Type:	Package
Title:	Multi Environment Trials Analysis
Version:	1.19.0
Maintainer:	Tiago Olivoto <tiagoolivoto@gmail.com>
Description:	Performs stability analysis of multi-environment trial data using parametric and non-parametric methods. Parametric methods includes Additive Main Effects and Multiplicative Interaction (AMMI) analysis by Gauch (2013) <doi:10.2135/cropsci2013.04.0241>, Ecovalence by Wricke (1965), Genotype plus Genotype-Environment (GGE) biplot analysis by Yan & Kang (2003) <doi:10.1201/9781420040371>, geometric adaptability index by Mohammadi & Amri (2008) <doi:10.1007/s10681-007-9600-6>, joint regression analysis by Eberhart & Russel (1966) <doi:10.2135/cropsci1966.0011183X000600010011x>, genotypic confidence index by Annicchiarico (1992), Murakami & Cruz's (2004) method, power law residuals (POLAR) statistics by Doring et al. (2015) <doi:10.1016/j.fcr.2015.08.005>, scale-adjusted coefficient of variation by Doring & Reckling (2018) <doi:10.1016/j.eja.2018.06.007>, stability variance by Shukla (1972) <doi:10.1038/hdy.1972.87>, weighted average of absolute scores by Olivoto et al. (2019a) <doi:10.2134/agronj2019.03.0220>, and multi-trait stability index by Olivoto et al. (2019b) <doi:10.2134/agronj2019.03.0221>. Non-parametric methods includes superiority index by Lin & Binns (1988) <doi:10.4141/cjps88-018>, nonparametric measures of phenotypic stability by Huehn (1990) <doi:10.1007/BF00024241>, TOP third statistic by Fox et al. (1990) <doi:10.1007/BF00040364>. Functions for computing biometrical analysis such as path analysis, canonical correlation, partial correlation, clustering analysis, and tools for inspecting, manipulating, summarizing and plotting typical multi-environment trial data are also provided.
License:	GPL-3
URL:	https://github.com/nepem-ufsc/metan, https://nepem-ufsc.github.io/metan/
BugReports:	https://github.com/nepem-ufsc/metan/issues
Depends:	R (≥ 4.1.0)
Imports:	dplyr (≥ 1.0.0), GGally, ggforce, ggplot2 (≥ 3.3.0), ggrepel, lme4, lmerTest, magrittr, mathjaxr, methods, patchwork, purrr, rlang (≥ 0.4.11), tibble, tidyr, tidyselect (≥ 1.0.0)
Suggests:	DT, knitr, rmarkdown, roxygen2, rstudioapi
VignetteBuilder:	knitr
RdMacros:	mathjaxr
Encoding:	UTF-8
Language:	en-US
LazyData:	true
LazyLoad:	true
RoxygenNote:	7.3.2
NeedsCompilation:	no
Packaged:	2024-12-13 23:52:54 UTC; tiago
Author:	Tiago Olivoto [aut, cre, cph]
Repository:	CRAN
Date/Publication:	2024-12-15 01:00:02 UTC

Pipe operator

Description

See ⁠magrittr::[\%>\%][magrittr::pipe]⁠ for details.

Usage

lhs %>% rhs

Annicchiarico's genotypic confidence index

Description

Stability analysis using the known genotypic confidence index (Annicchiarico, 1992).

Usage

Annicchiarico(.data, env, gen, rep, resp, prob = 0.25, verbose = TRUE)

Arguments

Value

A list where each element is the result for one variable and contains the following data frames:

• environments Contains the mean, environmental index and classification as favorable and unfavorable environments.

• general Contains the genotypic confidence index considering all environments.

• favorable Contains the genotypic confidence index considering favorable environments.

• unfavorable Contains the genotypic confidence index considering unfavorable environments.

Author(s)

Tiago Olivoto, tiagoolivoto@gmail.com

References

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

See Also

superiority(), ecovalence(), ge_stats()

Examples

library(metan)
Ann <- Annicchiarico(data_ge2,
                    env = ENV,
                    gen = GEN,
                    rep = REP,
                    resp = PH)
print(Ann)

Fox's stability function

Description

Performs a stability analysis based on the criteria of Fox et al. (1990), using the statistical "TOP third" only. A stratified ranking of the genotypes at each environment is done. The proportion of locations at which the genotype occurred in the top third are expressed in the output.

Usage

Fox(.data, env, gen, resp, verbose = TRUE)

Arguments

Value

An object of class Fox, which is a list containing the results for each variable used in the argument resp. For each variable, a tibble with the following columns is returned.

• GEN the genotype's code.

• mean the mean for the response variable.

• TOP The proportion of locations at which the

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Fox, P.N., B. Skovmand, B.K. Thompson, H.J. Braun, and R. Cormier. 1990. Yield and adaptation of hexaploid spring triticale. Euphytica 47:57-64. doi:10.1007/BF00040364.

Examples

library(metan)
out <- Fox(data_ge2, ENV, GEN, PH)
print(out)

Huehn's stability statistics

Description

Performs a stability analysis based on Huehn (1979) statistics. The four nonparametric measures of phenotypic stability are: S1 (mean of the absolute rank differences of a genotype over the n environments), S2 (variance among the ranks over the k environments), S3 (sum of the absolute deviations), and S6 (relative sum of squares of rank for each genotype).

Usage

Huehn(.data, env, gen, resp, verbose = TRUE)

Arguments

Value

An object of class Huehn, which is a list containing the results for each variable used in the argument resp. For each variable, a tibble with the following columns is returned.

• GEN The genotype's code.

• Y The mean for the response variable.

• S1 Mean of the absolute rank differences of a genotype over the n environments.

• S2 variance among the ranks over the k environments.

• S3 Sum of the absolute deviations.

• S6 Relative sum of squares of rank for each genotype.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

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

Examples

library(metan)
out <- Huehn(data_ge2, ENV, GEN, PH)
print(out)

Schmildt's genotypic confidence index

Description

Stability analysis using the known genotypic confidence index (Annicchiarico, 1992) modified by Schmildt et al. 2011.

Usage

Schmildt(.data, env, gen, rep, resp, prob = 0.05, verbose = TRUE)

Arguments

Value

A list where each element is the result for one variable and contains the following data frames:

• environments Contains the mean, environmental index and classification as favorables and unfavorables environments.

• general Contains the genotypic confidence index considering all environments.

• favorable Contains the genotypic confidence index considering favorable environments.

• unfavorable Contains the genotypic confidence index considering unfavorable environments.

Author(s)

Tiago Olivoto, tiagoolivoto@gmail.com

References

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

Schmildt, E.R., A.L. Nascimento, C.D. Cruz, and J.A.R. Oliveira. 2011. Avaliacao de metodologias de adaptabilidade e estabilidade de cultivares milho. Acta Sci. - Agron. 33:51-58. doi:10.4025/actasciagron.v33i1.5817

See Also

superiority(), ecovalence(), ge_stats(), Annicchiarico()

Examples

library(metan)
Sch <- Schmildt(data_ge2,
                env = ENV,
                gen = GEN,
                rep = REP,
                resp = PH)
print(Sch)

Select helper

Description

These functions allow you to select variables based operations with prefixes and suffixes and length of names.

• difference_var(): Select variables that start with a prefix AND NOT end wiht a suffix.

• intersect_var(): Select variables that start with a prefix AND end wiht a suffix.

• union_var(): Select variables that start with a prefix OR end wiht a suffix.

• width_of(): Select variables with width of n.

• width_greater_than(): Select variables with width greater than n.

• width_less_than(): Select variables with width less than n.

• lower_case_only(): Select variables that contains lower case only (e.g., "env").

• upper_case_only(): Select variables that contains upper case only (e.g., "ENV").

• title_case_only(): Select variables that contains upper case in the first character only (e.g., "Env").

Usage

difference_var(prefix, suffix)

intersect_var(prefix, suffix)

union_var(prefix, suffix)

width_of(n, vars = peek_vars(fn = "width_of"))

width_greater_than(n, vars = peek_vars(fn = "width_greater_than"))

width_less_than(n, vars = peek_vars(fn = "width_less_than"))

lower_case_only(vars = peek_vars(fn = "lower_case_only"))

upper_case_only(vars = peek_vars(fn = "upper_case_only"))

title_case_only(vars = peek_vars(fn = "title_case_only"))

Arguments

Examples

library(metan)


# Select variables that start with "C" and not end with "D".
data_ge2 %>%
select_cols(difference_var("C", "D"))

# Select variables that start with "C" and end with "D".
data_ge2 %>%
select_cols(intersect_var("C", "D"))

# Select variables that start with "C" or end with "D".
data_ge2 %>%
select_cols(union_var("C", "D"))

# Select variables with width name of 4
data_ge2 %>%
select_cols(width_of(4))

# Select variables with width name greater than 2
data_ge2 %>%
select_cols(width_greater_than(2))

# Select variables with width name less than 3
data_ge2 %>%
select_cols(width_less_than(3))

# Creating data with messy column names
df <- head(data_ge, 3)
colnames(df) <- c("Env", "gen", "Rep", "GY", "hm")
select_cols(df, lower_case_only())
select_cols(df, upper_case_only())
select_cols(df, title_case_only())

Shukla's stability variance parameter

Description

The function computes the Shukla's stability variance parameter (1972) and uses the Kang's nonparametric stability (rank sum) to imcorporate the mean performance and stability into a single selection criteria.

Usage

Shukla(.data, env, gen, rep, resp, verbose = TRUE)

Arguments

Value

An object of class Shukla, which is a list containing the results for each variable used in the argument resp. For each variable, a tibble with the following columns is returned.

• GEN the genotype's code.

• Y the mean for the response variable.

• ShuklaVar The Shukla's stability variance parameter.

• rMean The rank for Y (decreasing).

• rShukaVar The rank for ShukaVar.

• ssiShukaVar The simultaneous selection index (ssiShukaVar = rMean + rShukaVar).

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

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

Kang, M.S., and H.N. Pham. 1991. Simultaneous Selection for High Yielding and Stable Crop Genotypes. Agron. J. 83:161. doi:10.2134/agronj1991.00021962008300010037x

Examples

library(metan)
out <- Shukla(data_ge2,
             env = ENV,
             gen = GEN,
             rep = REP,
             resp = PH)

Smith-Hazel index

Description

Computes the Smith (1936) and Hazel (1943) index given economic weights and phenotypic and genotypic variance-covariance matrices. The Smith-Hazel index is computed as follows: \[\bf{b = P^{-1}Aw}\]

where \(\bf{P}\) and \(\bf{G}\) are phenotypic and genetic covariance matrices, respectively, and \(\bf{b}\) and \(\bf{w}\) are vectors of index coefficients and economic weightings, respectively.

The genetic worth \(I\) of an individual genotype based on traits x, y, ..., n, is calculated as:

where b the index coefficient for the traits x, y, ..., n, respectively, and G is the individual genotype BLUPs for the traits x, y, ..., n, respectively.

