Function dm2 conducts Diallel Method 2 analysis for RCBD and Alpha Lattice design.
Example 1: Diallel Method 2 analysis for RCBD design.
# Load the package
library(gpbStat)
#> Authors Nandan Patil and Lakshmi Gangavati.
#Load the dataset
data(dm2rcbd)
# View the structure of dataframe.
str(dm2rcbd)
#> Classes 'tbl_df', 'tbl' and 'data.frame': 240 obs. of 4 variables:
#> $ rep : chr "R1" "R1" "R1" "R1" ...
#> $ parent1: num 1 1 1 1 1 1 1 1 1 1 ...
#> $ parent2: num 1 2 3 4 5 6 7 8 9 10 ...
#> $ DTP : num 66.1 58.5 64.6 64.2 59.3 ...
# Conduct Line x Tester analysis
result = dm2(dm2rcbd, rep, parent1, parent2, DTP)
# View the output
result
#> $Means
#> Parent2
#> Parent1 1 2 3 4 5 6 7 8
#> 1 65.31769 56.88736 62.87728 62.19819 57.24611 61.77934 60.23199 59.45378
#> 2 56.88736 63.30941 62.59786 59.43587 56.45149 57.55432 54.75840 56.11425
#> 3 62.87728 62.59786 58.36095 58.25634 60.71883 55.22639 55.12505 54.39954
#> 4 62.19819 59.43587 58.25634 63.77961 57.15805 63.32091 62.43797 55.12414
#> 5 57.24611 56.45149 60.71883 57.15805 65.04595 55.25778 63.89851 59.23282
#> 6 61.77934 57.55432 55.22639 63.32091 55.25778 56.88325 57.10090 58.62343
#> 7 60.23199 54.75840 55.12505 62.43797 63.89851 57.10090 62.30133 58.96640
#> 8 59.45378 56.11425 54.39954 55.12414 59.23282 58.62343 58.96640 58.63107
#> 9 59.99343 57.79246 54.50506 54.49473 54.72035 57.53263 62.70356 63.63800
#> 10 59.99797 58.12088 59.31957 60.58825 61.87032 61.72040 62.36893 62.04768
#> 11 59.14957 58.54128 64.32069 57.06435 62.42775 62.55616 59.98320 57.74982
#> 12 61.39705 62.77292 56.14993 55.74474 59.85430 58.16224 55.39976 62.39437
#> 13 60.53815 61.92330 58.71091 58.35329 58.69939 63.75573 62.00640 62.53515
#> 14 58.17887 59.62638 60.77991 56.50338 58.24740 60.36659 54.76567 55.49799
#> 15 60.59376 62.45391 56.91712 54.69967 56.86290 57.49282 57.68658 58.62889
#> Parent2
#> Parent1 9 10 11 12 13 14 15
#> 1 59.99343 59.99797 59.14957 61.39705 60.53815 58.17887 60.59376
#> 2 57.79246 58.12088 58.54128 62.77292 61.92330 59.62638 62.45391
#> 3 54.50506 59.31957 64.32069 56.14993 58.71091 60.77991 56.91712
#> 4 54.49473 60.58825 57.06435 55.74474 58.35329 56.50338 54.69967
#> 5 54.72035 61.87032 62.42775 59.85430 58.69939 58.24740 56.86290
#> 6 57.53263 61.72040 62.55616 58.16224 63.75573 60.36659 57.49282
#> 7 62.70356 62.36893 59.98320 55.39976 62.00640 54.76567 57.68658
#> 8 63.63800 62.04768 57.74982 62.39437 62.53515 55.49799 58.62889
#> 9 59.77470 62.65702 60.58196 62.10251 59.52592 58.40839 55.08259
#> 10 62.65702 63.39327 62.95963 58.22418 57.78493 57.43079 59.65661
#> 11 60.58196 62.95963 64.44419 62.62254 62.53704 64.48712 62.86311
#> 12 62.10251 58.22418 62.62254 64.76169 60.89386 59.95167 62.43614
#> 13 59.52592 57.78493 62.53704 60.89386 61.82842 55.83338 63.19762
#> 14 58.40839 57.43079 64.48712 59.95167 55.83338 63.09888 55.26263
#> 15 55.08259 59.65661 62.86311 62.43614 63.19762 55.26263 58.64814
#>
#> $ANOVA
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 1 503.76789 503.7678929 979.33212 2.878133e-59
#> Genotypes 119 2050.09712 17.2277069 33.49091 1.434100e-58
