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)

#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)
#> 'data.frame':    240 obs. of  5 variables:
#>  $ replication: chr  "r1" "r1" "r1" "r1" ...
#>  $ block      : chr  "b2" "b5" "b6" "b12" ...
#>  $ parent1    : int  1 1 2 1 2 3 1 2 3 4 ...
#>  $ parent2    : int  1 2 2 3 3 3 4 4 4 4 ...
#>  $ TW         : num  27.7 27.7 44.6 44.6 34.1 ...

# Conduct Diallel Analysis
result1 = dm2(dm2alpha, replication, parent1, parent2, TW, block)

# View the output
result1
#> $Means
#>        Parent2
#> Parent1        1        2        3        4        5        6        7        8
#>      1  34.43711 34.43711 39.37157 33.06467 37.36522 34.53972 39.23268 41.75649
#>      2  34.43711 39.37157 38.69548 33.06467 37.36522 35.71489 36.45700 41.75649
#>      3  39.37157 38.69548 38.69548 27.84591 33.95838 35.71489 36.45700 32.21106
#>      4  33.06467 33.06467 27.84591 27.84591 33.95838 34.76627 37.79556 32.21106
#>      5  37.36522 37.36522 33.95838 33.95838 34.53972 34.76627 37.79556 36.55245
#>      6  34.53972 35.71489 35.71489 34.76627 34.76627 39.23268 32.30785 36.55245
#>      7  39.23268 36.45700 36.45700 37.79556 37.79556 32.30785 32.30785 29.98739
#>      8  41.75649 41.75649 32.21106 32.21106 36.55245 36.55245 29.98739 29.98739
#>      9  35.18432 35.18432 40.37017 40.37017 37.10259 37.10259 41.15481 41.15481
#>      10 37.65202 36.53618 36.53618 39.03769 39.03769 34.00577 34.00577 29.19375
#>      11 35.24205 31.97488 31.97488 32.49791 32.49791 42.04574 42.04574 28.60725
#>      12 37.11366 37.11366 34.85844 34.85844 35.99001 35.99001 32.81075 32.81075
#>      13 30.38480 30.38480 40.39449 40.39449 42.50756 42.50756 33.31475 33.31475
#>      14 32.96673 36.88250 36.88250 40.06831 40.06831 34.73526 34.73526 36.98097
#>      15 36.19758 34.07647 34.07647 35.96782 35.96782 34.17183 34.17183 33.36153
#>        Parent2
#> Parent1        9       10       11       12       13       14       15
#>      1  35.18432 37.65202 35.24205 37.11366 30.38480 32.96673 36.19758
#>      2  35.18432 36.53618 31.97488 37.11366 30.38480 36.88250 34.07647
#>      3  40.37017 36.53618 31.97488 34.85844 40.39449 36.88250 34.07647
#>      4  40.37017 39.03769 32.49791 34.85844 40.39449 40.06831 35.96782
#>      5  37.10259 39.03769 32.49791 35.99001 42.50756 40.06831 35.96782
#>      6  37.10259 34.00577 42.04574 35.99001 42.50756 34.73526 34.17183
#>      7  41.15481 34.00577 42.04574 32.81075 33.31475 34.73526 34.17183
#>      8  41.15481 29.19375 28.60725 32.81075 33.31475 36.98097 33.36153
#>      9  37.65202 29.19375 28.60725 28.81494 36.98787 36.98097 33.36153
#>      10 29.19375 35.24205 34.70764 28.81494 36.98787 34.43934 40.02420
#>      11 28.60725 34.70764 34.70764 29.38373 32.50283 34.43934 40.02420
#>      12 28.81494 28.81494 29.38373 29.38373 32.50283 29.15149 37.41538
#>      13 36.98787 36.98787 32.50283 32.50283 32.96673 29.15149 37.41538
#>      14 36.98097 34.43934 34.43934 29.15149 29.15149 36.19758 30.95810
#>      15 33.36153 40.02420 40.02420 37.41538 37.41538 30.95810 30.95810
#> 
#> $ANOVA
#>                    Df    Sum Sq  Mean Sq   F value    Pr(>F)
#> Replication         1   81.1883 81.18830 2.3477738 0.1287171