Usage

Smith_Hazel(
  .data,
  use_data = "blup",
  pcov = NULL,
  gcov = NULL,
  SI = 15,
  weights = NULL
)

Arguments

Details

When using the phenotypic means in .data, be sure the genotype's code are in rownames. If .data is an object of class gamem them the BLUPs for each genotype are used to compute the index. In this case, the genetic covariance components are estimated by mean cross products.

Value

An object of class hz containing:

• b: the vector of index coefficient.

• index: The genetic worth.

• sel_dif_trait: The selection differencial.

• sel_gen: The selected genotypes.

• gcov: The genotypic variance-covariance matrix

• pcov: The phenotypic variance-covariance matrix

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Smith, H.F. 1936. A discriminant function for plant selection. Ann. Eugen. 7:240-250. doi:10.1111/j.1469-1809.1936.tb02143.x

Hazel, L.N. 1943. The genetic basis for constructing selection indexes. Genetics 28:476-90. https://www.genetics.org/content/28/6/476.short

See Also

mtsi(), mgidi(), fai_blup()

Examples

vcov <- covcor_design(data_g, GEN, REP, everything())
means <- as.matrix(vcov$means)
pcov <- vcov$phen_cov
gcov <- vcov$geno_cov

index <- Smith_Hazel(means, pcov = pcov, gcov = gcov, weights = rep(1, 15))

Thennarasu's stability statistics

Description

Performs a stability analysis based on Thennarasu (1995) statistics.

Usage

Thennarasu(.data, env, gen, resp, verbose = TRUE)

Arguments

Value

An object of class Thennarasu, which is a list containing the results for each variable used in the argument resp. For each variable, a tibble with the columns GEN, N1, N2, N3 and N4 is returned.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

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.

Examples

library(metan)
out <- Thennarasu(data_ge, ENV, GEN, GY)
print(out)

Adjusted Coefficient of Variation

Description

Computes the scale-adjusted coefficient of variation, acv, (Doring and Reckling, 2018) to account for the systematic dependence of \(\sigma^2\) from \(\mu\). The acv is computed as follows: \[acv = \frac{\sqrt{10^{\tilde v_i}}}{\mu_i}\times 100\] where \(\tilde v_i\) is the adjusted logarithm of the variance computed as: \[\tilde v_i = a + (b - 2)\frac{1}{n}\sum m_i + 2m_i + e_i\] being \(a\) and \(b\) the coefficients of the linear regression for \(log_{10}\) of the variance over the \(log_{10}\) of the mean; \( m_i\) is the \(log_{10}\) of the mean, and \( e_i\) is the Power Law Residuals (POLAR), i.e., the residuals for the previously described regression.

Usage

acv(mean, var, na.rm = FALSE)

Arguments

Value

A tibble with the following columns

• mean The mean values.

• var The variance values;

• log10_mean The base 10 logarithm of mean;

• log10_var The base 10 logarithm of variance;

• POLAR The Power Law Residuals;

• cv The standard coefficient of variation;

• acv Adjusted coefficient of variation.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

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

Examples

################# Table 1 from Doring and Reckling (2018)  ###########

# Mean values
u <- c(0.5891, 0.6169, 0.7944, 1.0310, 1.5032, 3.8610, 4.6969, 6.1148,
       7.1526, 7.5348, 1.2229, 1.6321, 2.4293, 2.5011, 3.0161)

# Variances
v <- c(0.0064, 0.0141, 0.0218, 0.0318, 0.0314, 0.0766, 0.0620, 0.0822,
       0.1605, 0.1986, 0.0157, 0.0593, 0.0565, 0.1997, 0.2715)

library(metan)
acv(u, v)

AMMI-based stability indexes

Description

• ammi_indexes() computes several AMMI-based stability statistics. See Details for a detailed overview.

• AMMI_indexes() use ammi_indexes() instead.

Usage

ammi_indexes(.data, order.y = NULL, level = 0.95)

Arguments

Details

First, let's define some symbols: \(N'\) is the number of significant interation principal component axis (IPCs) that were retained in the AMMI model via F tests); \(\lambda_{n}\) is the singular value for th IPC and correspondingly \(\lambda_{n}^{2}\) its eigen value; \(\gamma_{in}\) is the eigenvector value for ith genotype; \(\delta_{jn}\) is the eigenvector value for the th environment. \(PC_{1}\), \(PC_{2}\), and \(PC_{n}\) are the scores of 1st, 2nd, and nth IPC; respectively; \(\theta_{1}\), \(\theta_{2}\), and \(\theta_{n}\) are percentage sum of squares explained by the 1st, 2nd, and nth IPC, respectively.

• AMMI Based Stability Parameter (ASTAB) (Rao and Prabhakaran 2005). \[ASTAB = \sum_{n=1}^{N'}\lambda_{n}\gamma_{in}^{2}\]

• AMMI Stability Index (ASI) (Jambhulkar et al. 2017) \[ASI = \sqrt{\left [ PC_{1}^{2} \times \theta_{1}^{2} \right ]+\left[ PC_{2}^{2} \times \theta_{2}^{2} \right ]}\]

• AMMI-stability value (ASV) (Purchase et al., 2000). \[ASV_{i}=\sqrt{\frac{SS_{IPCA1}}{SS_{IPCA2}}(\mathrm{IPC} \mathrm{A} 1)^{2}+(\mathrm{IPCA} 2)^{2}}\]

• Sum Across Environments of Absolute Value of GEI Modelled by AMMI (AVAMGE) (Zali et al. 2012) \[AV_{(AMGE)} = \sum_{j=1}^{E} \sum_{n=1}^{N'} \left |\lambda_{n}\gamma_{in} \delta_{jn} \right |\]

• Annicchiarico's D Parameter values (Da) (Annicchiarico 1997) \[D_{a} = \sqrt{\sum_{n=1}^{N'}(\lambda_{n}\gamma_{in})^2}\]

• Zhang's D Parameter (Dz) (Zhang et al. 1998) \[D_{z} = \sqrt{\sum_{n=1}^{N'}\gamma_{in}^{2}}\]

• Sums of the Averages of the Squared Eigenvector Values (EV) (Zobel 1994) \[EV = \sum_{n=1}^{N'}\frac{\gamma_{in}^2}{N'}\]

• Stability Measure Based on Fitted AMMI Model (FA) (Raju 2002) \[FA = \sum_{n=1}^{N'}\lambda_{n}^{2}\gamma_{in}^{2}\]

• Modified AMMI Stability Index (MASI) (Ajay et al. 2018) \[MASI = \sqrt{ \sum_{n=1}^{N'} PC_{n}^{2} \times \theta_{n}^{2}}\]

• Modified AMMI Stability Value (MASV) (Ajay et al. 2019) \[MASV = \sqrt{\sum_{n=1}^{N'-1}\left (\frac{SSIPC_{n}}{SSIPC_{n+1}} \right ) \times (PC_{n})^2 + \left (PC_{N'}\right )^2}\]

• Sums of the Absolute Value of the IPC Scores (SIPC) (Sneller et al. 1997) \[SIPC = \sum_{n=1}^{N'} | \lambda_{n}^{0.5}\gamma_{in}|\]

• Absolute Value of the Relative Contribution of IPCs to the Interaction (Za) (Zali et al. 2012) \[Za = \sum_{i=1}^{N'} | \theta_{n}\gamma_{in} |\]

• Weighted average of absolute scores (WAAS) (Olivoto et al. 2019) \[WAAS_i = \sum_{k = 1}^{p} |IPCA_{ik} \times \theta_{k}/ \sum_{k = 1}^{p}\theta_{k}\]

For all the statistics, simultaneous selection indexes (SSI) are also computed by summation of the ranks of the stability and mean performance, Y_R, (Farshadfar, 2008).

Value

A list where each element contains the result AMMI-based stability indexes for one variable.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Ajay BC, Aravind J, Abdul Fiyaz R, Bera SK, Kumar N, Gangadhar K, Kona P (2018). “Modified AMMI Stability Index (MASI) for stability analysis.” ICAR-DGR Newsletter, 18, 4–5.

Ajay BC, Aravind J, Fiyaz RA, Kumar N, Lal C, Gangadhar K, Kona P, Dagla MC, Bera SK (2019). “Rectification of modified AMMI stability value (MASV).” Indian Journal of Genetics and Plant Breeding (The), 79, 726–731. https://www.isgpb.org/article/rectification-of-modified-ammi-stability-value-masv.

Annicchiarico P (1997). “Joint regression vs AMMI analysis of genotype-environment interactions for cereals in Italy.” Euphytica, 94(1), 53–62. doi:10.1023/A:1002954824178

Farshadfar E (2008) Incorporation of AMMI stability value and grain yield in a single non-parametric index (GSI) in bread wheat. Pakistan J Biol Sci 11:1791–1796. doi:10.3923/pjbs.2008.1791.1796

Jambhulkar NN, Rath NC, Bose LK, Subudhi HN, Biswajit M, Lipi D, Meher J (2017). “Stability analysis for grain yield in rice in demonstrations conducted during rabi season in India.” Oryza, 54(2), 236–240. doi:10.5958/2249-5266.2017.00030.3

Olivoto T, LUcio ADC, Silva JAG, et al (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

Raju BMK (2002). “A study on AMMI model and its biplots.” Journal of the Indian Society of Agricultural Statistics, 55(3), 297–322.

Rao AR, Prabhakaran VT (2005). “Use of AMMI in simultaneous selection of genotypes for yield and stability.” Journal of the Indian Society of Agricultural Statistics, 59, 76–82.

Sneller CH, Kilgore-Norquest L, Dombek D (1997). “Repeatability of yield stability statistics in soybean.” Crop Science, 37(2), 383–390. doi:10.2135/cropsci1997.0011183X003700020013x

Zali H, Farshadfar E, Sabaghpour SH, Karimizadeh R (2012). “Evaluation of genotype × environment interaction in chickpea using measures of stability from AMMI model.” Annals of Biological Research, 3(7), 3126–3136.

Zhang Z, Lu C, Xiang Z (1998). “Analysis of variety stability based on AMMI model.” Acta Agronomica Sinica, 24(3), 304–309. http://zwxb.chinacrops.org/EN/Y1998/V24/I03/304.

Zobel RW (1994). “Stress resistance and root systems.” In Proceedings of the Workshop on Adaptation of Plants to Soil Stress. 1-4 August, 1993. INTSORMIL Publication 94-2, 80–99. Institute of Agriculture and Natural Resources, University of Nebraska-Lincoln.

Examples

library(metan)
model <-
  performs_ammi(data_ge,
                env = ENV,
                gen = GEN,
                rep = REP,
                resp = c(GY, HM))
model_indexes <- ammi_indexes(model)


# Alternatively (and more intuitively) using %>%
# If resp is not declared, all traits are analyzed
res_ind <- data_ge %>%
           performs_ammi(ENV, GEN, REP, verbose = FALSE) %>%
           ammi_indexes()

rbind_fill_id(res_ind, .id = "TRAIT")

Within-environment analysis of variance

Description

Performs a within-environment analysis of variance in randomized complete block or alpha-lattice designs and returns values such as Mean Squares, p-values, coefficient of variation, heritability, and accuracy of selection.

