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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 for fixed and random effects (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.

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)

dt <- potato

hr <- H2cal(data = dt
            , trait = "tubdw"
            , gen.name = "geno"
            , rep.n = 5
            , fixed.model = "0 + (1|bloque) + geno"
            , random.model = "1 + (1|bloque) + (1|geno)"
            , emmeans = TRUE
            , plot_diag = TRUE
            , outliers.rm = TRUE
            )


 hr$tabsmr
#>   trait rep geno env year     mean      std    min    max      V.g      V.e
#> 1 tubdw   5   15   1    1 31.71713 12.10921 11.628 53.154 129.7367 168.9607
#>        V.p repeatability      H2.s      H2.p      H2.c
#> 1 163.5288     0.7933567 0.7933567 0.8847729 0.8753661
 hr$blues
#> # A tibble: 15 x 6
#>    geno  tubdw    SE    df lower.CL upper.CL
#>    <fct> <dbl> <dbl> <dbl>    <dbl>    <dbl>
#>  1 G01    28.5  4.33  85.3    19.9      37.1
#>  2 G02    19.7  4.33  85.3    11.1      28.3
#>  3 G03    38.3  4.33  85.3    29.7      46.9
#>  4 G04    39.2  4.33  85.3    30.6      47.8
#>  5 G05    39.2  4.33  85.3    30.5      47.8
#>  6 G06    11.6  4.33  85.3     3.02     20.2
#>  7 G07    19.4  4.33  85.3    10.7      28.0
#>  8 G08    20.7  4.33  85.3    12.1      29.4
#>  9 G09    50.2  4.33  85.3    41.6      58.8
#> 10 G10    28.2  4.33  85.3    19.6      36.8
#> 11 G11    43.3  4.33  85.3    34.7      51.9
#> 12 G12    32.6  4.33  85.3    24.0      41.2
#> 13 G13    20.9  4.33  85.3    12.3      29.5
#> 14 G14    30.7  4.33  85.3    22.1      39.4
#> 15 G15    53.2  4.33  85.3    44.5      61.8
 hr$blups
#> # A tibble: 15 x 2
#>    geno  tubdw
#>    <chr> <dbl>
#>  1 G01    28.9
#>  2 G02    21.1
#>  3 G03    37.6
#>  4 G04    38.3
#>  5 G05    38.3
#>  6 G06    13.9
#>  7 G07    20.8
#>  8 G08    22.0
#>  9 G09    48.1
#> 10 G10    28.6
#> 11 G11    42.0
#> 12 G12    32.5
#> 13 G13    22.2
#> 14 G14    30.9
#> 15 G15    50.7