3.8989074
#> 2 -2.201279 0.05305477 2.1482244
#> 3 -7.172713 3.43759274 3.7351205
#> 4 3.792902 -2.73153863 -1.0613638
#> 5 1.879868 -0.95679396 -0.9230737
#>
#>
#> $CV
#> Trait1 Trait2 Trait3
#> 11.440345 2.020495 22.780202
#>
#> $Genetic.Variance.Covariance.
#> Phenotypic Variance Genotypic Variance Environmental Variance
#> Trait 1 -0.6697598 -8.588188 7.918429
#> Trait 2 -0.4152151 -3.274290 2.859074
#> Trait 3 -101.1137222 -239.031018 137.917296
#> Phenotypic coefficient of Variation Genotypic coefficient of Variation
#> Trait 1 NaN NaN
#> Trait 2 NaN NaN
#> Trait 3 NaN NaN
#> Environmental coefficient of Variation Broad sense heritability
#> Trait 1 11.440345 12.822788
#> Trait 2 2.020495 7.885767
#> Trait 3 22.780202 2.363982
#>
#> $Std.Error
#> S.E. gca for line S.E. gca for tester S.E. sca effect
#> Trait 1 0.8123232 0.6292229 1.4069851
#> Trait 2 0.4881150 0.3780922 0.8454399
#> Trait 3 3.3901487 2.6259979 5.8719097
#> S.E. (gi - gj)line S.E. (gi - gj)tester S.E. (sij - skl)tester
#> Trait 1 1.1487985 0.8898555 1.989777
#> Trait 2 0.6902988 0.5347031 1.195633
#> Trait 3 4.7943942 3.7137218 8.304134
#>
#> $C.D.
#> C.D. gca for line C.D. gca for tester C.D. sca effect
#> Trait 1 1.669754 1.2933861 2.892099
#> Trait 2 1.003335 0.7771797 1.737827
#> Trait 3 6.968550 5.3978159 12.069883
#> C.D. (gi - gj)line C.D. (gi - gj)tester C.D. (sij - skl)tester
#> Trait 1 2.361389 1.829124 4.090046
#> Trait 2 1.418929 1.099098 2.457658
#> Trait 3 9.855018 7.633664 17.069393
#>
#> $Add.Dom.Var
#> Cov H.S. (line) Cov H.S. (tester) Cov H.S. (average) Cov F.S. (average)
#> Trait 1 0.4608195 -0.1149399 0.03318511 -0.3379446
#> Trait 2 -0.2950635 -0.1532122 -0.03843094 -0.1627380
#> Trait 3 10.4145144 -2.3848209 0.76610579 -10.5634695
#> Addittive Variance(F=0) Addittive Variance(F=1) Dominance Variance(F=0)
#> Trait 1 0.1327405 0.06637023 -1.170148
#> Trait 2 -0.1537238 -0.07686188 0.724117
#> Trait 3 3.0644232 1.53221158 -32.985091
#> Dominance Variance(F=1)
#> Trait 1 -0.5850742
#> Trait 2 0.3620585
#> Trait 3 -16.4925453
#>
#> $Contribution.of.Line.Tester
#> Lines Tester Line x Tester
#> Trait 1 46.46927 6.859411 46.67132
#> Trait 2 7.66340 6.213647 86.12295
#> Trait 3 55.79441 3.435518 40.77007# Load the package
library(gpbStat)
#Load the dataset
data("rcbdltcmt")
# View the structure of dataframe.
str(rcbdltc)
#> Classes 'tbl_df', 'tbl' and 'data.frame': 60 obs. of 4 variables:
#> $ replication: num 1 2 3 4 1 2 3 4 1 2 ...
#> $ line : num 1 1 1 1 1 1 1 1 1 1 ...
#> $ tester : num 6 6 6 6 7 7 7 7 8 8 ...
#> $ yield : num 74.4 70.9 60.9 68 91.8 ...