#> Residuals 119 61.21353 0.5143994 NA NA
#>
#> $`Co efficient of ariation`
#> [1] 1.202472
#>
#> $`Diallel ANOVA`
#> Df Sum Sq Mean Sq F value Pr(>F)
#> gca 14 190.03 13.5738 52.775 < 2.2e-16 ***
#> sca 105 835.02 7.9525 30.920 < 2.2e-16 ***
#> Error 119 30.61 0.2572
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> $`Genetic variances`
#> Components
#> gca 0.7833266
#> sca 7.6953340
#> gca/sca 0.1017924
#>
#> $`Combining ability effects`
#> Parent1 Parent2 Parent3 Parent4 Parent5 Parent6
#> Parent1 0.9903421 -3.5909078 3.282732 2.2323001 -3.29618002 1.738335
#> Parent2 NA -0.1572282 4.150876 0.6175547 -2.94322206 -1.339114
#> Parent3 NA NA -1.040942 0.3217366 2.20783036 -2.783330
#> Parent4 NA NA NA -0.6696061 -1.72428674 4.939854
#> Parent5 NA NA NA NA -0.09320439 -3.699678
#> Parent6 NA NA NA NA NA -0.594485
#> Parent7 NA NA NA NA NA NA
#> Parent8 NA NA NA NA NA NA
#> Parent9 NA NA NA NA NA NA
#> Parent10 NA NA NA NA NA NA
#> Parent11 NA NA NA NA NA NA
#> Parent12 NA NA NA NA NA NA
#> Parent13 NA NA NA NA NA NA
#> Parent14 NA NA NA NA NA NA
#> Parent15 NA NA NA NA NA NA
#> Parent7 Parent8 Parent9 Parent10 Parent11 Parent12
#> Parent1 -0.2690067 -0.4373583 0.007025405 -1.6499496 -3.3924020 -0.02122193
#> Parent2 -4.5950278 -2.6293207 -1.046375687 -2.3794715 -2.8531208 2.50222266
#> Parent3 -3.3446630 -3.4603089 -3.450064238 -0.2970702 3.8099996 -3.23705191
#> Parent4 3.5969203 -3.1070514 -3.831733007 0.6002765 -3.8176735 -4.01358089
#> Parent5 4.4810596 0.4252294 -4.182515333 1.3059498 0.9693226 -0.48041658
#> Parent6 -1.8152715 0.3171145 -0.868947362 1.6573031 1.5990125 -1.67119915
#> Parent7 -0.1344958 0.2001023 3.841983864 1.8458473 -1.4339331 -4.89366893
#> Parent8 NA -0.7443537 5.386282248 2.1344515 -3.0574576 2.71080035
#> Parent9 NA NA -0.649082319 2.6485273 -0.3205932 2.32366496
#> Parent10 NA NA NA 1.0124292 0.3955646 -3.21617158
#> Parent11 NA NA NA NA 1.9064819 0.28813378
#> Parent12 NA NA NA NA NA 0.78277604
#> Parent13 NA NA NA NA NA NA
#> Parent14 NA NA NA NA NA NA
#> Parent15 NA NA NA NA NA NA
#> Parent13 Parent14 Parent15
#> Parent1 -1.01672572 -1.7045958 0.7342505
#> Parent2 1.51599938 0.8904886 3.7419789
#> Parent3 -0.81268115 2.9277286 -0.9111020
#> Parent4 -1.54164192 -1.7201357 -3.4998837
#> Parent5 -1.77193727 -0.5525174 -1.9130559
#> Parent6 3.78568415 2.0679497 -0.7818603
#> Parent7 1.57636353 -3.9929557 -1.0480845
#> Parent8 2.71496708 -2.6507822 0.5040763
#> Parent9 -0.38953293 0.1643507 -3.1374949
#> Parent10 -3.79202953 -2.4747643 -0.2249810
#> Parent11 0.06602831 3.6875123 2.0874612
#> Parent12 -0.45345331 0.2757705 2.7841964
#> Parent13 0.91938373 -3.9791285 3.4090766
#> Parent14 NA -0.7520286 -2.8545007
#> Parent15 NA NA -0.7759868
#>
#> $`Standard Error`
#> SE.gi SE.sii SE.sij SE.gi.gj SE.sii.sjj SE.sij.sik SE.sij.skl
#> 0.1188308 0.4783640 0.4456157 0.1739505 0.6271876 0.6958022 0.6737075
#>
#> $`Critical Diffiernece`
#> CD.gi CD.sii CD.sij CD.gi.gj CD.sii.sjj CD.sij.sik CD.sij.skl
#> 0.2352969 0.9472085 0.8823635 0.3444394 1.2418941 1.3777578 1.3340082
Example 2: Diallel Method 2 analysis for Alpha Lattice design.
