Mean performance and stability in multi-environment trials

This function implements the weighting method between mean performance and stability (Olivoto et al., 2019) considering different parametric and non-parametric stability indexes.

Usage

mps(
  .data,
  env,
  gen,
  rep,
  resp,
  block = NULL,
  by = NULL,
  random = "gen",
  performance = c("blupg", "blueg"),
  stability = "waasb",
  ideotype_mper = NULL,
  ideotype_stab = NULL,
  wmper = NULL,
  verbose = TRUE
)

Arguments

.data

The dataset containing the columns related to Environments, Genotypes, replication/block and response variable(s).

env

The name of the column that contains the levels of the environments.

gen

The name of the column that contains the levels of the genotypes.

rep

The name of the column that contains the levels of the replications/blocks.

resp

The response variable(s). To analyze multiple variables in a single procedure a vector of variables may be used. For example resp = c(var1, var2, var3).

block

Defaults to NULL. In this case, a randomized complete block design is considered. If block is informed, then an alpha-lattice design is employed considering block as random to make use of inter-block information, whereas the complete replicate effect is always taken as fixed, as no inter-replicate information was to be recovered (Mohring et al., 2015).

by

One variable (factor) to compute the function by. It is a shortcut to dplyr::group_by().This is especially useful, for example, when the researcher want to analyze environments within mega-environments. In this case, an object of class mps_grouped is returned.

random

The effects of the model assumed to be random. Defaults to random = "gen". See gamem_met() to see the random effects assumed depending on the experimental design of the trials.

performance

Wich considers as mean performance. Either blupg (for Best Linear Unbiased Prediction) or blueg (for Best Linear Unbiased Estimation)

stability

The stability method. One of the following:

"waasb" The weighted average of absolute scores (Olivoto et al. 2019).
"ecovalence" The Wricke's ecovalence (Wricke, 1965).
"Shukla" The Shukla's stability variance parameter (Shukla, 1972).
"hmgv" The harmonic mean of genotypic values (Resende, 2007).
"s2di" The deviations from the Eberhart and Russell regression (Eberhart and Russell, 1966).
"r2" The determination coefficient of the Eberhart and Russell regression (Eberhart and Russell, 1966)..
"rmse" The root mean squared error of the Eberhart and Russell regression (Eberhart and Russell, 1966).
"wi" Annicchiarico's genotypic confidence index (Annicchiarico, 1992).
"polar" Power Law Residuals as yield stability index (Doring et al., 2015).
"acv" Adjusted Coefficient of Variation (Doring and Reckling, 2018)
"pi" Lin e Binns' superiority index (Lin and Binns, 1988).
"gai" Geometric adaptability index (Mohammadi and Amri, 2008).
"s1", "s2", "s3", and "s6" Huehn's stability statistics (Huehn, 1979).
"n1", "n2", "n3", and "n4" Thennarasu's stability statistics (Thennarasu, 1995).
"asv", "ev", "za", and "waas" AMMI-based stability indexes (see ammi_indexes()).

ideotype_mper, ideotype_stab

The new maximum value after rescaling the response variable/stability index. By default, all variables in resp are rescaled so that de maximum value is 100 and the minimum value is 0 (i.e., ideotype_mper = NULL and ideotype_stab = NULL). It must be a character vector of the same length of resp if rescaling is assumed to be different across variables, e.g., if for the first variable smaller values are better and for the second one, higher values are better, then ideotype_mper = c("l, h") must be used. For stability index in which lower values are better, use ideotype_stab = "l". Character value of length 1 will be recycled with a warning message.

wmper

The weight for the mean performance. By default, all variables in resp have equal weights for mean performance and stability (i.e., wmper = 50). It must be a numeric vector of the same length of resp to assign different weights across variables, e.g., if for the first variable equal weights for mean performance and stability are assumed and for the second one, a higher weight for mean performance (e.g. 65) is assumed, then wmper = c(50, 65) must be used. Numeric value of length 1 will be recycled with a warning message.

verbose

Logical argument. If verbose = FALSE the code will run silently.