Usage

anova_ind(.data, env, gen, rep, resp, block = NULL, verbose = TRUE)

Arguments

Value

A list where each element is the result for one variable containing (1) individual: A tidy tbl_df with the results of the individual analysis of variance with the following column names, and (2) MSRatio: The ratio between the higher and lower residual mean square. The following columns are returned, depending on the experimental design

• For analysis in alpha-lattice designs:

  • MEAN: The grand mean.

  • ⁠DFG, DFCR, and DFIB_R, and DFE⁠: The degree of freedom for genotype, complete replicates, incomplete blocks within replicates, and error, respectively.

  • ⁠MSG, MSCR, MSIB_R⁠: The mean squares for genotype, replicates, incomplete blocks within replicates, and error, respectively.

  • ⁠FCG, FCR, FCIB_R⁠: The F-calculated for genotype, replicates and incomplete blocks within replicates, respectively.

  • ⁠PFG, PFCR, PFIB_R⁠: The P-values for genotype, replicates and incomplete blocks within replicates, respectively.

  • CV: coefficient of variation.

  • h2: broad-sense heritability.

  • AS: accuracy of selection (square root of h2)

• For analysis in randomized complete block design:

  • MEAN: The grand mean.

  • ⁠DFG, DFB, and DFE⁠: The degree of freedom for genotype blocks, and error, respectively.

  • ⁠MSG, MSB, and MSE⁠: The mean squares for genotype blocks, and error, respectively.

  • ⁠FCG and FCB⁠: The F-calculated for genotype and blocks, respectively.

  • ⁠PFG and PFB⁠: The P-values for genotype and blocks, respectively.

  • CV: coefficient of variation.

  • h2: broad-sense heritability.

  • h2MG: broad-sense heritability at a plot level.

  • AS: accuracy of selection (square root of h2)

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Patterson, H.D., and E.R. Williams. 1976. A new class of resolvable incomplete block designs. Biometrika 63:83-92.

Examples

library(metan)
# ANOVA for all variables in data
ind_an <- anova_ind(data_ge,
                    env = ENV,
                    gen = GEN,
                    rep = REP,
                    resp = everything())
# mean for each environment
get_model_data(ind_an)

# P-value for genotype effect
get_model_data(ind_an, "PFG")

Joint analysis of variance

Description

Performs a joint analysis of variance to check for the presence of genotype-vs-environment interactions using both randomized complete block and alpha-lattice designs.

Usage

anova_joint(.data, env, gen, rep, resp, block = NULL, verbose = TRUE)

Arguments

Value

A list where each element is the result for one variable containing the following objects:

• anova: The two-way ANOVA table

• model: The model of class lm.

• augment: Information about each observation in the dataset. This includes predicted values in the fitted column, residuals in the resid column, standardized residuals in the stdres column, the diagonal of the 'hat' matrix in the hat, and standard errors for the fitted values in the se.fit column.

• details: A tibble with the following data: Ngen, the number of genotypes; OVmean, the grand mean; Min, the minimum observed (returning the genotype and replication/block); Max the maximum observed, MinGEN the loser winner genotype, MaxGEN, the winner genotype.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Patterson, H.D., and E.R. Williams. 1976. A new class of resolvable incomplete block designs. Biometrika 63:83-92.

See Also

get_model_data() anova_ind()

Examples

library(metan)
# traditional usage approach
j_an <- anova_joint(data_ge,
                    env = ENV,
                    gen = GEN,
                    rep = REP,
                    resp = everything())
# Predicted values
get_model_data(j_an)

# Details
get_model_data(j_an, "details")

Arrange separate ggplots into the same graphic

Description

This is a wraper function around patchwork::wrap_plots() and patchwork::plot_annotation() to arrange ggplot2 objects.

Usage

arrange_ggplot(
  ...,
  nrow = NULL,
  ncol = NULL,
  widths = NULL,
  heights = NULL,
  guides = NULL,
  design = NULL,
  legend.position = "bottom",
  title = NULL,
  subtitle = NULL,
  caption = NULL,
  tag_levels = NULL,
  tag_prefix = NULL,
  tag_suffix = NULL,
  tag_sep = NULL,
  theme = NULL
)

Arguments

Value

A patchwork object

Examples

library(ggplot2)
library(metan)
p1 <- ggplot(mtcars, aes(wt, mpg)) +
      geom_point()

p2 <- ggplot(mpg, aes(class, hwy)) +
             geom_boxplot()

# Default plot
arrange_ggplot(p1, p2)

# Insert plot annotation, titles and subtitles
arrange_ggplot(p1, p2,
               ncol = 1,
               tag_levels = "1",
               tag_prefix = "P.",
               title = "My grouped ggplot",
               subtitle = "Made with arrange_ggplot()",
               caption = "P1 = scatter plot - P2 = boxplot")

Coerce to an object of class lpcor

Description

Functions to check if an object is of class lpcor, or coerce it if possible.

Usage

as.lpcor(...)

Arguments

Value

An object of class lpcor.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
library(dplyr)
mt_num = mtcars %>% select_if(., is.numeric)
lpdata = as.lpcor(cor(mt_num[1:5]),
                  cor(mt_num[1:5]),
                  cor(mt_num[2:6]),
                  cor(mt_num[4:8]))
is.lpcor(lpdata)

Fast way to create bar plots

Description

• plot_bars() Creates a bar plot based on one categorical variable and one numeric variable. It can be used to show the results of a one-way trial with qualitative treatments.

• plot_factbars() Creates a bar plot based on two categorical variables and one numeric variable. It can be used to show the results of a two-way trial with qualitative-qualitative treatment structure.

Usage

plot_bars(
  .data,
  x,
  y,
  order = NULL,
  y.lim = NULL,
  y.breaks = waiver(),
  y.expand = 0.05,
  y.contract = 0,
  xlab = NULL,
  ylab = NULL,
  n.dodge = 1,
  check.overlap = FALSE,
  color.bar = "black",
  fill.bar = "gray",
  lab.bar = NULL,
  lab.bar.hjust = 0.5,
  lab.bar.vjust = -0.5,
  lab.bar.angle = 0,
  size.text.bar = 5,
  values = FALSE,
  values.hjust = 0.5,
  values.vjust = 1.5,
  values.angle = 0,
  values.digits = 2,
  values.size = 4,
  lab.x.hjust = 0.5,
  lab.x.vjust = 1,
  lab.x.angle = 0,
  errorbar = TRUE,
  stat.erbar = "se",
  width.erbar = NULL,
  level = 0.95,
  invert = FALSE,
  width.bar = 0.9,
  size.line = 0.5,
  size.text = 12,
  fontfam = "sans",
  na.rm = TRUE,
  verbose = FALSE,
  plot_theme = theme_metan()
)

plot_factbars(
  .data,
  ...,
  resp,
  y.lim = NULL,
  y.breaks = waiver(),
  y.expand = 0.05,
  y.contract = 0,
  xlab = NULL,
  ylab = NULL,
  n.dodge = 1,
  check.overlap = FALSE,
  lab.bar = NULL,
  lab.bar.hjust = 0.5,
  lab.bar.vjust = -0.5,
  lab.bar.angle = 0,
  size.text.bar = 5,
  values = FALSE,
  values.hjust = 0.5,
  values.vjust = 1.5,
  values.angle = 0,
  values.digits = 2,
  values.size = 4,
  lab.x.hjust = 0.5,
  lab.x.vjust = 1,
  lab.x.angle = 0,
  errorbar = TRUE,
  stat.erbar = "se",
  width.erbar = NULL,
  level = 0.95,
  invert = FALSE,
  col = TRUE,
  palette = "Spectral",
  width.bar = 0.9,
  legend.position = "bottom",
  size.line = 0.5,
  size.text = 12,
  fontfam = "sans",
  na.rm = TRUE,
  verbose = FALSE,
  plot_theme = theme_metan()
)

Arguments

Value

An object of class ⁠gg, ggplot⁠.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

See Also

plot_lines(), plot_factlines()

Examples

library(metan)
# two categorical variables
plot_factbars(data_ge2,
              GEN,
              ENV,
              resp = PH)

# one categorical variable
p1 <- plot_bars(data_g, GEN, PH)
p2 <- plot_bars(data_g, GEN, PH,
                n.dodge = 2, # two rows for x labels
                y.expand = 0.1, # expand y scale
                y.contract = -0.75, # contract the lower limit
                errorbar = FALSE, # remove errorbar
                color.bar = "red", # color of bars
                fill.bar = alpha_color("cyan", 75), # create a transparent color
                lab.bar = letters[1:13]) # add labels
arrange_ggplot(p1, p2)

Bind cross-validation objects

Description

Helper function that combines objects of class cv_ammi, cv_ammif or cv_blup. It is useful when looking for a boxplot containing the RMSPD values of those cross-validation procedures.

Usage

bind_cv(..., bind = "boot", sort = TRUE)

Arguments

Value

An object of class cv_ammif. The results will depend on the argument bind. If bind = 'boot' then the RMSPD of all models in ... will be bind to a unique data frame. If bind = 'means' then the RMSPD mean of all models in ... will be bind to an unique data frame.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
# Two examples with only 5 resampling procedures
AMMI <- cv_ammi(data_ge,
                resp = GY,
                gen = GEN,
                env = ENV,
                rep = REP,
                nboot = 5)
BLUP <- cv_blup(data_ge,
                resp = GY,
                gen = GEN,
                env = ENV,
                rep = REP,
                nboot = 5)
bind_data <- bind_cv(AMMI, BLUP)
plot(bind_data)

print(bind_cv(AMMI, BLUP, bind = 'means'))

Stability indexes based on a mixed-effect model

Description

• 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.

Usage

hmgv(model)

rpgv(model)

hmrpgv(model)

blup_indexes(model)

Arguments

Details

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 \[HMRPG{V_i} = \frac{E}{{\sum\limits_{j = 1}^E {\frac{1}{{G{v_{ij}}/{\mu _j}}}} }}\]

Value

A tibble containing the indexes.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

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. Lúcio, 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

Examples

library(metan)
res_ind <- waasb(data_ge,
                 env = ENV,
                 gen = GEN,
                 rep = REP,
                 resp = c(GY, HM),
                 verbose = FALSE)
model_indexes <- blup_indexes(res_ind)
gmd(model_indexes)

Canonical correlation analysis

Description

Performs canonical correlation analysis with collinearity diagnostic, estimation of canonical loads, canonical scores, and hypothesis testing for correlation pairs.

Usage

can_corr(
  .data,
  FG,
  SG,
  by = NULL,
  use = "cor",
  test = "Bartlett",
  prob = 0.05,
  center = TRUE,
  stdscores = FALSE,
  verbose = TRUE,
  collinearity = TRUE
)

Arguments

Value

If .data is a grouped data passed from dplyr::group_by() then the results will be returned into a list-column of data frames.

• Matrix The correlation (or covariance) matrix of the variables

• MFG, MSG The correlation (or covariance) matrix for the variables of the first group or second group, respectively.

