Griffing: Diallel Analysis using Griffing Approach

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/Griffing.R

Description

Griffing is used for performing Diallel Analysis using Griffing's Approach.

Usage

1
Griffing(y, Rep, Cross1, Cross2, data, Method, Model)

Arguments

y

Numeric Response Vector

Rep

Replicate as factor

Cross1

Cross 1 as factor

Cross2

Cross 2 as factor

data

A data.frame

Method

Method for Diallel Analysis using Griffing's approach. It can take 1, 2, 3, or 4 as argument depending on the method being used.

  1. Method-I (Parents + F_{1}'s + reciprocals);

  2. Method-II (Parents and one set of F_{1}'s);

  3. Method-III (One set of F_{1}'s and reciprocals);

  4. Method-IV (One set of F_{1}'s only).

Model

Model for Diallel Analysis using Griffing's approach. It can take 1 or 2 as arguments depending on the model being used.

  1. Fixed Effects Model;

  2. Random Effects Model.

Details

Diallel Analysis using Griffing's approach.

Value

Means Means

ANOVA Analysis of Variance (ANOVA) table

Genetic.Components Genetic Components

Effects Effects of Crosses

StdErr Standard Errors of Crosses

Author(s)

Muhammad Yaseen (myaseen208@gmail.com)

References

  1. Griffing, B. (1956) Concept of General and Specific Combining Ability in relation to Diallel Crossing Systems. Australian Journal of Biological Sciences, 9(4), 463–493.

  2. Singh, R. K. and Chaudhary, B. D. (2004) Biometrical Methods in Quantitative Genetic Analysis. New Delhi: Kalyani.

See Also

Hayman , GriffingData1 , GriffingData2 , GriffingData3 , GriffingData4

Examples

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#-------------------------------------------------------------
## Diallel Analysis with Griffing's Aproach Method 1 & Model 1
#-------------------------------------------------------------
Griffing1Data1 <-
 Griffing(
     y      = Yield
   , Rep    = Rep
   , Cross1 = Cross1
   , Cross2 = Cross2
   , data   = GriffingData1
   , Method = 1
   , Model  = 1
 )
names(Griffing1Data1)
Griffing1Data1
Griffing1Data1Means <- Griffing1Data1$Means
Griffing1Data1ANOVA <- Griffing1Data1$ANOVA
Griffing1Data1Genetic.Components <- Griffing1Data1$Genetic.Components
Griffing1Data1Effects <- Griffing1Data1$Effects
Griffing1Data1StdErr <- as.matrix(Griffing1Data1$StdErr)


#--------------------------------------------------------------
## Diallel Analysis with Griffing's Aproach Method 1 & Model 2
#--------------------------------------------------------------
Griffing2Data1 <-
 Griffing(
     y      = Yield
   , Rep    = Rep
   , Cross1 = Cross1
   , Cross2 = Cross2
   , data   = GriffingData1
   , Method = 1
   , Model  = 2
 )
names(Griffing2Data1)
Griffing2Data1
Griffing2Data1Means <- Griffing2Data1$Means
Griffing2Data1ANOVA <- Griffing2Data1$ANOVA
Griffing2Data1Genetic.Components <- Griffing2Data1$Genetic.Components


#--------------------------------------------------------------
## Diallel Analysis with Griffing's Aproach Method 2 & Model 1
#--------------------------------------------------------------
Griffing1Data2 <-
 Griffing(
     y      = Yield
   , Rep    = Rep
   , Cross1 = Cross1
   , Cross2 = Cross2
   , data   = GriffingData2
   , Method = 2
   , Model  = 1
 )
names(Griffing1Data2)
Griffing1Data2
Griffing1Data2Means <- Griffing1Data2$Means
Griffing1Data2ANOVA <- Griffing1Data2$ANOVA
Griffing1Data2Genetic.Components <- Griffing1Data2$Genetic.Components
Griffing1Data2Effects <- Griffing1Data2$Effects
Griffing1Data2StdErr <- as.matrix(Griffing1Data2$StdErr)


