Genetic models

North Carolina Designs I, II and Line x Tester analysis

• Carolina I: set, male, female, progeny, replication.
   model  y ~ set + replication(set) + male(set) + female(male,set) + replication(female,male,set) + error.
  
  set is set
  set:replication is  replication(set)
  set:male is  male(set)
  set:male:female is female(male,set)
  set:replication:male:female is replication(female,male,set)
  Residuals is error              
  
  > library(agricolae)
  > data(carolina1)
  > # str(carolina1)
  > output<-carolina(model=1,carolina1)
  
  Response(y):  yield
  
  Analysis of Variance Table
  Response: y
                              Df  Sum Sq Mean Sq F value    Pr(>F)   
  set                          1  0.5339  0.5339  7.2120 0.0099144 **
  set:replication              2  2.9894  1.4947 20.1914 4.335e-07 ***
  set:male                     4 22.1711  5.5428 74.8743 < 2.2e-16 ***
  set:male:female              6  4.8250  0.8042 10.8630 1.311e-07 ***
  set:replication:male:female 10  3.2072  0.3207  4.3325 0.0002462 ***
  Residuals                   48  3.5533  0.0740                     
  ---
  Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

  CV: 8.286715    Mean: 3.283333
  
  > output[][-1]
  $var.m
  [1] 0.3948843
  
  $var.f
  [1] 0.08057407
  
  $var.A
  [1] 1.579537
  
  $var.D
  [1] -1.257241
   

• Carolina II: set, male, female, replication
  model  y ~ set + replication(set) + male(set) + female(set) + female*male(set) + error.
  
  set is set
  set:replication is  replication(set)
  set:male is  male(set)
  set:female is female(male,set)
  set:male:female is interaction female*male(set)
  Residuals is error 
  
  > data(carolina2)
  > majes<-subset(carolina2,carolina2[,1]==1)
  > majes<-majes[,c(2,5,4,3,6:8)]
  > output<-carolina(model=2,majes[,c(1:4,6)])

  Response(y):  yield
  
  Analysis of Variance Table
  Response: y
                  Df  Sum Sq Mean Sq F value    Pr(>F)   
  set              1  847836  847836 45.6296 1.097e-09 ***
  set:replication  4  144345   36086  1.9421  0.109652   
  set:male         8  861053  107632  5.7926 5.032e-06 ***
  set:female       8  527023   65878  3.5455  0.001227 **
  set:male:female 32  807267   25227  1.3577  0.129527   
  Residuals       96 1783762   18581                     
  ---
  Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

  CV: 19.08779    Mean: 714.13

  > output[][-1]
  $var.m
  [1] 2746.815
  
  $var.f
  [1] 1355.024
  
  $var.mf
  [1] 2215.415
  
  $var.Am
  [1] 10987.26
  
  $var.Af
  [1] 5420.096
  
  $var.D
  [1] 8861.66
   

• Line x Tester Analysis. It makes the Line x Tester Genetic Analysis. It also estimates the general and specific combinatory ability effects and the line and tester genetic contribution.
  Output: Standard Errors for combining ability effects. Componentes geneticos. Variancias. Contribucion proporcional. ANOVA with parents and crosses. ANOVA for line X tester analysis. ANOVA for line X tester analysis including parents. GCA Effects. Lines Effects. Testers Effects. Standard Errors for Combining Ability Effects. Genetic Components. Proportional contribution of lines, testers and their interactions. to total variance.

  > library(agricolae)
  > data(LxT)
  > str(LxT)
  'data.frame': 92 obs. of 4 variables:
  $ replication: int 1 2 3 4 1 2 3 4 1 2 ...
  $ line : int 1 1 1 1 1 1 1 1 1 1 ...
  $ tester : int 6 6 6 6 7 7 7 7 8 8 ...
  $ yield : num 74.4 70.9 60.9 68.0 91.8 ...
  > attach(LxT)
  > analisis<-lineXtester(replication, line, tester, yield)

  ANOVA with parents and crosses
  ==============================
                      Df      Sum Sq    Mean Sq F value Pr(>F)
  Replications         3    83.00012   27.66671   0.304 0.8224
  Treatments          22 32553.20239 1479.69102  16.249 0.0000
  Parents              7  6299.88519  899.98360   9.883 0.0000
  Parents vs. Crosses  1    53.66287   53.66287   0.589 0.4455
  Crosses             14 26199.65433 1871.40388  20.551 0.0000
  Error               66  6010.03298   91.06111              
  Total               91 38646.23549                         

  ANOVA for line X tester analysis
  ================================
                  Df    Sum Sq   Mean Sq F value Pr(>F)
  Lines            4 10318.361 2579.5904   1.457 0.3009
  Testers          2  1718.926  859.4629   0.485 0.6327
  Lines X Testers  8 14162.367 1770.2959  19.441 0.0000
  Error           66  6010.033   91.0611      

  ANOVA for line X tester analysis including parents
  ==================================================
                      Df      Sum Sq    Mean Sq F value Pr(>F)
  Replications         3    83.00012   27.66671   0.304 0.8224
  Treatments          22 32553.20239 1479.69102  16.249 0.0000
  Parents              7  6299.88519  899.98360   9.883 0.0000
  Parents vs. Crosses  1    53.66287   53.66287   0.589 0.4455
  Crosses             14 26199.65433 1871.40388  20.551 0.0000
  Lines                4 10318.36140 2579.59035   1.457 0.3009
  Testers              2  1718.92577  859.46289   0.485 0.6327
  Lines X Testers      8 14162.36716 1770.29590  19.441 0.0000
  Error               66  6010.03298   91.06111              
  Total               91 38646.23549                           

  GCA Effects:
  ===========
  Lines Effects:
        1       2       3       4       5
   -9.960  -0.718  23.817 -13.870   0.732

  Testers Effects:
       6      7      8
   0.292  6.404 -6.697  

  SCA Effects:
  ===========
       Testers
  Lines       6       7       8
      1  -8.019  24.959 -16.940
      2 -12.546   5.717   6.828
      3  -9.461  -4.918  14.378
      4  33.136 -14.321 -18.815
      5  -3.111 -11.438  14.548

  Standard Errors for Combining Ability Effects:
  =============================================

  S.E. (gca for line)   : 2.754710
  S.E. (gca for tester) : 2.133789
  S.E. (sca effect)     : 4.771297
  S.E. (gi - gj)line    : 3.895748
  S.E. (gi - gj)tester  : 3.017633
  S.E. (sij - skl)tester: 6.747633  

  Genetic Components:
  ==================
  Cov H.S. (line)   : 67.4412
  Cov H.S. (tester) : -45.54165
  Cov H.S. (average): 2.680894
  Cov F.S. (average): 411.3472

  F = 0, Aditive genetic variance : 42.8943
  F = 1, Aditive genetic variance : 10.72357
  F = 0, Variance due to Dominance: 1679.235
  F = 1, Variance due to Dominance: 419.8087
  
  Proportional contribution of lines, testers
   and their interactions to total variance
  ===========================================
  Contributions of lines  : 39.38358
  Contributions of testers: 6.560872
  Contributions of lxt    : 54.05555