• MFG_SG The correlation (or covariance) matrix for the variables of the first group with the second group.

• Coef_FG, Coef_SG Matrix of the canonical coefficients of the first group or second group, respectively.

• Loads_FG, Loads_SG Matrix of the canonical loadings of the first group or second group, respectively.

• Score_FG, Score_SG Canonical scores for the variables in FG and SG, respectively.

• Crossload_FG, Crossload_FG Canonical cross-loadings for FG variables on the SG scores, and cross-loadings for SG variables on the FG scores, respectively.

• SigTest A dataframe with the correlation of the canonical pairs and hypothesis testing results.

• collinearity A list with the collinearity diagnostic for each group of variables.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Olivoto, T., V.Q. Souza, M. Nardino, I.R. Carvalho, M. Ferrari, A.J. Pelegrin, V.J. Szareski, and D. Schmidt. 2017. Multicollinearity in path analysis: a simple method to reduce its effects. Agron. J. 109:131-142. doi:10.2134/agronj2016.04.0196

Examples

library(metan)

cc1 <- can_corr(data_ge2,
               FG = c(PH, EH, EP),
               SG = c(EL, ED, CL, CD, CW, KW, NR))


# Canonical correlations for each environment
cc3 <- data_ge2 %>%
       can_corr(FG = c(PH, EH, EP),
                SG = c(EL, ED, CL, CD, CW, KW, NR),
                by = ENV,
                verbose = FALSE)

Clustering analysis

Description

Performs clustering analysis with selection of variables.

Usage

clustering(
  .data,
  ...,
  by = NULL,
  scale = FALSE,
  selvar = FALSE,
  verbose = TRUE,
  distmethod = "euclidean",
  clustmethod = "average",
  nclust = NA
)

Arguments

Details

When selvar = TRUE a variable selection algorithm is executed. The objective is to select a group of variables that most contribute to explain the variability of the original data. The selection of the variables is based on eigenvalue/eigenvectors solution based on the following steps.

1. compute the distance matrix and the cophenetic correlation with the original variables (all numeric variables in dataset);

2. compute the eigenvalues and eigenvectors of the correlation matrix between the variables;

3. Delete the variable with the largest weight (highest eigenvector in the lowest eigenvalue);

4. Compute the distance matrix and cophenetic correlation with the remaining variables;

5. Compute the Mantel's correlation between the obtained distances matrix and the original distance matrix;

6. Iterate steps 2 to 5 p - 2 times, where p is the number of original variables.

At the end of the p - 2 iterations, a summary of the models is returned. The distance is calculated with the variables that generated the model with the largest cophenetic correlation. I suggest a careful evaluation aiming at choosing a parsimonious model, i.e., the one with the fewer number of variables, that presents acceptable cophenetic correlation and high similarity with the original distances.

Value

• data The data that was used to compute the distances.

• cutpoint The cutpoint of the dendrogram according to Mojena (1977).

• distance The matrix with the distances.

• de The distances in an object of class dist.

• hc The hierarchical clustering.

• Sqt The total sum of squares.

• tab A table with the clusters and similarity.

• clusters The sum of square and the mean of the clusters for each variable.

• cofgrap If selectvar = TRUE, then, cofpgrap is a ggplot2-based graphic showing the cophenetic correlation for each model (with different number of variables). Else, will be a NULL object.

• statistics If selectvar = TRUE, then, statistics shows the summary of the models fitted with different number of variables, including cophenetic correlation, Mantel's correlation with the original distances (all variables) and the p-value associated with the Mantel's test. Else, will be a NULL object.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Mojena, R. 2015. Hierarchical grouping methods and stopping rules: an evaluation. Comput. J. 20:359-363. doi:10.1093/comjnl/20.4.359

Examples

library(metan)

# All rows and all numeric variables from data
d1 <- clustering(data_ge2)

# Based on the mean for each genotype
mean_gen <-
 data_ge2 %>%
 mean_by(GEN) %>%
 column_to_rownames("GEN")

d2 <- clustering(mean_gen)


# Select variables for compute the distances
d3 <- clustering(mean_gen, selvar = TRUE)

# Compute the distances with standardized data
# Define 4 clusters
d4 <- clustering(data_ge,
                 by = ENV,
                 scale = TRUE,
                 nclust = 4)

Computes the coincidence index of genotype selection

Description

Computes the coincidence index (Hamblin and Zimmermann, 1986) as follows:

where A is the number of selected genotypes common to different methods; C is the number of expected genotypes selected by chance; and M is the number of genotypes selected according to the selection intensity.

Usage

coincidence_index(..., total, sel1 = NULL, sel2 = NULL)

Arguments

Value

A list with the following elements:

• coincidence: A data frame with the coincidence index, number of common genotypes and the list of common genotypes for each model combination.

• coincidence_mat: A matrix-like containing the coincidence index.

• genotypes: The number of common genotypes for all models, i.e., the insersection of the selected genotypes of all models

References

Hamblin, J., and M.J. de O. Zimmermann. 1986. Breeding Common Bean for Yield in Mixtures. p. 245-272. In Plant Breeding Reviews. John Wiley & Sons, Inc., Hoboken, NJ, USA.doi:10.1002/9781118061015.ch8

Examples

sel1 <- paste("G", 1:30, sep = "")
sel2 <- paste("G", 16:45, sep = "")
coincidence_index(sel1 = sel1, sel2 = sel2, total = 150)

Collinearity Diagnostics

Description

Perform a (multi)collinearity diagnostic of a correlation matrix of predictor variables using several indicators, as shown by Olivoto et al. (2017).

Usage

colindiag(.data, ..., by = NULL, n = NULL)

Arguments

Value

If .data is a grouped data passed from dplyr::group_by() then the results will be returned into a list-column of data frames.

• cormat A symmetric Pearson's coefficient correlation matrix between the variables

• corlist A hypothesis testing for each of the correlation coefficients

• evalevet The eigenvalues with associated eigenvectors of the correlation matrix

• indicators A data.frame with the following indicators

• VIF The Variance Inflation Factors, being the diagonal elements of the inverse of the correlation matrix.

• cn The Condition Number of the correlation matrix, given by the ratio between the largest and smallest eigenvalue.

• det The determinant of the correlation matrix.

• ncorhigh Number of correlation greather than |0.8|.

• largest_corr The largest correlation (in absolute value) observed.

• smallest_corr The smallest correlation (in absolute value) observed.

• weight_var The variables with largest eigenvector (largest weight) in the eigenvalue of smallest value, sorted in decreasing order.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Olivoto, T., V.Q. Souza, M. Nardino, I.R. Carvalho, M. Ferrari, A.J. Pelegrin, V.J. Szareski, and D. Schmidt. 2017. Multicollinearity in path analysis: a simple method to reduce its effects. Agron. J. 109:131-142. doi:10.2134/agronj2016.04.0196

Examples

# Using the correlation matrix
library(metan)

cor_iris <- cor(iris[,1:4])
n <- nrow(iris)

col_diag <- colindiag(cor_iris, n = n)


# Using a data frame
col_diag_gen <- data_ge2 %>%
                group_by(GEN) %>%
                colindiag()

# Diagnostic by levels of a factor
# For variables with "N" in variable name
col_diag_gen <- data_ge2 %>%
                group_by(GEN) %>%
                colindiag(contains("N"))

Pairwise combinations of variables

Description

Pairwise combinations of variables that will be the result of a function applied to each combination.

Usage

comb_vars(.data, order = "first", FUN = "+", verbose = TRUE)

Arguments

Value

A data frame containing all possible combination of variables. Each combination is the result of the function in FUN applied to the two variables.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
data <- data.frame(A = rnorm(n = 5, mean = 10, sd = 3),
                  B = rnorm(n = 5, mean = 120, sd = 30),
                  C = rnorm(n = 5, mean = 40, sd = 10),
                  D = rnorm(n = 5, mean = 1100, sd = 200),
                  E = rnorm(n = 5, mean = 2, sd = 1))
comb1 <- comb_vars(data)
comb2 <- comb_vars(data, FUN = '*', order = 'second')

Confidence interval for correlation coefficient

Description

Computes the half-width confidence interval for correlation coefficient using the nonparametric method proposed by Olivoto et al. (2018).

The half-width confidence interval is computed according to the following equation:

where \(n\) is the sample size and \(r\) is the correlation coefficient.

Usage

corr_ci(
  .data = NA,
  ...,
  r = NULL,
  n = NULL,
  by = NULL,
  sel.var = NULL,
  verbose = TRUE
)

Arguments

Value

A tibble containing the values of the correlation, confidence interval, upper and lower limits for all combination of variables.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Olivoto, T., A.D.C. Lucio, V.Q. Souza, M. Nardino, M.I. Diel, B.G. Sari, D.. K. Krysczun, D. Meira, and C. Meier. 2018. Confidence interval width for Pearson's correlation coefficient: a Gaussian-independent estimator based on sample size and strength of association. Agron. J. 110:1-8. doi:10.2134/agronj2016.04.0196

Examples

library(metan)

CI1 <- corr_ci(data_ge2)

# By each level of the factor 'ENV'
CI2 <- corr_ci(data_ge2, CD, TKW, NKE,
               by = ENV,
               verbose = FALSE)
CI2

Linear and partial correlation coefficients

Description

Computes Pearson's linear correlation or partial correlation with p-values

Usage

corr_coef(
  data,
  ...,
  type = c("linear", "partial"),
  method = c("pearson", "kendall", "spearman"),
  use = c("pairwise.complete.obs", "everything", "complete.obs"),
  by = NULL,
  verbose = TRUE
)

Arguments

Details

The partial correlation coefficient is a technique based on matrix operations that allow us to identify the association between two variables by removing the effects of the other set of variables present (Anderson 2003) A generalized way to estimate the partial correlation coefficient between two variables (i and j ) is through the simple correlation matrix that involves these two variables and m other variables from which we want to remove the effects. The estimate of the partial correlation coefficient between i and j excluding the effect of m other variables is given by: \[r_{ij.m} = \frac{{- {a_{ij}}}}{{\sqrt {{a_{ii}}{a_{jj}}}}}\]

Where \(r_{ij.m}\) is the partial correlation coefficient between variables i and j, without the effect of the other m variables; \(a_{ij}\) is the ij-order element of the inverse of the linear correlation matrix; \(a_{ii}\), and \(a_{jj}\) are the elements of orders ii and jj, respectively, of the inverse of the simple correlation matrix.

Value

A list with the correlation coefficients and p-values

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Anderson, T. W. 2003. An introduction to multivariate statistical analysis. 3rd ed. Wiley-Interscience.

Examples

library(metan)

# All numeric variables
all <- corr_coef(data_ge2)


# Select variable
sel <-
  corr_coef(data_ge2,
            EP, EL, CD, CL)
sel$cor

# Select variables, partial correlation
sel <-
  corr_coef(data_ge2,
            EP, EL, CD, CL,
            type = "partial")
sel$cor

Focus on section of a correlation matrix

Description

Select a set of variables from a correlation matrix to keep as the columns, and exclude these or all other variables from the rows.