#--------------------------------------------------------------
## Diallel Analysis with Griffing's Aproach Method 2 & Model 2
#--------------------------------------------------------------
Griffing2Data2 <-
 Griffing(
     y      = Yield
   , Rep    = Rep
   , Cross1 = Cross1
   , Cross2 = Cross2
   , data   = GriffingData2
   , Method = 2
   , Model  = 2
 )
names(Griffing2Data2)
Griffing2Data2
Griffing2Data2Means <- Griffing2Data2$Means
Griffing2Data2ANOVA <- Griffing2Data2$ANOVA
Griffing2Data2Genetic.Components <- Griffing2Data2$Genetic.Components


#--------------------------------------------------------------
## Diallel Analysis with Griffing's Aproach Method 3 & Model 1
#--------------------------------------------------------------
Griffing1Data3 <-
 Griffing(
     y      = Yield
   , Rep    = Rep
   , Cross1 = Cross1
   , Cross2 = Cross2
   , data   = GriffingData3
   , Method = 3
   , Model  = 1
 )
names(Griffing1Data3)
Griffing1Data3
Griffing1Data3Means <- Griffing1Data3$Means
Griffing1Data3ANOVA <- Griffing1Data3$ANOVA
Griffing1Data3Genetic.Components <- Griffing1Data3$Genetic.Components
Griffing1Data3Effects <- Griffing1Data3$Effects
Griffing1Data3StdErr <- as.matrix(Griffing1Data3$StdErr)


#--------------------------------------------------------------
## Diallel Analysis with Griffing's Aproach Method 3 & Model 2
#--------------------------------------------------------------
Griffing2Data3 <-
 Griffing(
     y       = Yield
   , Rep     = Rep
   , Cross1  = Cross1
   , Cross2  = Cross2
   , data    = GriffingData3
   , Method  = 3
   , Model   = 2
 )
names(Griffing2Data3)
Griffing2Data3
Griffing2Data3Means <- Griffing2Data3$Means
Griffing2Data3ANOVA <- Griffing2Data3$ANOVA
Griffing2Data3Genetic.Components <- Griffing2Data3$Genetic.Components


#--------------------------------------------------------------
## Diallel Analysis with Griffing's Aproach Method 4 & Model 1
#--------------------------------------------------------------
Griffing1Data4 <-
 Griffing(
     y       = Yield
   , Rep     = Rep
   , Cross1  = Cross1
   , Cross2  = Cross2
   , data    = GriffingData4
   , Method  = 4
   , Model   = 1
 )
names(Griffing1Data4)
Griffing1Data4
Griffing1Data4Means <- Griffing1Data4$Means
Griffing1Data4ANOVA <- Griffing1Data4$ANOVA
Griffing1Data4Genetic.Components <- Griffing1Data4$Genetic.Components
Griffing1Data4Effects <- Griffing1Data4$Effects
Griffing1Data4StdErr <- as.matrix(Griffing1Data4$StdErr)


#--------------------------------------------------------------
## Diallel Analysis with Griffing's Aproach Method 4 & Model 2
#--------------------------------------------------------------
Griffing2Data4 <-
 Griffing(
     y       = Yield
   , Rep     = Rep
   , Cross1  = Cross1
   , Cross2  = Cross2
   , data    = GriffingData4
   , Method  = 4
   , Model   = 2
 )
names(Griffing2Data4)
Griffing2Data4
Griffing2Data4Means <- Griffing2Data4$Means
Griffing2Data4ANOVA <- Griffing2Data4$ANOVA
Griffing2Data4Genetic.Components <- Griffing2Data4$Genetic.Components

