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Broad-sense heritability in plant breeding

Source: R/H2cal.R
H2cal.Rd

Heritability in plant breeding on a genotype difference basis

Usage

H2cal(
  data,
  trait,
  gen.name,
  rep.n,
  env.n = 1,
  year.n = 1,
  env.name = NULL,
  year.name = NULL,
  fixed.model,
  random.model,
  summary = FALSE,
  emmeans = FALSE,
  weights = NULL,
  plot_diag = FALSE,
  outliers.rm = FALSE,
  trial = NULL
)

Arguments

data

Experimental design data frame with the factors and traits.

trait

Name of the trait.

gen.name

Name of the genotypes.

rep.n

Number of replications in the experiment.

env.n

Number of environments (default = 1). See details.

year.n

Number of years (default = 1). See details.

env.name

Name of the environments (default = NULL). See details.

year.name

Name of the years (default = NULL). See details.

fixed.model

The fixed effects in the model (BLUEs). See examples.

random.model

The random effects in the model (BLUPs). See examples.

summary

Print summary from random model (default = FALSE).

emmeans

Use emmeans for calculate the BLUEs (default = FALSE).

weights

an optional vector of ‘prior weights’ to be used in the fitting process (default = NULL).

plot_diag

Show diagnostic plots using ggplot2 and cowplot (default = FALSE).

outliers.rm

Remove outliers (default = FALSE). See references.

trial

Column with the name of the trial in the results (default = NULL).

Value

list

Details

The function allows to made the calculation for individual or multi-environmental trials (MET) using fixed and random model.

  1. The variance components based in the random model and the population summary information based in the fixed model (BLUEs).

  2. Heritability under three approaches: Standard (ANOVA), Cullis (BLUPs) and Piepho (BLUEs).

  3. Best Linear Unbiased Estimators (BLUEs), fixed effect.

  4. Best Linear Unbiased Predictors (BLUPs), random effect.

  5. Table with the outliers removed for each model.

For individual experiments is necessary provide the {trait}, {gen.name}, {rep.n}.

For MET experiments you should {env.n} and {env.name} and/or {year.n} and {year.name} according your experiment.

The BLUEs calculation based in the pairwise comparison could be time consuming with the increase of the number of the genotypes. You can specify {emmeans = FALSE} and the calculate of the BLUEs will be faster.

If {emmeans = FALSE} you should change 1 by 0 in the fixed model for exclude the intersect in the analysis and get all the genotypes BLUEs.

Diagnostic plots are produced with ggplot2 and assembled with cowplot. If {outliers.rm = FALSE}, fixed and random model diagnostics are displayed in one combined panel. If {outliers.rm = TRUE}, fixed and random diagnostics are displayed in separate panels comparing before and after cleaning.

For more information review the references.

References

Bernal Vasquez, Angela Maria, et al. “Outlier Detection Methods for Generalized Lattices: A Case Study on the Transition from ANOVA to REML.” Theoretical and Applied Genetics, vol. 129, no. 4, Apr. 2016.

Buntaran, H., Piepho, H., Schmidt, P., Ryden, J., Halling, M., and Forkman, J. (2020). Cross validation of stagewise mixed model analysis of Swedish variety trials with winter wheat and spring barley. Crop Science, 60(5).

Schmidt, P., J. Hartung, J. Bennewitz, and H.P. Piepho. 2019. Heritability in Plant Breeding on a Genotype Difference Basis. Genetics 212(4).

Schmidt, P., J. Hartung, J. Rath, and H.P. Piepho. 2019. Estimating Broad Sense Heritability with Unbalanced Data from Agricultural Cultivar Trials. Crop Science 59(2).

Tanaka, E., and Hui, F. K. C. (2019). Symbolic Formulae for Linear Mixed Models. In H. Nguyen (Ed.), Statistics and Data Science. Springer.

Zystro, J., Colley, M., and Dawson, J. (2018). Alternative Experimental Designs for Plant Breeding. In Plant Breeding Reviews. John Wiley and Sons, Ltd.

Author

Maria Belen Kistner

Flavio Lozano Isla

Examples


library(inti)
 