Usage

corr_focus(model, ...)

Arguments

Value

A tibble

Examples

corr_coef(data_ge2) |> corr_focus(PH)

Visualization of a correlation matrix

Description

Graphical and numerical visualization of a correlation matrix

Usage

corr_plot(
  .data,
  ...,
  col.by = NULL,
  upper = "corr",
  lower = "scatter",
  decimal.mark = ".",
  axis.labels = FALSE,
  show.labels.in = "show",
  size.axis.label = 12,
  size.varnames = 12,
  col.varnames = "black",
  diag = TRUE,
  diag.type = "histogram",
  bins = 20,
  col.diag = "gray",
  alpha.diag = 1,
  col.up.panel = "gray",
  col.lw.panel = "gray",
  col.dia.panel = "gray",
  prob = 0.05,
  col.sign = "green",
  alpha.sign = 0.15,
  lab.position = "tr",
  progress = NULL,
  smooth = FALSE,
  col.smooth = "red",
  confint = TRUE,
  size.point = 1,
  shape.point = 19,
  alpha.point = 0.7,
  fill.point = NULL,
  col.point = "black",
  size.line = 0.5,
  minsize = 2,
  maxsize = 3,
  pan.spacing = 0.15,
  digits = 2,
  export = FALSE,
  file.type = "pdf",
  file.name = NULL,
  width = 8,
  height = 7,
  resolution = 300
)

Arguments

Value

An object of class ⁠gg, ggmatrix⁠.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
dataset <- data_ge2 %>% select_cols(1:7)

# Default plot setting
corr_plot(dataset)

# Chosing variables to be correlated
corr_plot(dataset, PH, EH, EL)


# Axis labels, similar to the function pairs()
# Gray scale
corr_plot(dataset, PH, EH, EL,
          shape.point = 19,
          size.point = 2,
          alpha.point = 0.5,
          alpha.diag = 0,
          pan.spacing = 0,
          col.sign = 'gray',
          alpha.sign = 0.3,
          axis.labels = TRUE)

corr_plot(dataset, PH, EH, EL,
          prob = 0.01,
          shape.point = 21,
          col.point = 'black',
          fill.point = 'orange',
          size.point = 2,
          alpha.point = 0.6,
          maxsize = 4,
          minsize = 2,
          smooth = TRUE,
          size.line = 1,
          col.smooth = 'black',
          col.sign = 'cyan',
          col.up.panel = 'black',
          col.lw.panel = 'black',
          col.dia.panel = 'black',
          pan.spacing = 0,
          lab.position = 'tl')

Sample size planning for a desired Pearson's correlation confidence interval

Description

Find the required (sufficient) sample size for computing a Pearson correlation coefficient with a desired confidence interval (Olivoto et al., 2018) as follows \[n = {\left[ {\frac{{C{I_w}}}{{{{0.45304}^r} \times 2.25152}}} \right]^{{\rm{ - 0}}{\rm{.50089}}}}\]

where \(CI_w\) is desired confidence interval and \(r\) is the correlation coefficient.

Usage

corr_ss(r, CI, verbose = TRUE)

Arguments

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Olivoto, T., A.D.C. Lucio, V.Q. Souza, M. Nardino, M.I. Diel, B.G. Sari, D.. K. Krysczun, D. Meira, and C. Meier. 2018. Confidence interval width for Pearson's correlation coefficient: a Gaussian-independent estimator based on sample size and strength of association. Agron. J. 110:1-8. doi:10.2134/agronj2016.04.0196

Examples

corr_ss(r = 0.60, CI = 0.1)

Correlation between stability indexes

Description

Computes the Spearman's rank correlation between the parametric and nonparametric stability indexes computed with the function ge_stats().

Usage

corr_stab_ind(x, stats = "all", plot = TRUE, ...)

Arguments

Details

The argument stats is used to chose the statistics to show the ranks. Allowed values are "all" (All statistics, default), "par" (Parametric statistics), "nonpar" (Non-parametric statistics), "ammi" (AMMI-based stability statistics), or the following values that can be combined into comma-separated character vector. "Y" (Response variable), "Var" (Genotype's variance), "Shukla" (Shukla's variance), ⁠"Wi_g", "Wi_f", "Wi_u"⁠ (Annichiarrico's genotypic confidence index for all, favorable and unfavorable environments, respectively), "Ecoval" (Wricke's ecovalence), "Sij" (Deviations from the joint-regression analysis), "R2" (R-squared from the joint-regression analysis), "ASTAB" (AMMI Based Stability Parameter), "ASI" (AMMI Stability Index), "ASV" (AMMI-stability value), "AVAMGE" (Sum Across Environments of Absolute Value of GEI Modelled by AMMI ), "Da" (Annicchiarico's D Parameter values), "Dz" (Zhang's D Parameter), "EV" (Sums of the Averages of the Squared Eigenvector Values), "FA" (Stability Measure Based on Fitted AMMI Model), "MASV" (Modified AMMI Stability Value), "SIPC" (Sums of the Absolute Value of the IPC Scores), "Za" (Absolute Value of the Relative Contribution of IPCs to the Interaction), "WAAS" (Weighted average of absolute scores), "HMGV" (Harmonic mean of the genotypic value), "RPGV" (Relative performance of the genotypic values), "HMRPGV" (Harmonic mean of the relative performance of the genotypic values), ⁠"Pi_a", "Pi_f", "Pi_u"⁠ (Superiority indexes for all, favorable and unfavorable environments, respectively), "Gai" (Geometric adaptability index), "S1" (mean of the absolute rank differences of a genotype over the n environments), "S2" (variance among the ranks over the k environments), "S3" (sum of the absolute deviations), "S6" (relative sum of squares of rank for each genotype), ⁠"N1", "N2", "N3", "N4"⁠ (Thennarasu"s statistics)).

Value

A list with the data (ranks) correlation, p-values and a heat map showing the correlation coefficients.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
model <- ge_stats(data_ge, ENV, GEN, REP, GY)
a <- corr_stab_ind(model)

Generate correlated variables

Description

Generate correlated variables using a vector of know values and desired maximum and minimum correlations

Usage

correlated_vars(
  y,
  min_cor = -1,
  max_cor = 1,
  nvars,
  constant = NULL,
  operation = "*",
  x = NULL
)

Arguments

Value

A data frame with the y variable and the correlated variables.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
y <- rnorm(n = 10)
cor_vars <- correlated_vars(y, nvar = 6)
plot(cor_vars)

Variance-covariance matrices for designed experiments

Description

Compute variance-covariance and correlation matrices using data from a designed (RCBD or CRD) experiment.

Usage

covcor_design(.data, gen, rep, resp, design = "RCBD", by = NULL, type = NULL)

Arguments

Value

An object of class covcor_design containing the following items:

• geno_cov The genotypic covariance.

• phen_cov The phenotypic covariance.

• resi_cov The residual covariance.

• geno_cor The phenotypic correlation.

• phen_cor The phenotypic correlation.

• resi_cor The residual correlation.

If .data is a grouped data passed from dplyr::group_by() then the results will be returned into a list-column of data frames.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
# List of matrices
data <- subset(data_ge2, ENV == 'A1')
matrices <- covcor_design(data,
                          gen = GEN,
                          rep = REP,
                          resp = c(PH, EH, NKE, TKW))

# Genetic correlations
gcor <- covcor_design(data,
                      gen = GEN,
                      rep = REP,
                      resp = c(PH, EH, NKE, TKW),
                      type = 'gcor')

# Residual (co)variance matrix for each environment
rcov <- covcor_design(data_ge2,
                      gen = GEN,
                      rep = REP,
                      resp = c(PH, EH, CD, CL),
                      by = ENV,
                      type = "rcov")

Cross-validation procedure

Description

Cross-validation for estimation of AMMI models

THe original dataset is split into two datasets: training set and validation set. The 'training' set has all combinations (genotype x environment) with N-1 replications. The 'validation' set has the remaining replication. The splitting of the dataset into modeling and validation sets depends on the design informed. For Completely Randomized Block Design (default), and alpha-lattice design (declaring block arguments), complete replicates are selected within environments. The remained replicate serves as validation data. If design = 'RCD' is informed, completely randomly samples are made for each genotype-by-environment combination (Olivoto et al. 2019). The estimated values considering naxis-Interaction Principal Component Axis are compared with the 'validation' data. The Root Mean Square Prediction Difference (RMSPD) is computed. At the end of boots, a list is returned.

IMPORTANT: If the data set is unbalanced (i.e., any genotype missing in any environment) the function will return an error. An error is also observed if any combination of genotype-environment has a different number of replications than observed in the trial.

Usage

cv_ammi(
  .data,
  env,
  gen,
  rep,
  resp,
  block = NULL,
  naxis = 2,
  nboot = 200,
  design = "RCBD",
  verbose = TRUE
)

Arguments

Value

An object of class cv_ammi with the following items: * RMSPD: A vector with nboot-estimates of the Root Mean Squared Prediction Difference between predicted and validating data.

• RMSPDmean: The mean of RMSPDmean estimates.

• Estimated: A data frame that contain the values (predicted, observed, validation) of the last loop.

• Modeling: The dataset used as modeling data in the last loop

• Testing: The dataset used as testing data in the last loop.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Olivoto, T., A.D.C. Lúcio, 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

Patterson, H.D., and E.R. Williams. 1976. A new class of resolvable incomplete block designs. Biometrika 63:83-92.

See Also

cv_ammif(), cv_blup()

Examples

library(metan)
model <- cv_ammi(data_ge,
                env = ENV,
                gen = GEN,
                rep = REP,
                resp = GY,
                nboot = 5,
                naxis = 2)

Cross-validation procedure

Description

Cross-validation for estimation of all AMMI-family models

cv_ammif provides a complete cross-validation of replicate-based data using AMMI-family models. By default, the first validation is carried out considering the AMMIF (all possible axis used). Considering this model, the original dataset is split up into two datasets: training set and validation set. The 'training' set has all combinations (genotype x environment) with N-1 replications. The 'validation' set has the remaining replication. The splitting of the dataset into modeling and validation sets depends on the design informed. For Completely Randomized Block Design (default), and alpha-lattice design (declaring block arguments), complete replicates are selected within environments. The remained replicate serves as validation data. If design = 'RCD' is informed, completely randomly samples are made for each genotype-by-environment combination (Olivoto et al. 2019). The estimated values for each member of the AMMI-family model are compared with the 'validation' data. The Root Mean Square Prediction Difference (RMSPD) is computed. At the end of boots, a list is returned.

IMPORTANT: If the data set is unbalanced (i.e., any genotype missing in any environment) the function will return an error. An error is also observed if any combination of genotype-environment has a different number of replications than observed in the trial.

Usage

cv_ammif(
  .data,
  env,
  gen,
  rep,
  resp,
  nboot = 200,
  block,
  design = "RCBD",
  verbose = TRUE
)

Arguments

Value

An object of class cv_ammif with the following items:

• RMSPD: A vector with nboot-estimates of the Root Mean Squared Prediction Difference between predicted and validating data.