Example output

[1] "Means"              "ANOVA"              "Genetic.Components"
[4] "Effects"            "StdErr"            
$Means
        Cross1  Cross2  Cross3  Cross4   Cross5  Cross6   Cross7  Cross8
Cross1  85.645  87.010  90.455 114.945 120.2900  68.550 107.6425  52.640
Cross2  80.690  98.260 111.575  88.170  99.9300  73.265  97.6400  85.650
Cross3 102.230 104.555  74.070 100.645  94.2850 100.885 111.5400 117.735
Cross4 119.115  89.310 102.675  91.640  85.2850 105.795  64.4500  46.855
Cross5 111.290 102.890  88.265  83.390  54.1025  84.150  81.9350  94.820
Cross6  68.835  71.295  99.575 108.665  87.9650 100.390 121.6100  53.740
Cross7 109.265  87.820 108.445  57.650  78.7500 115.670  90.9600 125.270
Cross8  48.720  83.145 115.400  46.740  93.3200  60.240 118.1700  82.000

$ANOVA
             Df  Sum Sq Mean Sq F value Pr(>F)    
gca           7  3804.6  543.52 18.8868 <2e-16 ***
sca          28 22060.8  787.89 27.3783 <2e-16 ***
reciprocals  28   365.5   13.05  0.4536 0.9923    
Error       189  5439.0   28.78                   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

$Genetic.Components
             Components
gca         32.17141650
sca        759.10757646
Reciprocal  -7.86141946
gca/sca      0.04238058

$Effects
          Cross1     Cross2    Cross3     Cross4     Cross5      Cross6
Cross1  0.061875 -7.4284375 -3.494687 29.6575000 27.3050000 -20.1831250
Cross2  3.160000  0.4679688  7.821719  0.9614062 12.5189063 -17.0017188
Cross3 -5.887500  3.5100000  9.026719  5.3226562 -6.1748438   2.3895312
Cross4 -2.085000 -0.5700000 -1.015000 -3.4379687 -0.6476562  21.8542187
Cross5  4.500000 -1.4800000  3.010000  0.9475000 -2.3254687  -0.4307813
Cross6 -0.142500  0.9850000  0.655000 -1.4350000 -1.9075000  -1.9348437
Cross7 -0.811250  4.9100000  1.547500  3.4000000  1.5925000   2.9700000
Cross8  1.960000  1.2525000  1.167500  0.0575000  0.7500000  -3.2500000
           Cross7     Cross8
Cross1  10.405781 -31.034687
Cross2  -5.724063   2.276719
Cross3   2.979687  25.887969
Cross4 -33.498125 -31.417344
Cross5 -15.318125  14.742656
Cross6  22.588750 -22.727969
Cross7   7.237500  32.829688
Cross8   3.550000  -9.095781

$StdErr
 [1]  2.173069  8.130878  5.807770  6.570742  3.285371 11.380858 10.896342
 [8]  9.856113  8.692274  8.047482  9.292432

[1] "Means"              "ANOVA"              "Genetic.Components"
$Means
        Cross1  Cross2  Cross3  Cross4   Cross5  Cross6   Cross7  Cross8
Cross1  85.645  87.010  90.455 114.945 120.2900  68.550 107.6425  52.640
Cross2  80.690  98.260 111.575  88.170  99.9300  73.265  97.6400  85.650
Cross3 102.230 104.555  74.070 100.645  94.2850 100.885 111.5400 117.735
Cross4 119.115  89.310 102.675  91.640  85.2850 105.795  64.4500  46.855
Cross5 111.290 102.890  88.265  83.390  54.1025  84.150  81.9350  94.820
Cross6  68.835  71.295  99.575 108.665  87.9650 100.390 121.6100  53.740
Cross7 109.265  87.820 108.445  57.650  78.7500 115.670  90.9600 125.270
Cross8  48.720  83.145 115.400  46.740  93.3200  60.240 118.1700  82.000

$ANOVA
             Df  Sum Sq Mean Sq F value Pr(>F)    
gca           7  3804.6  543.52  0.6898 0.6798    
sca          28 22060.8  787.89 27.3783 <2e-16 ***
reciprocals  28   365.5   13.05  0.4536 0.9797    
Error       189  5439.0   28.78                   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