# Load the package
library(gpbStat)
#Load the dataset
data(dm2alpha)
# View the structure of dataframe.
str(dm2alpha)
#> Classes 'tbl_df', 'tbl' and 'data.frame': 480 obs. of 5 variables:
#> $ rep : chr "R1" "R1" "R1" "R1" ...
#> $ blk : num 1 1 1 1 1 1 1 1 1 1 ...
#> $ parent1: num 1 1 1 1 2 2 3 3 4 4 ...
#> $ parent2: num 1 1 13 13 11 11 10 10 10 10 ...
#> $ TW : num 27.7 27.7 44.6 44.6 34.1 ...
# Conduct Line x Tester analysis
result1 = dm2(dm2alpha, rep, parent1, parent2, TW, blk)
# View the output
result1
#> $Means
#> Parent2
#> Parent1 1 2 3 4 5 6 7 8
#> 1 27.35716 42.49592 33.33549 38.38259 41.04511 31.68449 40.38514 33.82362
#> 2 42.49592 29.41499 44.78182 29.44646 33.69656 30.86238 41.08097 26.01838
#> 3 33.33549 44.78182 30.40429 42.71467 39.02395 31.39843 41.13707 29.02640
#> 4 38.38259 29.44646 42.71467 29.45758 28.65377 34.15101 31.69933 33.15276
#> 5 41.04511 33.69656 39.02395 28.65377 29.63547 42.93362 36.19820 31.57199
#> 6 31.68449 30.86238 31.39843 34.15101 42.93362 25.56161 41.79217 34.14662
#> 7 40.38514 41.08097 41.13707 31.69933 36.19820 41.79217 28.38963 31.41263
#> 8 33.82362 26.01838 29.02640 33.15276 31.57199 34.14662 31.41263 27.89065
#> 9 40.08071 39.09142 40.97035 38.80323 33.53286 33.89595 30.64368 20.45790
#> 10 44.45401 27.78430 36.77403 24.96920 39.67590 39.82497 26.91861 41.47731
#> 11 38.93248 33.91690 34.27300 39.67739 31.79479 34.18531 32.33842 25.94789
#> 12 35.94649 35.47457 38.04122 41.06441 29.22585 41.56607 24.87163 43.49301
#> 13 43.91240 42.46279 43.14500 36.59900 32.59368 39.35168 37.02426 41.04036
#> 14 40.59316 27.52325 40.65135 30.00840 30.70765 38.86631 40.89827 41.16348
#> 15 40.08879 37.06153 29.02207 30.12130 31.40344 32.97605 34.64001 37.82528
#> Parent2
#> Parent1 9 10 11 12 13 14 15
#> 1 40.08071 44.45401 38.93248 35.94649 43.91240 40.59316 40.08879
#> 2 39.09142 27.78430 33.91690 35.47457 42.46279 27.52325 37.06153
#> 3 40.97035 36.77403 34.27300 38.04122 43.14500 40.65135 29.02207
#> 4 38.80323 24.96920 39.67739 41.06441 36.59900 30.00840 30.12130
#> 5 33.53286 39.67590 31.79479 29.22585 32.59368 30.70765 31.40344
#> 6 33.89595 39.82497 34.18531 41.56607 39.35168 38.86631 32.97605
#> 7 30.64368 26.91861 32.33842 24.87163 37.02426 40.89827 34.64001
#> 8 20.45790 41.47731 25.94789 43.49301 41.04036 41.16348 37.82528
#> 9 29.10623 32.92903 36.17057 36.66664 37.38611 31.58198 22.20694
#> 10 32.92903 28.44400 34.95221 29.16054 33.26105 37.60354 40.63187
#> 11 36.17057 34.95221 30.19585 33.11510 43.40287 38.55817 38.29352
#> 12 36.66664 29.16054 33.11510 30.46528 31.92854 35.81305 33.62252
#> 13 37.38611 33.26105 43.40287 31.92854 31.17509 40.13448 33.56593
#> 14 31.58198 37.60354 38.55817 35.81305 40.13448 28.17794 36.73569
#> 15 22.20694 40.63187 38.29352 33.62252 33.56593 36.73569 28.68100
#>
#> $ANOVA
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 1 119.02466 119.0246631 376.146982 2.493852e-57
#> Treatments 119 14135.57471 118.7863421 375.393829 1.216712e-312
#> Replication:Block 11 13.96149 1.2692264 4.011065 1.574599e-05
