dm2 : Diallel Method 2 analysis for RCBD and Alpha Lattice

Nandan Patil

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