$Genetic.Components
            Components
gca        -14.4404522
sca        426.1656570
Reciprocal  -7.8614195
Error       28.7777288
Additive   -28.8809045
Dominant   426.1656570
gca/sca     -0.0338846

[1] "Means"              "ANOVA"              "Genetic.Components"
[4] "Effects"            "StdErr"            
$Means
       Cross1 Cross2  Cross3  Cross4   Cross5  Cross6   Cross7  Cross8
Cross1 85.645  87.01  90.455 114.945 120.2900  68.550 107.6425  52.640
Cross2     NA  98.26 111.575  88.170  99.9300  73.265  97.6400  85.650
Cross3     NA     NA  74.070 100.645  94.2850 100.885 111.5400 117.735
Cross4     NA     NA      NA  91.640  85.2850 105.795  64.4500  46.855
Cross5     NA     NA      NA      NA  54.1025  84.150  81.9350  94.820
Cross6     NA     NA      NA      NA       NA 100.390 121.6100  53.740
Cross7     NA     NA      NA      NA       NA      NA  90.9600 125.270
Cross8     NA     NA      NA      NA       NA      NA       NA  82.000

$ANOVA
       Df  Sum Sq Mean Sq F value    Pr(>F)    
gca     7  1850.9  264.41  9.4698 4.546e-09 ***
sca    28 12529.1  447.47 16.0259 < 2.2e-16 ***
Error 105  2931.8   27.92                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

$Genetic.Components
          Components
gca      23.64917067
sca     419.54647702
gca/sca   0.05636842

$Effects
        Cross1    Cross2    Cross3    Cross4    Cross5     Cross6     Cross7
Cross1 -0.3135 -5.718694 -5.823694 27.249806 34.647306 -21.080194   9.689056
Cross2      NA  2.380250 12.602556 -2.218944 11.593556 -19.058944  -3.007194
Cross3      NA        NA  5.930250  6.706056  2.398556   5.011056   7.342806
Cross4      NA        NA        NA -2.653250  1.982056  18.504556 -31.163694
Cross5      NA        NA        NA        NA -4.705750  -1.087944 -11.626194
Cross6      NA        NA        NA        NA        NA  -0.718250  24.061306
Cross7      NA        NA        NA        NA        NA         NA   7.605000
Cross8      NA        NA        NA        NA        NA         NA         NA
            Cross8
Cross1 -30.1836944
Cross2   0.1325556
Cross3  28.6675556
Cross4 -33.6289444
Cross5  16.3885556
Cross6 -28.6789444
Cross7  34.5278056
Cross8  -7.5247500

$StdErr
[1]  2.386553  7.315797  6.364141  3.608129  8.838075 10.824387 10.205330

[1] "Means"              "ANOVA"              "Genetic.Components"
$Means
       Cross1 Cross2  Cross3  Cross4   Cross5  Cross6   Cross7  Cross8
Cross1 85.645  87.01  90.455 114.945 120.2900  68.550 107.6425  52.640
Cross2     NA  98.26 111.575  88.170  99.9300  73.265  97.6400  85.650
Cross3     NA     NA  74.070 100.645  94.2850 100.885 111.5400 117.735
Cross4     NA     NA      NA  91.640  85.2850 105.795  64.4500  46.855
Cross5     NA     NA      NA      NA  54.1025  84.150  81.9350  94.820
Cross6     NA     NA      NA      NA       NA 100.390 121.6100  53.740
Cross7     NA     NA      NA      NA       NA      NA  90.9600 125.270
Cross8     NA     NA      NA      NA       NA      NA       NA  82.000

$ANOVA
       Df  Sum Sq Mean Sq F value Pr(>F)    
gca     7  1850.9  264.41  0.5909 0.7577    
sca    28 12529.1  447.47 16.0259 <2e-16 ***
Error 105  2931.8   27.92                   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