#> Residuals 348 110.11808 0.3164313 NA NA
#>
#> $`Co efficient of Variation`
#> [1] 1.61958
#>
#> $`Diallel ANOVA`
#> Df Sum Sq Mean Sq F value Pr(>F)
#> gca 14 426.45 30.4610 192.53 < 2.2e-16 ***
#> sca 105 3107.44 29.5947 187.05 < 2.2e-16 ***
#> Error 348 55.06 0.1582
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> $`Genetic variances`
#> Components
#> gca 1.78251579
#> sca 29.43645009
#> gca/sca 0.06055471
#>
#> $`Combining ability effects`
#> Parent1 Parent2 Parent3 Parent4 Parent5 Parent6
#> Parent1 2.597242 5.4716266 -5.722693 2.074094 4.5619327 -5.8239812
#> Parent2 NA -0.3055515 8.626427 -3.959244 0.1161762 -3.7432926
#> Parent3 NA NA 1.728342 7.275079 3.4096730 -5.2411431
#> Parent4 NA NA NA -1.021348 -4.2108209 0.2611291
#> Parent5 NA NA NA NA -0.8466641 8.8690525
#> Parent6 NA NA NA NA NA 0.1786286
#> Parent7 NA NA NA NA NA NA
#> Parent8 NA NA NA NA NA NA
#> Parent9 NA NA NA NA NA NA
#> Parent10 NA NA NA NA NA NA
#> Parent11 NA NA NA NA NA NA
#> Parent12 NA NA NA NA NA NA
#> Parent13 NA NA NA NA NA NA
#> Parent14 NA NA NA NA NA NA
#> Parent15 NA NA NA NA NA NA
#> Parent7 Parent8 Parent9 Parent10 Parent11 Parent12
#> Parent1 3.520122 -1.7778316 4.1092049 7.61928458 1.58917985 -1.100913
#> Parent2 7.118745 -6.6802772 6.0227089 -6.14762984 -0.52360436 1.329953
#> Parent3 5.140953 -5.7061525 5.8677482 0.80820502 -2.20139737 1.862709
#> Parent4 -1.547097 1.1698986 6.4503167 -8.24693355 5.95268778 7.635596
#> Parent5 2.777088 -0.5855568 1.0052635 6.28508873 -2.10459794 -4.377651
#> Parent6 7.345758 0.9637843 0.3430592 5.40886339 -0.73937420 6.937277
#> Parent7 -0.464820 -1.1267574 -2.2657611 -6.85405119 -1.94281704 -9.113715
#> Parent8 NA -1.7283924 -11.1879623 8.96821914 -7.06976769 10.771234
#> Parent9 NA NA -1.3583416 0.04988729 2.78285876 3.574818
#> Parent10 NA NA NA -0.49512040 0.70127249 -4.794502
#> Parent11 NA NA NA NA 0.01345319 -1.348521
#> Parent12 NA NA NA NA NA -0.282435
#> Parent13 NA NA NA NA NA NA
#> Parent14 NA NA NA NA NA NA
#> Parent15 NA NA NA NA NA NA
#> Parent13 Parent14 Parent15
#> Parent1 4.0862845 2.5884329 3.9451073
#> Parent2 5.5394600 -7.5786873 3.8206419
#> Parent3 4.1877770 3.5155204 -6.2527140
#> Parent4 0.3914685 -4.3777359 -2.4037925
#> Parent5 -3.7885337 -3.8531754 -1.2963405
#> Parent6 1.9441758 3.2801999 -0.7490210
#> Parent7 0.2602011 5.9556033 1.5583885
#> Parent8 5.5398779 7.4843913 6.0072244
#> Parent9 1.5155698 -2.4671683 -9.9811671
#> Parent10 -3.4727071 2.6911768 7.5805421
#> Parent11 6.1605348 3.1372344 4.7336270
#> Parent12 -5.0179056 0.6879984 0.3585124
#> Parent13 2.4962779 2.2307154 -2.4767881
#> Parent14 NA 0.6748851 2.5143593
#> Parent15 NA NA -1.1861555
#>
#> $`Standard Error`
#> SE.gi SE.sii SE.sij SE.gi.gj SE.sii.sjj SE.sij.sik SE.sij.skl
#> 0.09320058 0.37518712 0.34950218 0.13643168 0.49191142 0.54572672 0.52839763
#>
#> $`Critical Diffiernece`
#> CD.gi CD.sii CD.sij CD.gi.gj CD.sii.sjj CD.sij.sik CD.sij.skl
#> 0.1833073 0.7379196 0.6874024 0.2683344 0.9674935 1.0733376 1.0392547