#> Treatments        119 3086.8726 25.94011 0.7501265 0.9324158
#> Replication:Block  22  774.0140 35.18245 1.0173933 0.4515091
#> Residuals          97 3354.3545 34.58097        NA        NA
#> 
#> $`Co efficient of Variation`
#> [1] 16.69164
#> 
#> $`Diallel ANOVA`
#>        Df  Sum Sq Mean Sq F value Pr(>F)
#> gca    14  214.93  15.352  0.8879 0.5740
#> sca   105 1328.50  12.652  0.7318 0.9414
#> Error  97 1677.18  17.291               
#> 
#> $`Genetic variances`
#>          Components
#> gca     -0.11400667
#> sca     -4.63807702
#> gca/sca  0.02458059
#> 
#> $`Combining ability effects`
#>            Parent1    Parent2   Parent3    Parent4     Parent5    Parent6
#> Parent1  0.5702231 -2.2282544 2.8031705 -2.0245991  0.36891376 -2.4197435
#> Parent2         NA  0.8645744 1.8327300 -2.3189504  0.07456246 -1.5389250
#> Parent3         NA         NA 0.7676086 -7.4407375 -3.23531254 -1.4419592
#> Parent4         NA         NA        NA -0.7115204 -1.75618353 -0.9114479
#> Parent5         NA         NA        NA         NA  1.19551556 -2.8184839
#> Parent6         NA         NA        NA         NA          NA  1.1586731
#> 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   3.2437392  6.971173 -1.39206575  2.0295979  0.4837521  3.5065499
#> Parent2   0.1737017  6.676821 -1.68641706  0.6194025 -3.0777614  3.2121986
#> Parent3   0.2706675 -2.771642  3.59640003  0.7163682 -2.9807956  1.0539489
#> Parent4   3.0883589 -1.292513  5.07552903  4.6970040 -0.9786428  2.5330779
#> Parent5   1.1813229  1.141844 -0.09908242  2.7899680 -2.8856788  1.7576095
#> Parent6  -4.2695400  1.178686 -0.06223995 -2.2051039  6.6989990  1.7944520
#> Parent7   0.1881555 -4.415855  4.96049545 -1.2345864  7.6695165 -0.4142896
#> Parent8          NA -1.015472  6.16412289 -4.8429771 -4.5653485  0.7893378
#> Parent9          NA        NA  0.77559560 -6.6340446 -6.3564160 -4.9975405
#> Parent10         NA        NA          NA -0.1783598  0.6979297 -4.0435851
#> Parent11         NA        NA          NA         NA -1.0424929 -2.6106636
#> Parent12         NA        NA          NA         NA         NA -2.1936764
#> 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  -5.47456663 -2.6662196  0.6663589
#> Parent2  -5.76891793  0.9552010 -1.7490983
#> Parent3   4.33773631  1.0521668 -1.6521325
#> Parent4   5.81686532  5.7171100  1.7183466
#> Parent5   6.02289319  3.8100741 -0.1886894
#> Parent6   6.05973565 -1.4861358 -1.9478368
#> Parent7  -2.16254868 -0.5156182 -0.9773192
#> Parent8  -0.95892124  2.9337212 -0.5839923
#> Parent9   0.92312510  1.1426537 -2.3750598
#> Parent10  1.87708054 -0.4450236  5.2415658
#> Parent11 -1.74382435  0.4191094  6.1056988
#> Parent12 -0.59264080 -3.7175549  4.6480600
#> Parent13  0.05858292 -5.9698143  2.3958007
#> Parent14          NA -0.1678390 -3.8350536
#> Parent15          NA         NA -0.2695682
#> 
#> $`Standard Error`
#>      SE.gi     SE.sii     SE.sij   SE.gi.gj SE.sii.sjj SE.sij.sik SE.sij.skl 
#>  0.9743109  3.9221739  3.6536657  1.4262451  5.1423997  5.7049802  5.5238233 
#> 
#> $`Critical Diffiernece`
#>      CD.gi     CD.sii     CD.sij   CD.gi.gj CD.sii.sjj CD.sij.sik CD.sij.skl 
#>   1.933737   7.784429   7.251515   2.830702  10.206240  11.322806  10.963260