$Genetic.Components
            Components
gca       -18.30547704
sca       419.54647702
Error      27.92161709
Additive  -36.61095407
Dominance 419.54647702
gca/sca    -0.04363158

[1] "Means"              "ANOVA"              "Genetic.Components"
[4] "Effects"            "StdErr"            
$Means
        Cross1  Cross2  Cross3  Cross4  Cross5  Cross6   Cross7  Cross8
Cross1      NA  87.010  90.455 114.945 120.290  68.550 107.6425  52.640
Cross2  80.690      NA 111.575  88.170  99.930  73.265  97.6400  85.650
Cross3 102.230 104.555      NA 100.645  94.285 100.885 111.5400 117.735
Cross4 119.115  89.310 102.675      NA  85.285 105.795  64.4500  46.855
Cross5 111.290 102.890  88.265  83.390      NA  84.150  81.9350  94.820
Cross6  68.835  71.295  99.575 108.665  87.965      NA 121.6100  53.740
Cross7 109.265  87.820 108.445  57.650  78.750 115.670       NA 125.270
Cross8  48.720  83.145 115.400  46.740  93.320  60.240 118.1700      NA

$ANOVA
             Df  Sum Sq Mean Sq F value Pr(>F)    
gca           7  5612.4  801.78 26.4344 <2e-16 ***
sca          20 18336.3  916.82 30.2273 <2e-16 ***
reciprocals  28   365.5   13.05  0.4304 0.9948    
Error       165  5004.6   30.33                   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

$Genetic.Components
            Components
gca         64.2871004
sca        443.2433587
Reciprocal  -8.6379207
gca/sca      0.1450379

$Effects
            Cross1    Cross2    Cross3    Cross4     Cross5     Cross6
Cross1 -0.08609375 -6.038958 -8.989792 31.245625  22.266042 -17.637708
Cross2  3.16000000 -1.647135  4.293750  4.516667   9.447083 -12.489167
Cross3 -5.88750000  3.510000 13.796198  1.993333 -16.131250   0.017500
Cross4 -2.08500000 -0.570000 -1.015000 -5.751719  -3.520833  26.565417
Cross5  4.50000000 -1.480000  3.010000  0.947500   1.987865  -2.346667
Cross6 -0.14250000  0.985000  0.655000 -1.435000  -1.907500  -5.205885
Cross7 -0.81125000  4.910000  1.547500  3.400000   1.592500   2.970000
Cross8  1.96000000  1.252500  1.167500  0.057500   0.750000  -3.250000
           Cross7    Cross8
Cross1   8.322083 -29.16729
Cross2  -5.840625   6.11125
Cross3  -4.021458  22.83792
Cross4 -33.416042 -27.38417
Cross5 -21.863125  12.14875
Cross6  23.628125 -17.73750
Cross7   8.595573  33.19104
Cross8   3.550000 -11.68880

$StdErr
[1] 2.347428 5.195172 6.147010 3.548978 7.935756 7.097956

[1] "Means"              "ANOVA"              "Genetic.Components"
$Means
        Cross1  Cross2  Cross3  Cross4  Cross5  Cross6   Cross7  Cross8
Cross1      NA  87.010  90.455 114.945 120.290  68.550 107.6425  52.640
Cross2  80.690      NA 111.575  88.170  99.930  73.265  97.6400  85.650
Cross3 102.230 104.555      NA 100.645  94.285 100.885 111.5400 117.735
Cross4 119.115  89.310 102.675      NA  85.285 105.795  64.4500  46.855
Cross5 111.290 102.890  88.265  83.390      NA  84.150  81.9350  94.820
Cross6  68.835  71.295  99.575 108.665  87.965      NA 121.6100  53.740
Cross7 109.265  87.820 108.445  57.650  78.750 115.670       NA 125.270
Cross8  48.720  83.145 115.400  46.740  93.320  60.240 118.1700      NA