• RMSPDmean: The mean of RMSPDmean estimates.

• Estimated: A data frame that contain the values (predicted, observed, validation) of the last loop.

• Modeling: The dataset used as modeling data in the last loop

• Testing: The dataset used as testing data in the last loop.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Patterson, H.D., and E.R. Williams. 1976. A new class of resolvable incomplete block designs. Biometrika 63:83-92.

See Also

cv_ammi(), cv_blup()

Examples

library(metan)
model <- cv_ammif(data_ge2,
                  env = ENV,
                  gen = GEN,
                  rep = REP,
                  resp = EH,
                  nboot = 5)
plot(model)

Cross-validation procedure

Description

Cross-validation for blup prediction.

This function provides a cross-validation procedure for mixed models using replicate-based data. By default, complete blocks are randomly selected within each environment. In each iteration, the original dataset is split up into two datasets: training and validation data. The 'training' set has all combinations (genotype x environment) with R - 1 replications. The 'validation' set has the remaining replication. The estimated values are compared with the 'validation' data and the Root Means Square Prediction Difference (Olivoto et al. 2019) is computed. At the end of boots, a list is returned.

Usage

cv_blup(
  .data,
  env,
  gen,
  rep,
  resp,
  block = NULL,
  nboot = 200,
  random = "gen",
  verbose = TRUE
)

Arguments

Details

Six models may be fitted depending upon the values in block and random 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.

IMPORTANT: An error is returned if any combination of genotype-environment has a different number of replications than observed in the trial.

Value

An object of class cv_blup with the following items: * RMSPD: A vector with nboot-estimates of the root mean squared prediction difference between predicted and validating data. * RMSPDmean The mean of RMSPDmean estimates.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Olivoto, T., A.D.C. Lúcio, 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

Patterson, H.D., and E.R. Williams. 1976. A new class of resolvable incomplete block designs. Biometrika 63:83-92.

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

See Also

cv_ammi(), cv_ammif()

Examples

library(metan)
model <- cv_blup(data_ge,
                 env = ENV,
                 gen = GEN,
                 rep = REP,
                 resp = GY,
                 nboot = 5)

Data from an alpha lattice design

Description

Alpha lattice design of spring oats

Format

A tibble with 72 observations on the following 5 variables.

• PLOT Plot number

• REP Replicate code

• BLOCK Incomplete block code

• GEN Genotype code

• YIELD Observed dry matter yield (tonnes/ha)

Details

A spring oats trial grown in Craibstone. There were 24 varieties in 3 replicates, each consisting of 6 incomplete blocks of 4 plots. Planted in a resolvable alpha design. The plots were laid out in a single line.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Source

J. A. John & E. R. Williams (1995). Cyclic and computer generated designs, Chapman and Hall, London. Page 146.

Single maize trial

Description

This dataset contain data on 15 traits assessed in 13 maize hybrids. The experimental design was a RCBD with 3 blocks and 1 replications per block. It is used as an example in the function gamem() of the metan package.

Format

A tibble with 39 observations on the following 17 variables.

• GEN A factor with 13 levels; each level represents one maize hybrid.

• REP A factor with 3 levels; each level represents one replication/block.

• PH Plant height, in cm.

• EH Ear height, in cm.

• EP Ear position, i.e., the ratio EH/PH.

• EL Ear length, in cm.

• ED Ear diameter, in mm.

• CL Cob length, in cm.

• CD Cob diameter, in mm.

• CW Cob weight, in g.

• KW Kernel weight, in cm.

• NR Number of rows.

• NKR Number of kernels per row.

• CDED Cob diameter / Ear diameter ratio.

• PERK Percentage of kernels.

• TKW Thousand-kernel weight

• NKE Number of kernels per row.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Source

Personal data

Multi-environment trial of oat

Description

This dataset contain data on two variables assessed in 10 genotypes growing in 14 environments. The experimental design was a RCBD with 3 replicates (blocks). This data provide examples for several functions of metan package.

Format

A tibble with 420 observations on the following 5 variables.

• ENV A factor with 14 levels; each level represents one cultivation environment.

• GEN A factor with 10 levels; each level represents one genotype.

• REP A factor with 3 levels; each level represents one replication/block.

• GY A continuous variable (grain yield) observed in each plot.

• HM A continuous variable (hectoliter mass) observed in each plot.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Source

Personal data

Multi-environment trial of maize

Description

This dataset contain data on 15 traits assessed in 13 maize hybrids growing in 4 environments. The experimental design was a RCBD with 3 blocks and 1 replications per block. It may be used as example in several functions of metan package.

Format

A tibble with 156 observations on the following 18 variables.

• ENV A factor with 4 levels; each level represents one cultivation environment.

• GEN A factor with 13 levels; each level represents one maize hybrid.

• REP A factor with 3 levels; each level represents one replication/block.

• PH Plant height, in cm.

• EH Ear height, in cm.

• EP Ear position, i.e., the ratio EH/PH.

• EL Ear length, in cm.

• ED Ear diameter, in mm.

• CL Cob length, in cm.

• CD Cob diameter, in mm.

• CW Cob weight, in g.

• KW Kernel weight, in cm.

• NR Number of rows.

• NKR Number of kernels per row.

• CDED Cob diameter / Ear diameter ratio.

• PERK Percentage of kernels.

• TKW Thousand-kernel weight

• NKE Number of kernels per row.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Source

Personal data

Simulate genotype and genotype-environment data

Description

• g_simula() simulate replicated genotype data.

• ge_simula() simulate replicated genotype-environment data.

Usage

ge_simula(
  ngen,
  nenv,
  nrep,
  nvars = 1,
  gen_eff = 20,
  env_eff = 15,
  rep_eff = 5,
  ge_eff = 10,
  res_eff = 5,
  intercept = 100,
  seed = NULL
)

g_simula(
  ngen,
  nrep,
  nvars = 1,
  gen_eff = 20,
  rep_eff = 5,
  res_eff = 5,
  intercept = 100,
  seed = NULL
)

Arguments

Details

The functions simulate genotype or genotype-environment data given a desired number of genotypes, environments and effects. All effects are sampled from an uniform distribution. For example, given 10 genotypes, and gen_eff = 30, the genotype effects will be sampled as runif(10, min = -30, max = 30). Use the argument seed to ensure reproducibility. If more than one trait is used (nvars > 1), the effects and seed can be passed as a numeric vector. Single numeric values will be recycled with a warning when more than one trait is used.

Value

A data frame with the simulated traits

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
# Genotype data (5 genotypes and 3 replicates)
gen_data <-
   g_simula(ngen = 5,
            nrep = 3,
            seed = 1)
gen_data
inspect(gen_data, plot = TRUE)

aov(V1 ~ GEN + REP, data = gen_data) %>% anova()

# Genotype-environment data
# 5 genotypes, 3 environments, 4 replicates and 2 traits
df <-
ge_simula(ngen = 5,
          nenv = 3,
          nrep = 4,
          nvars = 2,
          seed = 1)
ge_plot(df, ENV, GEN, V1)
aov(V1 ~ ENV*GEN + ENV/REP, data = df) %>% anova()

# Change genotype effect (trait 1 with fewer differences among genotypes)
# Define different intercepts for the two traits
df2 <-
ge_simula(ngen = 10,
          nenv = 3,
          nrep = 4,
          nvars = 2,
          gen_eff = c(1, 50),
          intercept = c(80, 1500),
          seed = 1)
ge_plot(df2, ENV, GEN, V2)

Descriptive statistics

Description

• desc_stat() Computes the most used measures of central tendency, position, and dispersion.

• desc_wider() is useful to put the variables in columns and grouping variables in rows. The table is filled with a statistic chosen with the argument stat.

Usage

desc_stat(
  .data = NULL,
  ...,
  by = NULL,
  stats = "main",
  hist = FALSE,
  level = 0.95,
  digits = 4,
  na.rm = FALSE,
  verbose = TRUE,
  plot_theme = theme_metan()
)

desc_wider(.data, which)

Arguments

Value

• desc_stats() returns a tibble with the statistics in the columns and variables (with possible grouping factors) in rows.

• desc_wider() returns a tibble with variables in columns and grouping factors in rows.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
#===============================================================#
# Example 1: main statistics (coefficient of variation, maximum,#
# mean, median, minimum, sample standard deviation, standard    #
# error and confidence interval of the mean) for all numeric    #
# variables in data                                             #
#===============================================================#

desc_stat(data_ge2)

#===============================================================#
#Example 2: robust statistics using a numeric vector as input   #
# data
#===============================================================#
vect <- data_ge2$TKW
desc_stat(vect, stats = "robust")

#===============================================================#
# Example 3: Select specific statistics. In this example, NAs   #
# are removed before analysis with a warning message            #
#===============================================================#
desc_stat(c(12, 13, 19, 21, 8, NA, 23, NA),
          stats = c('mean, se, cv, n, n.valid'),
          na.rm = TRUE)

#===============================================================#
# Example 4: Select specific variables and compute statistics by#
# levels of a factor variable (GEN)                             #
#===============================================================#
stats <-
  desc_stat(data_ge2,
            EP, EL, EH, ED, PH, CD,
            by = GEN)
stats

# To get a 'wide' format with the maximum values for all variables
desc_wider(stats, max)

#===============================================================#
# Example 5: Compute all statistics for all numeric variables   #
# by two or more factors. Note that group_by() was used to pass #
# grouped data to the function desc_stat()                      #
#===============================================================#

data_ge2 %>%
  group_by(ENV, GEN) %>%
  desc_stat()

Alternative to dplyr::do for doing anything

Description

Provides an alternative to the dplyr:do() using nest(), mutate() and map() to apply a function to a grouped data frame.

Usage

doo(.data, .fun, ..., unnest = TRUE)

Arguments

Details

If the applied function returns a data frame, then the output will be automatically unnested. Otherwise, the output includes the grouping variables and a column named "data" , which is a "list-columns" containing the results for group combinations.

Value

a data frame

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
# Head the first two lines of each environment
data_ge2 %>%
 group_by(ENV) %>%
 doo(~head(., 2))

# Genotype analysis for each environment using 'gafem()'
# variable PH
data_ge2 %>%
  group_by(ENV) %>%
  doo(~gafem(., GEN, REP, PH, verbose = FALSE))

Stability analysis based on Wricke's model

Description

The function computes the ecovalence (Wricke, 1965) for stability analysis.

Usage

ecovalence(.data, env, gen, rep, resp, verbose = TRUE)

Arguments

Value

An object of class ecovalence containing the results for each variable used in the argument resp.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

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

Examples

library(metan)
out <- ecovalence(data_ge2,
                 env = ENV,
                 gen = GEN,
                 rep = REP,
                 resp = PH)

Dissimilarity between environments

Description

Computes the dissimilarity between environments based on several approaches. See the section details for more details.