md <- met %>%
  H2cal(trait = "yield",
  gen.name = "cultivar",
  rep.n = 2,
  env.name = "env",
  env.n = 18,
  fixed.model = ~ 0 + env + (1 | env:rep:alpha) + cultivar,
  random.model = ~ 1 + env +
    (1 | env:rep) + (1 | env:rep:alpha) +
    (1 | cultivar:env) + (1 | cultivar),
  summary = TRUE,
  plot_diag = TRUE,
  outliers.rm = TRUE,
  emmeans = FALSE
)
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: yield ~ 1 + env + (1 | env:rep) + (1 | env:rep:alpha) + (1 |  
#>     cultivar:env) + (1 | cultivar)
#>    Data: dt.rm
#> Weights: weights
#> 
#> REML criterion at convergence: 11329.1
#> 
#> Scaled residuals: 
#>     Min      1Q  Median      3Q     Max 
#> -4.0239 -0.3641  0.0002  0.3969  2.1831 
#> 
#> Random effects:
#>  Groups        Name        Variance Std.Dev.
#>  cultivar:env  (Intercept) 2107.0   45.90   
#>  env:rep:alpha (Intercept) 1030.8   32.11   
#>  env:rep       (Intercept)  382.4   19.55   
#>  cultivar      (Intercept)  712.1   26.69   
#>  Residual                   880.4   29.67   
#> Number of obs: 1055, groups:  
#> cultivar:env, 536; env:rep:alpha, 251; env:rep, 36; cultivar, 30
#> 
#> Fixed effects:
#>                       Estimate Std. Error t value
#> (Intercept)            1066.29      19.26  55.355
#> envmiddle_07bm28_2016  -358.80      26.29 -13.648
#> envmiddle_07bm29_2016  -613.09      26.46 -23.168
#> envmiddle_07bm32_2016   -12.32      26.64  -0.462
#> envmiddle_07bm36_2016  -431.05      26.64 -16.183
#> envmiddle_07bm37_2016  -515.39      26.64 -19.348
#> envmiddle_07bm39_2016   144.85      26.64   5.438
#> envnorth_07bm25_2016   -439.09      26.29 -16.703
#> envnorth_07bm26_2016    -47.97      26.32  -1.823
#> envnorth_07bm38_2016   -105.29      26.64  -3.953
#> envnorth_07bm40_2016   -276.36      26.64 -10.376
#> envnorth_07bm41_2016   -138.43      26.66  -5.192
#> envsouth_07bm20_2016   -218.75      26.31  -8.314
#> envsouth_07bm21_2016     31.50      26.32   1.197
#> envsouth_07bm22_2016   -167.38      26.29  -6.367
#> envsouth_07bm23_2016   -140.88      26.31  -5.355
#> envsouth_07bm30_2016   -421.47      26.72 -15.775
#> envsouth_07bm35_2016   -233.93      26.73  -8.751
#> 
#> Correlation matrix not shown by default, as p = 18 > 12.
#> Use print(g.ran.sum, correlation=TRUE)  or
#>     vcov(g.ran.sum)        if you need it



