Genotype analysis in multi-environment trials using mixed-effect or random-effect models.
gamem_met( .data, env, gen, rep, resp, block = NULL, random = "gen", prob = 0.05, verbose = TRUE )
.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 |
block | Defaults to |
random | The effects of the model assumed to be random. Defaults to
|
prob | The probability for estimating confidence interval for BLUP's prediction. |
verbose | Logical argument. If |
An object of class waasb
with the following items for each
variable:
fixed Test for fixed effects.
random Variance components for random effects.
LRT The Likelihood Ratio Test for the random effects.
BLUPgen The random effects and estimated BLUPS for genotypes (If
random = "gen"
or random = "all"
)
BLUPenv The random effects and estimated BLUPS for environments,
(If random = "env"
or random = "all"
).
BLUPint The random effects and estimated BLUPS of all genotypes in all environments.
MeansGxE The phenotypic means of genotypes in the environments.
Details A list summarizing the results. The following information
are shown: Nenv
, the number of environments in the analysis;
Ngen
the number of genotypes in the analysis; Mean
the grand
mean; SE
the standard error of the mean; SD
the standard
deviation. CV
the coefficient of variation of the phenotypic means,
estimating WAASB, Min
the minimum value observed (returning the
genotype and environment), Max
the maximum value observed (returning
the genotype and environment); MinENV
the environment with the lower
mean, MaxENV
the environment with the larger mean observed,
MinGEN
the genotype with the lower mean, MaxGEN
the genotype
with the larger.
ESTIMATES A tibble with the genetic parameters (if random =
"gen"
or random = "all"
) with the following columns: Phenotypic
variance
the phenotypic variance; Heritability
the broad-sense
heritability; GEr2
the coefficient of determination of the interaction
effects; h2mg
the heritability on the mean basis;
Accuracy
the selective accuracy; rge
the genotype-environment
correlation; CVg
the genotypic coefficient of variation; CVr
the residual coefficient of variation; CV ratio
the ratio between
genotypic and residual coefficient of variation.
residuals The residuals of the model.
formula The formula used to fit the model.
The nature of the effects in the model is chosen with the argument
random
. By default, the experimental design considered in each
environment is a randomized complete block design. If block
is
informed, a resolvable alpha-lattice design (Patterson and Williams, 1976) is
implemented. The following six models can be fitted depending on the values
of random
and block
arguments.
Model 1: block = NULL
and random = "gen"
(The
default option). This model considers a Randomized Complete Block Design in
each environment assuming genotype and genotype-environment interaction as
random effects. Environments and blocks nested within environments are
assumed to fixed factors.
Model 2: block = NULL
and random = "env"
. This
model considers a Randomized Complete Block Design in each environment
treating environment, genotype-environment interaction, and blocks nested
within environments as random factors. Genotypes are assumed to be fixed
factors.
Model 3: block = NULL
and random = "all"
. This
model considers a Randomized Complete Block Design in each environment
assuming a random-effect model, i.e., all effects (genotypes, environments,
genotype-vs-environment interaction and blocks nested within environments)
are assumed to be random factors.
Model 4: block
is not NULL
and random =
"gen"
. This model considers an alpha-lattice design in each environment
assuming genotype, genotype-environment interaction, and incomplete blocks
nested within complete replicates as random to make use of inter-block
information (Mohring et al., 2015). Complete replicates nested within
environments and environments are assumed to be fixed factors.
Model 5: block
is not NULL
and random =
"env"
. This model considers an alpha-lattice design in each environment
assuming genotype as fixed. All other sources of variation (environment,
genotype-environment interaction, complete replicates nested within
environments, and incomplete blocks nested within replicates) are assumed
to be random factors.
Model 6: block
is not NULL
and random =
"all"
. This model considers an alpha-lattice design in each environment
assuming all effects, except the intercept, as random factors.
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
Mohring, J., E. Williams, and H.-P. Piepho. 2015. Inter-block information: to recover or not to recover it? TAG. Theor. Appl. Genet. 128:1541-54. doi: 10.1007/s00122-015-2530-0
Patterson, H.D., and E.R. Williams. 1976. A new class of resolvable incomplete block designs. Biometrika 63:83-92.
Tiago Olivoto tiagoolivoto@gmail.com
# \donttest{ library(metan) #===============================================================# # Example 1: Analyzing all numeric variables assuming genotypes # # as random effects # #===============================================================# model <- gamem_met(data_ge, env = ENV, gen = GEN, rep = REP, resp = everything())#>#>#>#>#> --------------------------------------------------------------------------- #> 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#>#>#> # A tibble: 9 x 3 #> Parameters GY HM #> <chr> <dbl> <dbl> #> 1 Phenotypic variance 0.181 5.52 #> 2 Heritability 0.154 0.0887 #> 3 GEIr2 0.313 0.397 #> 4 h2mg 0.815 0.686 #> 5 Accuracy 0.903 0.828 #> 6 rge 0.370 0.435 #> 7 CVg 6.26 1.46 #> 8 CVr 11.6 3.50 #> 9 CV ratio 0.538 0.415#===============================================================# # Example 2: Unbalanced trials # # assuming all factors as random effects # #===============================================================# un_data <- data_ge %>% remove_rows(1:3) %>% droplevels() model2 <- gamem_met(un_data, env = ENV, gen = GEN, rep = REP, random = "all", resp = GY)#>#>#>#>#> --------------------------------------------------------------------------- #> P-values for Likelihood Ratio Test of the analyzed traits #> --------------------------------------------------------------------------- #> model GY #> COMPLETE NA #> GEN 1.31e-05 #> REP(ENV) 9.23e-08 #> ENV 9.33e-17 #> GEN:ENV 2.11e-11 #> --------------------------------------------------------------------------- #> All variables with significant (p < 0.05) genotype-vs-environment interactionget_model_data(model2)#>#>#> # A tibble: 9 x 2 #> Parameters GY #> <chr> <dbl> #> 1 Phenotypic variance 0.907 #> 2 Heritability 0.0308 #> 3 GEIr2 0.314 #> 4 h2mg 0.813 #> 5 Accuracy 0.902 #> 6 rge 0.371 #> 7 CVg 6.24 #> 8 CVr 11.6 #> 9 CV ratio 0.536# }