Value

An object of class mps with the following items.

observed: The observed value on a genotype-mean basis.
performance: The performance for genotypes (BLUPs or BLUEs)
performance_res: The rescaled values of genotype's performance, considering ideotype_mper.
stability: The stability for genotypes, chosen with argument stability.
stability_res: The rescaled values of genotype's stability, considering ideotype_stab.
mps_ind: The mean performance and stability for the traits.
h2: The broad-sense heritability for the traits.
perf_method: The method for measuring genotype's performance.
wmper: The weight for the mean performance.
sense_mper: The goal for genotype's performance (l = lower, h = higher).
stab_method: The method for measuring genotype's stability.
wstab: The weight for the mean stability.
sense_stab: The goal for genotype's stability (l = lower, h = higher).

References

Annicchiarico, P. 1992. Cultivar adaptation and recommendation from alfalfa trials in Northern Italy. J. Genet. Breed. 46:269-278.

Doring, T.F., S. Knapp, and J.E. Cohen. 2015. Taylor's power law and the stability of crop yields. F. Crop. Res. 183: 294-302. doi:10.1016/j.fcr.2015.08.005

Doring, T.F., and M. Reckling. 2018. Detecting global trends of cereal yield stability by adjusting the coefficient of variation. Eur. J. Agron. 99: 30-36. doi:10.1016/j.eja.2018.06.007

Eberhart, S.A., and W.A. Russell. 1966. Stability parameters for comparing Varieties. Crop Sci. 6:36-40. doi:10.2135/cropsci1966.0011183X000600010011x

Huehn, V.M. 1979. Beitrage zur erfassung der phanotypischen stabilitat. EDV Med. Biol. 10:112.

Lin, C.S., and M.R. Binns. 1988. A superiority measure of cultivar performance for cultivar x location data. Can. J. Plant Sci. 68:193-198. doi:10.4141/cjps88-018

Mohammadi, R., & Amri, A. (2008). Comparison of parametric and non-parametric methods for selecting stable and adapted durum wheat genotypes in variable environments. Euphytica, 159(3), 419-432. doi:10.1007/s10681-007-9600-6

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. doi:10.2134/agronj2019.03.0220

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

Shukla, G.K. 1972. Some statistical aspects of partitioning genotype-environmental components of variability. Heredity. 29:238-245. doi:10.1038/hdy.1972.87

Thennarasu, K. 1995. On certain nonparametric procedures for studying genotype x environment interactions and yield stability. Ph.D. thesis. P.J. School, IARI, New Delhi, India.

Wricke, G. 1965. Zur berechnung der okovalenz bei sommerweizen und hafer. Z. Pflanzenzuchtg 52:127-138.

Author

Tiago Olivoto tiagoolivoto@gmail.com

Examples

# \donttest{
library(metan)
# The same approach as mtsi()
# mean performance and stability for GY and HM
# mean performance: The genotype's BLUP
# stability: the WAASB index (lower is better)
# weights: equal for mean performance and stability

model <-
mps(data_ge,
    env = ENV,
    gen = GEN,
    rep = REP,
    resp = everything())
#> Evaluating trait GY |======================                      | 50% 00:00:01 
Evaluating trait HM |============================================| 100% 00:00:03 

#> Method: REML/BLUP
#> Random effects: GEN, GEN:ENV
#> Fixed effects: ENV, REP(ENV)
#> Denominador DF: Satterthwaite's method
#> ---------------------------------------------------------------------------
#> P-values for Likelihood Ratio Test of the analyzed traits
#> ---------------------------------------------------------------------------
#>     model       GY       HM
#>  COMPLETE       NA       NA
#>       GEN 1.11e-05 5.07e-03
#>   GEN:ENV 2.15e-11 2.27e-15
#> ---------------------------------------------------------------------------
#> All variables with significant (p < 0.05) genotype-vs-environment interaction
#> Mean performance: blupg
#> Stability: waasb

# The mean performance and stability after rescaling
model$mps_ind
#> # A tibble: 10 × 3
#>    GEN      GY    HM
#>    <chr> <dbl> <dbl>
#>  1 G1     57.6  56.2
#>  2 G10     0    35.0
#>  3 G2     59.9  17.8
#>  4 G3     95.5  67.9
#>  5 G4     45.7  58.6
#>  6 G5     40.0  61.1
#>  7 G6     45.9  85.5
#>  8 G7     45.2  51.3
#>  9 G8     77.3  90.6
#> 10 G9     16.3  58.7
# }