# Conduct Line x Tester analysis
result1 = ltcmt(rcbdltcmt, replication, line, tester, rcbdltcmt[,4:5])
# View the output
result1
#> $Mean
#> $Mean$ph
#> Tester
#> Line 1 2 3
#> 1 188.25 184.65 168.40
#> 2 169.80 188.00 202.00
#> 3 177.50 177.25 197.75
#> 4 172.00 171.25 183.25
#> 5 197.75 202.00 175.50
#>
#> $Mean$eh
#> Tester
#> Line 1 2 3
#> 1 71.45 80.675 72.25
#> 2 79.50 95.500 97.25
#> 3 90.00 91.500 100.50
#> 4 81.00 80.000 88.00
#> 5 102.25 102.500 87.00
#>
#>
#> $ANOVA
#> $ANOVA$ph
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 442.4927 147.4976 0.5028866 0.68235896
#> Crosses 14 7885.4240 563.2446 1.9203581 0.05197320
#> Lines 4 1816.0907 454.0227 1.6010303 0.19053280
#> Testers 2 213.1320 106.5660 0.3757861 0.68888394
#> Lines X Testers 8 5856.2013 732.0252 2.5813568 0.02068038
#> Error 42 12318.6773 293.3018 NA NA
#> Total 59 20646.5940 NA NA NA
#>
#> $ANOVA$eh
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 162.4298 54.14328 0.6740871 5.727648e-01
#> Crosses 14 5957.8783 425.56274 5.2982817 1.239227e-05
#> Lines 4 3942.9167 985.72917 12.5449584 6.156545e-07
#> Testers 2 302.4323 151.21617 1.9244642 1.577768e-01
#> Lines X Testers 8 1712.5293 214.06617 2.7243296 1.541154e-02
#> Error 42 3373.4777 80.32090 NA NA
#> Total 59 9493.7858 NA NA NA
#>
#>
#> $GCA.Line
#> Trait 1 Trait 2
#> Line 1 -3.2566667 -13.166667
#> Line 2 2.9100000 2.791667
#> Line 3 0.4766667 6.041667
#> Line 4 -8.1900000 -4.958333
#> Line 5 8.0600000 9.291667
#>
#> $GCA.Tester
#> Trait 1 Trait 2
#> Tester 1 -2.63 -3.118333
#> Tester 2 0.94 2.076667
#> Tester 3 1.69 1.041667
#>
#> $SCA
#> $SCA$`Trait 1`
#> Tester
#> Line 1 2 3
#> 1 10.446667 3.276667 -13.72333
#> 2 -14.170000 0.460000 13.71000
#> 3 -4.036667 -7.856667 11.89333
#> 4 -0.870000 -5.190000 6.06000
#> 5 8.630000 9.310000 -17.94000
#>
#> $SCA$`Trait 2`
#> Tester
#> Line 1 2 3
#> 1 -0.2233333 3.806667 -3.583333
#> 2 -8.1316667 2.673333 5.458333
#> 3 -0.8816667 -4.576667 5.458333
#> 4 1.1183333 -5.076667 3.958333
#> 5 8.1183333 3.173333 -11.291667
#>
#>
#> $CV
#> [1] 9.323348 10.189134
#>
#> $Genetic.Variance.Covariance
#> Phenotypic Variance Genotypic Variance Environmental Variance
#> Trait 1 397.2386 103.93675 293.3018
#> Trait 2 173.1758 92.85487 80.3209
#> Phenotypic coefficient of Variation Genotypic coefficient of Variation
#> Trait 1 10.85026 5.550078
#> Trait 2 14.96120 10.955327
#> Environmental coefficient of Variation Broad sense heritability
#> Trait 1 9.323348 0.2616482
#> Trait 2 10.189134 0.5361886
#>
#> $Std.Error
#> S.E. gca for line S.E. gca for tester S.E. sca effect
#> Trait 1 4.943867 3.829503 8.563029
#> Trait 2 2.587162 2.004007 4.481096
#> S.E. (gi - gj)line S.E. (gi - gj)tester S.E. (sij - skl)tester
#> Trait 1 6.991684 5.415735 12.109951
#> Trait 2 3.658800 2.834094 6.337227
#>
#> $C.D.
#> C.D. gca for line C.D. gca for tester C.D. sca effect
#> Trait 1 9.892655 7.662817 17.134581
#> Trait 2 5.176900 4.010009 8.966653
#> C.D. (gi - gj)line C.D. (gi - gj)tester C.D. (sij - skl)tester
#> Trait 1 13.990327 10.836860 24.23196
#> Trait 2 7.321242 5.671009 12.68076
#>
#> $Add.Dom.Var
#> Cov H.S. (line) Cov H.S. (tester) Cov H.S. (average) Cov F.S. (average)
#> Trait 1 -23.16688 -31.27296 -4.475243 37.37585
#> Trait 2 64.30525 -3.14250 5.607864 88.76549
#> Addittive Variance(F=0) Addittive Variance(F=1) Dominance Variance(F=0)
#> Trait 1 -17.90097 -8.950486 219.36166
#> Trait 2 22.43145 11.215727 66.87263
#> Dominance Variance(F=1)
#> Trait 1 109.68083
#> Trait 2 33.43632
#>
#> $Contribution.of.Line.Tester
#> Lines Tester Line x Tester
#> Trait 1 23.03098 2.702860 74.26616
#> Trait 2 66.17988 5.076175 28.74395