$ANOVA
             Df  Sum Sq Mean Sq F value Pr(>F)    
gca           7  5612.4  801.78  0.8745 0.5431    
sca          20 18336.3  916.82 30.2273 <2e-16 ***
reciprocals  28   365.5   13.05  0.4304 0.9801    
Error       165  5004.6   30.33                   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

$Genetic.Components
             Components
gca         -9.58679273
sca        443.24335872
Reciprocal  -8.63792065
Error       30.33073115
Additive   -19.17358546
Dominant   443.24335872
gca/sca     -0.02162873

[1] "Means"              "ANOVA"              "Genetic.Components"
[4] "Effects"            "StdErr"            
$Means
       Cross2  Cross3  Cross4  Cross5  Cross6   Cross7  Cross8
Cross2  87.01  90.455 114.945 120.290  68.550 107.6425  52.640
Cross3     NA 111.575  88.170  99.930  73.265  97.6400  85.650
Cross4     NA      NA 100.645  94.285 100.885 111.5400 117.735
Cross5     NA      NA      NA  85.285 105.795  64.4500  46.855
Cross6     NA      NA      NA      NA  84.150  81.9350  94.820
Cross7     NA      NA      NA      NA      NA 121.6100  53.740
Cross8     NA      NA      NA      NA      NA       NA 125.270

$ANOVA
      Df Sum Sq Mean Sq F value    Pr(>F)    
gca    7 3126.9  446.70  14.323 5.667e-12 ***
sca   20 9304.6  465.23  14.917 < 2.2e-16 ***
Error 81 2526.2   31.19                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

$Genetic.Components
        Components
gca      69.251646
sca     434.040776
gca/sca   0.159551

$Effects
           Cross1     Cross2     Cross3    Cross4     Cross5     Cross6
Cross1 -0.8596875 -3.9395833 -14.474583 30.177917  26.431250 -16.525417
Cross2         NA -0.5751042   6.360833  3.118333   5.786667 -12.095000
Cross3         NA         NA  13.404896  1.613333 -13.838333   1.545000
Cross4         NA         NA         NA -6.757604  -2.675833  26.617500
Cross5         NA         NA         NA        NA   2.334063  -4.119167
Cross6         NA         NA         NA        NA         NA  -6.449271
Cross7         NA         NA         NA        NA         NA         NA
Cross8         NA         NA         NA        NA         NA         NA
           Cross7     Cross8
Cross1   5.551667 -27.221250
Cross2  -4.735417   5.504167
Cross3  -4.815417  23.609167
Cross4 -31.742917 -27.108333
Cross5 -23.349583  11.765000
Cross6  25.108750 -20.531667
Cross7  10.566146  33.982917
Cross8         NA -11.663437

$StdErr
[1] 2.553607 5.651474 4.179321 3.860692 8.632769 7.721383

[1] "Means"              "ANOVA"              "Genetic.Components"
$Means
       Cross2  Cross3  Cross4  Cross5  Cross6   Cross7  Cross8
Cross2  87.01  90.455 114.945 120.290  68.550 107.6425  52.640
Cross3     NA 111.575  88.170  99.930  73.265  97.6400  85.650
Cross4     NA      NA 100.645  94.285 100.885 111.5400 117.735
Cross5     NA      NA      NA  85.285 105.795  64.4500  46.855
Cross6     NA      NA      NA      NA  84.150  81.9350  94.820
Cross7     NA      NA      NA      NA      NA 121.6100  53.740
Cross8     NA      NA      NA      NA      NA       NA 125.270

$ANOVA
      Df Sum Sq Mean Sq F value Pr(>F)    
gca    7 3126.9  446.70  0.9602 0.4853    
sca   20 9304.6  465.23 14.9173 <2e-16 ***
Error 81 2526.2   31.19                   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

$Genetic.Components
            Components
gca       -3.088483348
sca      434.040775861
Error     31.187045285
Additive  -6.176966696
Dominant 434.040775861
gca/sca   -0.007115653

DiallelAnalysisR documentation built on Feb. 25, 2021, 5:06 p.m.