Skip to contents


  • hmgv() Computes the harmonic mean of genotypic values (HMGV).

  • rpgv() Computes the relative performance of the genotypic values (RPGV).

  • hmrpgv() Computes the harmonic mean of the relative performance of genotypic values (HMRPGV).

  • blup_indexes() Is a wrapper around the above functions that also computes the WAASB index (Olivoto et al. 2019) if an object computed with waasb() is used as input data.








An object of class waasb computed with waasb() or gamem_met().


A tibble containing the indexes.


The indexes computed with this function have been used to select genotypes with stability performance in a mixed-effect model framework. Some examples are in Alves et al (2018), Azevedo Peixoto et al. (2018), Dias et al. (2018) and Colombari Filho et al. (2013).

The HMGV index is computed as \[HMG{V_i} = \frac{E}{{\sum\limits_{j = 1}^E {\frac{1}{{G{v_{ij}}}}}}}\]

where \(E\) is the number of environments included in the analysis, \(Gv_{ij}\) is the genotypic value (BLUP) for the ith genotype in the jth environment.

The RPGV index is computed as \[RPGV_i = \frac{1}{E}{\sum\limits_{j = 1}^E {Gv_{ij}} /\mathop \mu \nolimits_j }\]

The HMRPGV index is computed as \[HMRPG{V_i} = \frac{E}{{\sum\limits_{j = 1}^E {\frac{1}{{G{v_{ij}}/{\mu _j}}}} }}\]


Alves, R.S., L. de Azevedo Peixoto, P.E. Teodoro, L.A. Silva, E.V. Rodrigues, M.D.V. de Resende, B.G. Laviola, and L.L. Bhering. 2018. Selection of Jatropha curcas families based on temporal stability and adaptability of genetic values. Ind. Crops Prod. 119:290-293. doi:10.1016/J.INDCROP.2018.04.029

Azevedo Peixoto, L. de, P.E. Teodoro, L.A. Silva, E.V. Rodrigues, B.G. Laviola, and L.L. Bhering. 2018. Jatropha half-sib family selection with high adaptability and genotypic stability. PLoS One 13:e0199880. doi:10.1371/journal.pone.0199880

Colombari Filho, J.M., M.D.V. de Resende, O.P. de Morais, A.P. de Castro, E.P. Guimaraes, J.A. Pereira, M.M. Utumi, and F. Breseghello. 2013. Upland rice breeding in Brazil: a simultaneous genotypic evaluation of stability, adaptability and grain yield. Euphytica 192:117-129. doi:10.1007/s10681-013-0922-2

Dias, P.C., A. Xavier, M.D.V. de Resende, M.H.P. Barbosa, F.A. Biernaski, R.A. Estopa. 2018. Genetic evaluation of Pinus taeda clones from somatic embryogenesis and their genotype x environment interaction. Crop Breed. Appl. Biotechnol. 18:55-64. doi:10.1590/1984-70332018v18n1a8

Olivoto, T., A.D.C. L\'ucio, J.A.G. da silva, V.S. Marchioro, V.Q. de Souza, and E. Jost. 2019. Mean performance and stability in multi-environment trials I: Combining features of AMMI and BLUP techniques. Agron. J. 111:2949-2960. doi:10.2134/agronj2019.03.0220

Resende MDV (2007) Matematica e estatistica na analise de experimentos e no melhoramento genetico. Embrapa Florestas, Colombo


Tiago Olivoto


# \donttest{
res_ind <- waasb(data_ge,
                 env = ENV,
                 gen = GEN,
                 rep = REP,
                 resp = c(GY, HM),
                 verbose = FALSE)
model_indexes <- blup_indexes(res_ind)
#> Class of the model: blup_ind
#> Variable extracted: HMRPGV
#> # A tibble: 10 × 3
#>    GEN      GY    HM
#>    <chr> <dbl> <dbl>
#>  1 G1    0.967 0.981
#>  2 G10   0.896 1.01 
#>  3 G2    1.02  0.973
#>  4 G3    1.10  0.991
#>  5 G4    0.988 0.999
#>  6 G5    0.952 1.02 
#>  7 G6    0.952 1.01 
#>  8 G7    1.03  0.998
#>  9 G8    1.12  1.02 
#> 10 G9    0.917 0.995
# }