 md$tabsmr
#> # A tibble: 1 × 18
#>   trait   rep  geno   env  year  mean   std   min   max   V.g V.gxl V.gxlxy
#>   <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>   <dbl>
#> 1 yield     2    30    18     1  50.5  25.8 -15.5  106.  712. 2107.       0
#> # ℹ 6 more variables: V.e <dbl>, V.p <dbl>, repeatability <dbl>, H2.s <dbl>,
#> #   H2.p <dbl>, H2.c <dbl>
 md$blues
#> # A tibble: 29 × 3
#>    cultivar yield smith.w
#>    <chr>    <dbl>   <dbl>
#>  1 23286     29.8  0.0126
#>  2 23524    -15.5  0.0129
#>  3 24054     62.3  0.0126
#>  4 24521     75.2  0.0126
#>  5 24984     52.9  0.0126
#>  6 25512     37.5  0.0131
#>  7 25965     30.4  0.0126
#>  8 26362     34.7  0.0120
#>  9 26742     58.0  0.0129
#> 10 26777     34.1  0.0124
#> # ℹ 19 more rows
 md$blups 
#> # A tibble: 30 × 2
#>    cultivar yield
#>    <chr>    <dbl>
#>  1 22455    1027.
#>  2 23286    1048.
#>  3 23524    1017.
#>  4 24054    1076.
#>  5 24521    1088.
#>  6 24984    1073.
#>  7 25512    1061.
#>  8 25965    1055.
#>  9 26362    1054.
#> 10 26742    1075.
#> # ℹ 20 more rows
 md$outliers
#> $fixed
#>     index                env rep alpha cultivar     yield      resi    res_MAD
#> 108   108  south_07bm21_2016   2     1    27609 1177.4254  175.7415   4.558418
#> 376   378 middle_07bm27_2016   2     7    26362  875.4764 -160.2806  -4.157392
#> 416   418 middle_07bm27_2016   2     8    28950 1345.2563  239.2646   6.206094
#> 486   488 middle_07bm29_2016   2     7    24054  236.6704 -196.0316  -5.084709
#> 515   521 middle_07bm29_2016   1     7    27599  626.0585  181.9093   4.718400
#> 520   527 middle_07bm29_2016   1     7    27609   83.1913 -233.4284  -6.054713
#> 521   528 middle_07bm29_2016   2     6    27609  149.2549 -179.7321  -4.661929
#> 552   561  south_07bm30_2016   1     3    26777  294.0247 -266.3388  -6.908350
#> 578   587  south_07bm30_2016   1     3    27609  309.0891 -181.2963  -4.702502
#> 582   591  south_07bm30_2016   1     3    28128  815.9065  186.9957   4.850334
#> 588   597  south_07bm30_2016   1     6    28950  551.0540 -163.0237  -4.228543
#> 589   598  south_07bm30_2016   2     2    28950  366.6649 -197.0120  -5.110139
#> 655   664  south_07bm35_2016   2     2    23286  519.1671 -262.8217  -6.817124
#> 698   707  south_07bm35_2016   1     4    27609  256.9020 -424.3367 -11.006533
#> 699   708  south_07bm35_2016   2     5    27609  345.2121 -355.3906  -9.218194
#> 704   713  south_07bm35_2016   1     6    28209 1018.5923  180.8066   4.689800
#> 708   717  south_07bm35_2016   1     2    28950  568.7687 -258.2803  -6.699327
#>      rawp.BHStud         adjp        bholm out_flag
#> 108 5.154036e-06 5.154036e-06 5.437508e-03  OUTLIER
#> 376 3.219018e-05 3.219018e-05 3.389626e-02  OUTLIER
#> 416 5.431779e-10 5.431779e-10 5.779413e-07  OUTLIER
#> 486 3.681896e-07 3.681896e-07 3.906492e-04  OUTLIER
#> 515 2.377069e-06 2.377069e-06 2.517316e-03  OUTLIER
#> 520 1.406685e-09 1.406685e-09 1.495306e-06  OUTLIER
#> 521 3.132588e-06 3.132588e-06 3.308013e-03  OUTLIER
#> 552 4.903189e-12 4.903189e-12 5.231703e-09  OUTLIER
#> 578 2.569931e-06 2.569931e-06 2.718987e-03  OUTLIER
#> 582 1.232538e-06 1.232538e-06 1.306491e-03  OUTLIER
#> 588 2.352101e-05 2.352101e-05 2.479114e-02  OUTLIER
#> 589 3.219225e-07 3.219225e-07 3.418817e-04  OUTLIER
#> 655 9.288126e-12 9.288126e-12 9.901142e-09  OUTLIER
#> 698 0.000000e+00 0.000000e+00 0.000000e+00  OUTLIER
#> 699 0.000000e+00 0.000000e+00 0.000000e+00  OUTLIER
#> 704 2.734723e-06 2.734723e-06 2.890603e-03  OUTLIER
#> 708 2.093814e-11 2.093814e-11 2.229912e-08  OUTLIER
#> 
#> $random
#>     index                env rep alpha cultivar     yield       resi   res_MAD
#> 387   389 middle_07bm27_2016   1     5    27543 1225.2806   78.79465  4.089582
#> 392   394 middle_07bm27_2016   2     3    27548 1204.8185   85.86587  4.456591
#> 407   409 middle_07bm27_2016   1     6    27669 1273.3470   93.39383  4.847305
#> 415   417 middle_07bm27_2016   1     5    28950 1108.5987  -92.21395 -4.786067
#> 416   418 middle_07bm27_2016   2     8    28950 1345.2563  146.18893  7.587465
#> 515   521 middle_07bm29_2016   1     7    27599  626.0585   88.56392  4.596624
#> 552   561  south_07bm30_2016   1     3    26777  294.0247 -161.53662 -8.384037
#> 553   562  south_07bm30_2016   2     2    26777  529.5605   85.30100  4.427273
#> 582   591  south_07bm30_2016   1     3    28128  815.9065   96.78572  5.023350
#> 654   663  south_07bm35_2016   1     1    23286  942.9373  152.02098  7.890158
#> 655   664  south_07bm35_2016   2     2    23286  519.1671 -189.68244 -9.844855
#> 698   707  south_07bm35_2016   1     4    27609  256.9020 -127.00325 -6.591694
#> 704   713  south_07bm35_2016   1     6    28209 1018.5923  106.56969  5.531156
#> 708   717  south_07bm35_2016   1     2    28950  568.7687  -88.59804 -4.598395
#>      rawp.BHStud         adjp        bholm out_flag
#> 387 4.321510e-05 4.321510e-05 4.563515e-02  OUTLIER
#> 392 8.327338e-06 8.327338e-06 8.810324e-03  OUTLIER
#> 407 1.251498e-06 1.251498e-06 1.329091e-03  OUTLIER
#> 415 1.700810e-06 1.700810e-06 1.804559e-03  OUTLIER
#> 416 3.264056e-14 3.264056e-14 3.479483e-11  OUTLIER
#> 515 4.293904e-06 4.293904e-06 4.547245e-03  OUTLIER
#> 552 0.000000e+00 0.000000e+00 0.000000e+00  OUTLIER
#> 553 9.543189e-06 9.543189e-06 1.008715e-02  OUTLIER
#> 582 5.077786e-07 5.077786e-07 5.397686e-04  OUTLIER
#> 654 3.108624e-15 3.108624e-15 3.316902e-12  OUTLIER
#> 655 0.000000e+00 0.000000e+00 0.000000e+00  OUTLIER
#> 698 4.348366e-11 4.348366e-11 4.631010e-08  OUTLIER
#> 704 3.181277e-08 3.181277e-08 3.384879e-05  OUTLIER
#> 708 4.257577e-06 4.257577e-06 4.513032e-03  OUTLIER
#>