Usage

env_dissimilarity(.data, env, gen, rep, resp)

Arguments

Details

Roberteson (1959) proposed the partition of the mean square of the genotype-environment interaction (MS_GE) into single (S) and complex (C) parts, where S = \frac{1}{2}(\sqrt{Q1}-\sqrt{Q2})^2) and C = (1-r)\sqrt{Q1-Q2}, being r the correlation between the genotype's average in the two environments; and Q1 and Q2 the genotype mean square in the environments 1 and 2, respectively. Cruz and Castoldi (1991) proposed a new decomposition of the MS_GE, in which the complex part is given by C = \sqrt{(1-r)^3\times Q1\times Q2}.

Value

A list with the following matrices:

• SPART_CC: The percentage of the single (non cross-over) part of the interaction between genotypes and pairs of environments according to the method proposed by Cruz and Castoldi (1991).

• CPART_CC: The percentage of the complex (cross-over) part of the interaction between genotypes and pairs of environments according to the method proposed by Cruz and Castoldi (1991).

• SPART_RO: The percentage of the single (non cross-over) part of the interaction between genotypes and pairs of environments according to the method proposed by Robertson (1959).

• CPART_RO: The percentage of the complex (cross-over) part of the interaction between genotypes and pairs of environments according to the method proposed by Robertson (1959).

• MSGE: Interaction mean square between genotypes and pairs of environments.

• SSGE: Interaction sum of square between genotypes and pairs of environments.

• correlation: Correlation coefficients between genotypes's average in each pair of environment.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Cruz, C.D., Castoldi, F. (1991). Decomposicao da interacao genotipos x ambientes em partes simples e complexa. Ceres, 38:422-430.

Robertson, A. (1959). Experimental design on the measurement of heritabilities and genetic correlations. biometrical genetics. New York: Pergamon Press.

Examples

library(metan)
mod <- env_dissimilarity(data_ge, ENV, GEN, REP, GY)
print(mod)

Environment stratification

Description

Computes environment stratification based on factor analysis.

Usage

env_stratification(
  .data,
  env,
  gen,
  resp,
  use = "complete.obs",
  mineval = 1,
  verbose = TRUE
)

Arguments

Value

An object of class env_stratification which is a list with one element per analyzed trait. For each trait, the following values are given.

• data The genotype-environment means.

• cormat: The correlation matrix among the environments.

• PCA: The eigenvalues and explained variance.

• FA: The factor analysis.

• env_strat: The environmental stratification.

• mega_env_code: The environments within each mega-environment.

• mega_env_stat: The statistics for each mega-environment.

• KMO: The result for the Kaiser-Meyer-Olkin test.

• MSA: The measure of sampling adequacy for individual variable.

• communalities_mean: The communalities' mean.

• initial_loadings: The initial loadings.

Author(s)

Tiago Olivoto, tiagoolivoto@gmail.com

References

Murakami, D.M.D., and C.D.C. Cruz. 2004. Proposal of methodologies for environment stratification and analysis of genotype adaptability. Crop Breed. Appl. Biotechnol. 4:7-11.

See Also

env_dissimilarity()

Examples

library(metan)
model <-
env_stratification(data_ge,
                   env = ENV,
                   gen = GEN,
                   resp = everything())
gmd(model)

Multi-trait selection index

Description

Multitrait index based on factor analysis and ideotype-design proposed by Rocha et al. (2018).

Usage

fai_blup(
  .data,
  use_data = "blup",
  DI = NULL,
  UI = NULL,
  SI = 15,
  mineval = 1,
  verbose = TRUE
)

Arguments

Value

An object of class fai_blup with the following items:

• data The data (BLUPS) used to compute the index.

• eigen The eigenvalues and explained variance for each axis.

• FA The results of the factor analysis.

• canonical_loadings The canonical loadings for each factor retained.

• FAI A list with the FAI-BLUP index for each ideotype design.

• sel_dif_trait A list with the selection differential for each ideotype design.

• sel_gen The selected genotypes.

• ideotype_construction A list with the construction of the ideotypes.

• total_gain A list with the total gain for variables to be increased or decreased.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Rocha, J.R.A.S.C.R, J.C. Machado, and P.C.S. Carneiro. 2018. Multitrait index based on factor analysis and ideotype-design: proposal and application on elephant grass breeding for bioenergy. GCB Bioenergy 10:52-60. doi:10.1111/gcbb.12443

Examples

library(metan)

mod <- waasb(data_ge,
             env = ENV,
             gen = GEN,
             rep = REP,
             resp = c(GY, HM))

FAI <- fai_blup(mod,
                SI = 15,
                DI = c('max, max'),
                UI = c('min, min'))

Find possible outliers in a dataset

Description

Find possible outliers in the dataset.

Usage

find_outliers(
  .data = NULL,
  var = NULL,
  by = NULL,
  plots = FALSE,
  coef = 1.5,
  verbose = TRUE,
  plot_theme = theme_metan()
)

Arguments

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)

find_outliers(data_ge2, var = PH, plots = TRUE)

# Find outliers within each environment
find_outliers(data_ge2, var = PH, by = ENV)

Genotype analysis by fixed-effect models

Description

One-way analysis of variance of genotypes conducted in both randomized complete block and alpha-lattice designs.

Usage

gafem(
  .data,
  gen,
  rep,
  resp,
  block = NULL,
  by = NULL,
  prob = 0.05,
  verbose = TRUE
)

Arguments

Details

gafem analyses data from a one-way genotype testing experiment. By default, a randomized complete block design is used according to the following model: \[Y_{ij} = m + g_i + r_j + e_{ij}\] where \(Y_{ij}\) is the response variable of the ith genotype in the jth block; m is the grand mean (fixed); \(g_i\) is the effect of the ith genotype; \(r_j\) is the effect of the jth replicate; and \(e_{ij}\) is the random error.

When block is informed, then a resolvable alpha design is implemented, according to the following model:

where where \(y_{ijk}\) is the response variable of the ith genotype in the kth block of the jth replicate; m is the intercept, \(t_i\) is the effect for the ith genotype \(r_j\) is the effect of the jth replicate, \(b_{jk}\) is the effect of the kth incomplete block of the jth replicate, and \(e_{ijk}\) is the plot error effect corresponding to \(y_{ijk}\). All effects, except the random error are assumed to be fixed.

Value

A list where each element is the result for one variable containing the following objects:

• anova: The one-way ANOVA table.

• model: The model with of lm.

• augment: Information about each observation in the dataset. This includes predicted values in the fitted column, residuals in the resid column, standardized residuals in the stdres column, the diagonal of the 'hat' matrix in the hat, and standard errors for the fitted values in the se.fit column.

• hsd: The Tukey's 'Honest Significant Difference' for genotype effect.

• details: A tibble with the following data: Ngen, the number of genotypes; OVmean, the grand mean; Min, the minimum observed (returning the genotype and replication/block); Max the maximum observed, MinGEN the loser winner genotype, MaxGEN, the winner genotype.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Patterson, H.D., and E.R. Williams. 1976. A new class of resolvable incomplete block designs. Biometrika 63:83-92.

See Also

get_model_data() gamem()

Examples

library(metan)
# RCBD
rcbd <- gafem(data_g,
             gen = GEN,
             rep = REP,
             resp = c(PH, ED, EL, CL, CW))

# Fitted values
get_model_data(rcbd)

# ALPHA-LATTICE DESIGN
alpha <- gafem(data_alpha,
              gen = GEN,
              rep = REP,
              block = BLOCK,
              resp = YIELD)

# Fitted values
get_model_data(alpha)

Geometric adaptability index

Description

Performs a stability analysis based on the geometric mean (GAI), according to the following model (Mohammadi and Amri, 2008): \[GAI = \sqrt[E]{{\mathop {\bar Y}\nolimits_1 + \mathop {\bar Y}\nolimits_2 + ... + \mathop {\bar Y}\nolimits_i }}\] where \(\bar Y_1\), \(\bar Y_2\), and \(\bar Y_i\) are the mean yields of the first, second and i-th genotypes across environments, and E is the number of environments

Usage

gai(.data, env, gen, resp, verbose = TRUE)

Arguments

Value

An object of class gai, which is a list containing the results for each variable used in the argument resp. For each variable, a tibble with the following columns is returned.

• GEN the genotype's code.

• GAI Geometric adaptability index

• GAI_R The rank for the GAI value.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

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.

Examples

library(metan)
out <- gai(data_ge2,
           env = ENV,
           gen = GEN,
           resp = c(EH, PH, EL, CD, ED, NKE))

Genotype analysis by mixed-effect models

Description

Analysis of genotypes in single experiments using mixed-effect models with estimation of genetic parameters.

Usage

gamem(
  .data,
  gen,
  rep,
  resp,
  block = NULL,
  by = NULL,
  prob = 0.05,
  verbose = TRUE
)

Arguments

Details

gamem analyses data from a one-way genotype testing experiment. By default, a randomized complete block design is used according to the following model: \[Y_{ij} = m + g_i + r_j + e_{ij}\] where \(Y_{ij}\) is the response variable of the ith genotype in the jth block; m is the grand mean (fixed); \(g_i\) is the effect of the ith genotype (assumed to be random); \(r_j\) is the effect of the jth replicate (assumed to be fixed); and \(e_{ij}\) is the random error.

When block is informed, then a resolvable alpha design is implemented, according to the following model:

where where \(y_{ijk}\) is the response variable of the ith genotype in the kth block of the jth replicate; m is the intercept, \(t_i\) is the effect for the ith genotype \(r_j\) is the effect of the jth replicate, \(b_{jk}\) is the effect of the kth incomplete block of the jth replicate, and \(e_{ijk}\) is the plot error effect corresponding to \(y_{ijk}\).

Value

An object of class gamem or gamem_grouped, which is a list with the following items for each element (variable):

• fixed: Test for fixed effects.

• random: Variance components for random effects.

• LRT: The Likelihood Ratio Test for the random effects.

• BLUPgen: The estimated BLUPS for genotypes

• ranef: The random effects of the model

• modellme The mixed-effect model of class lmerMod.

• residuals The residuals of the mixed-effect model.

• model_lm The fixed-effect model of class lm.

• residuals_lm The residuals of the fixed-effect model.

• Details: A tibble with the following data: Ngen, the number of genotypes; OVmean, the grand mean; Min, the minimum observed (returning the genotype and replication/block); Max the maximum observed, MinGEN the winner genotype, MaxGEN, the loser genotype.

• ESTIMATES: A tibble with the values:

  • Gen_var, the genotypic variance and ;

  • rep:block_var block-within-replicate variance (if an alpha-lattice design is used by informing the block in block);

  • Res_var, the residual variance;

  • ⁠Gen (%), rep:block (%), and Res (%)⁠ the respective contribution of variance components to the phenotypic variance;

  • H2, broad-sense heritability;

  • h2mg, heritability on the entry-mean basis;

  • Accuracy, the accuracy of selection (square root of h2mg);

  • CVg, genotypic coefficient of variation;

  • CVr, residual coefficient of variation;

  • ⁠CV ratio⁠, the ratio between genotypic and residual coefficient of variation.

• formula The formula used to fit the mixed-model.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

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

See Also

get_model_data() waasb()

Examples

library(metan)

# fitting the model considering an RCBD
# Genotype as random effects

rcbd <- gamem(data_g,
             gen = GEN,
             rep = REP,
             resp = c(PH, ED, EL, CL, CW, KW, NR, TKW, NKE))

# Likelihood ratio test for random effects
get_model_data(rcbd, "lrt")


# Variance components
get_model_data(rcbd, "vcomp")

# Genetic parameters
get_model_data(rcbd, "genpar")

# random effects
get_model_data(rcbd, "ranef")

# Predicted values
predict(rcbd)

# fitting the model considering an alpha-lattice design
# Genotype and block-within-replicate as random effects
# Note that block effect was now informed.

alpha <- gamem(data_alpha,
               gen = GEN,
               rep = REP,
               block = BLOCK,
               resp = YIELD)
# Genetic parameters
get_model_data(alpha, "genpar")

# Random effects
get_model_data(alpha, "ranef")

Genotype-environment analysis by mixed-effect models

Description

Genotype analysis in multi-environment trials using mixed-effect or random-effect models.

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.

Usage

gamem_met(
  .data,
  env,
  gen,
  rep,
  resp,
  block = NULL,
  by = NULL,
  random = "gen",
  prob = 0.05,
  verbose = TRUE
)

Arguments

Value

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.

• modellme The mixed-effect model of class lmerMod.

• residuals The residuals of the mixed-effect model.

• model_lm The fixed-effect model of class lm.

• residuals_lm The residuals of the fixed-effect model.

• 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.

• formula The formula used to fit the mixed-model.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Olivoto, T., A.D.C. Lúcio, 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.

See Also

mtsi() waas() get_model_data() plot_scores()

Examples

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())
# Distribution of random effects (first variable)
plot(model, type = "re")

# Genetic parameters
get_model_data(model, "genpar")



#===============================================================#
# 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)
get_model_data(model2)

Adjusted Coefficient of Variation as yield stability index

Description

Performs a stability analysis based on the scale-adjusted coefficient of variation (Doring and Reckling, 2018). For more details see acv()

Usage

ge_acv(.data, env, gen, resp, verbose = TRUE)

Arguments

Value

An object of class ge_acv, which is a list containing the results for each variable used in the argument resp. For each variable, a tibble with the following columns is returned.

• GEN the genotype's code.

• ACV The adjusted coefficient of variation

• ACV_R The rank for the ACV value.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

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

Examples

library(metan)
out <- ge_acv(data_ge2, ENV, GEN, c(EH, PH, EL, CD, ED, NKE))
gmd(out)

Cluster genotypes or environments

Description

Performs clustering for genotypes or tester environments based on a dissimilarity matrix.

Usage

ge_cluster(
  .data,
  env = NULL,
  gen = NULL,
  resp = NULL,
  table = FALSE,
  distmethod = "euclidean",
  clustmethod = "ward.D",
  scale = TRUE,
  cluster = "env",
  nclust = NULL
)

Arguments

Value

• data The data that was used to compute the distances.

• cutpoint The cutpoint of the dendrogram according to Mojena (1977).

• distance The matrix with the distances.

• de The distances in an object of class dist.

• hc The hierarchical clustering.

• cophenetic The cophenetic correlation coefficient between distance matrix and cophenetic matrix

• Sqt The total sum of squares.

• tab A table with the clusters and similarity.

• clusters The sum of square and the mean of the clusters for each genotype (if cluster = "env" or environment (if cluster = "gen").

• labclust The labels of genotypes/environments within each cluster.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Mojena, R. 2015. Hierarchical grouping methods and stopping rules: an evaluation. Comput. J. 20:359-363. doi:10.1093/comjnl/20.4.359

Ouyang, Z., R.P. Mowers, A. Jensen, S. Wang, and S. Zheng. 1995. Cluster analysis for genotype x environment interaction with unbalanced data. Crop Sci. 35:1300-1305. doi:10.2135/cropsci1995.0011183X003500050008x

Examples

library(metan)

d1 <- ge_cluster(data_ge, ENV, GEN, GY, nclust = 3)
plot(d1, nclust = 3)

Details for genotype-environment trials

Description

Provide details for genotype-environment trials

Usage

ge_details(.data, env, gen, resp)

Arguments

Value

A tibble with the following results for each variable:

• Mean: The grand mean.

• SE: The standard error of the mean.

• SD: The standard deviation.

• CV: The coefficient of variation.

• ⁠Min,Max⁠: The minimum and maximum value, indicating the genotype and environment of occurence.

• ⁠MinENV, MinGEN⁠: The environment and genotype with the lower mean.

• ⁠MaxENV, MaxGEN⁠: The environment and genotype with the higher mean.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
details <- ge_details(data_ge2, ENV, GEN, everything())
print(details)

Genotype-environment effects

Description

This is a helper function that computes the genotype-environment effects, i.e., the residual effect of the additive model

Usage

ge_effects(.data, env, gen, resp, type = "ge", verbose = TRUE)

Arguments

Value

A list where each element is the result for one variable that contains a two-way table with genotypes in rows and environments in columns.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
ge_eff <- ge_effects(data_ge, ENV, GEN, GY)
gge_eff <- ge_effects(data_ge, ENV, GEN, GY, type = "gge")
plot(ge_eff)

Stability analysis and environment stratification

Description

This function computes the stability analysis and environmental stratification using factor analysis as proposed by Murakami and Cruz (2004).

Usage

ge_factanal(.data, env, gen, rep, resp, mineval = 1, verbose = TRUE)

Arguments

Value

An object of class ge_factanal with the following items:

• data: The data used to compute the factor analysis.

• cormat: The correlation matrix among the environments.

• PCA: The eigenvalues and explained variance.

• FA: The factor analysis.

• env_strat: The environmental stratification.

• KMO: The result for the Kaiser-Meyer-Olkin test.

• MSA: The measure of sampling adequacy for individual variable.

• communalities: The communalities.

• communalities.mean: The communalities' mean.

• initial.loadings: The initial loadings.

• finish.loadings: The final loadings after varimax rotation.

• canonical.loadings: The canonical loadings.

• scores.gen: The scores for genotypes for the first and second factors.

Author(s)

Tiago Olivoto, tiagoolivoto@gmail.com

References

Murakami, D.M.D., and C.D.C. Cruz. 2004. Proposal of methodologies for environment stratification and analysis of genotype adaptability. Crop Breed. Appl. Biotechnol. 4:7-11.

See Also

superiority(), ecovalence(), ge_stats(), ge_reg()

Examples

library(metan)
model <- ge_factanal(data_ge2,
                     env = ENV,
                     gen = GEN,
                     rep = REP,
                     resp = PH)

Genotype-environment means

Description

Computes genotype-environment interaction means

Usage

ge_means(.data, env, gen, resp)

Arguments

Value

A list where each element is the result for one variable containing:

• ge_means: A two-way table with the means for genotypes (rows) and environments (columns).

• gen_means: A tibble with the means for genotypes.

• env_means: A tibble with the means for environments.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
means_ge <- ge_means(data_ge, ENV, GEN, resp = everything())

# Genotype-environment interaction means
get_model_data(means_ge)

# Environment means
get_model_data(means_ge, what = "env_means")

# Genotype means
get_model_data(means_ge, what = "gen_means")

Graphical analysis of genotype-vs-environment interaction

Description

This function produces a line plot for a graphical interpretation of the genotype-vs-environment interaction. By default, environments are in the x axis whereas the genotypes are depicted by different lines. The y axis contains the value of the selected variable. A heatmap can also be created.

Usage

ge_plot(
  .data,
  env,
  gen,
  resp,
  type = 1,
  values = TRUE,
  text_col_pos = c("top", "bottom"),
  text_row_pos = c("left", "right"),
  average = TRUE,
  row_col = TRUE,
  row_col_type = c("average", "sum"),
  order_g = NULL,
  order_e = NULL,
  xlab = NULL,
  ylab = NULL,
  width_bar = 1.5,
  heigth_bar = 15,
  plot_theme = theme_metan(),
  colour = TRUE
)

Arguments

Value

An object of class ⁠gg, ggplot⁠.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
ge_plot(data_ge2, ENV, GEN, PH)
ge_plot(data_ge, ENV, GEN, GY, type = 2)

Power Law Residuals as yield stability index

Description

Performs a stability analysis based on the Power Law Residuals (POLAR) statistics (Doring et al., 2015). POLAR is the residuals from the linear regression of \(log(\sigma^2\)) against \(log(\mu\)) and can be used as a measure of crop stability with lower stability (relative to all samples with that mean yield) indicated by more positive POLAR values, and higher stability (relative to all samples with that mean yield) indicated by more negative POLAR values.

Usage

ge_polar(.data, env, gen, resp, base = 10, verbose = TRUE)

Arguments

Value

An object of class ge_acv, which is a list containing the results for each variable used in the argument resp. For each variable, a tibble with the following columns is returned.

• GEN the genotype's code.

• POLAR The Power Law Residuals

• POLAR_R The rank for the ACV value.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

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

Examples

library(metan)
out <- ge_polar(data_ge2, ENV, GEN, c(EH, PH, EL, CD, ED, NKE))
gmd(out)

Eberhart and Russell's regression model

Description

Regression-based stability analysis using the Eberhart and Russell (1966) model.

Usage

ge_reg(.data, env, gen, rep, resp, verbose = TRUE)

Arguments

Value

An object of class ge_reg with the folloing items for each variable:

• data: The data with means for genotype and environment combinations and the environment index

• anova: The analysis of variance for the regression model.

• regression: A data frame with the following columns: GEN, the genotypes; b0 and b1 the intercept and slope of the regression, respectively; t(b1=1) the calculated t-value; pval_t the p-value for the t test; s2di the deviations from the regression (stability parameter); F(s2di=0) the F-test for the deviations; pval_f the p-value for the F test; RMSE the root-mean-square error; R2 the determination coefficient of the regression.

• b0_variance: The variance of b0.

• b1_variance: The variance of b1.

Author(s)

Tiago Olivoto, tiagoolivoto@gmail.com

References

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

See Also

superiority(), ecovalence(), ge_stats()

Examples

library(metan)
reg <- ge_reg(data_ge2,
             env = ENV,
             gen = GEN,
             rep = REP,
             resp = PH)
plot(reg)

Parametric and non-parametric stability statistics

Description

ge_stats() computes parametric and non-parametric stability statistics given a data set with environment, genotype, and block factors.

Usage

ge_stats(.data, env, gen, rep, resp, verbose = TRUE, prob = 0.05)

Arguments

Details

The function computes the statistics and ranks for the following stability indexes.

• "Y" (Response variable),

• "CV" (coefficient of variation)

• "ACV" (adjusted coefficient of variation calling ge_acv() internally)

• POLAR (Power Law Residuals, calling ge_polar() internally)

• "Var" (Genotype's variance)

• "Shukla" (Shukla's variance, calling Shukla() internally)

• ⁠"Wi_g", "Wi_f", "Wi_u"⁠ (Annichiarrico's genotypic confidence index for all, favorable and unfavorable environments, respectively, calling Annicchiarico() internally )

• "Ecoval" (Wricke's ecovalence, ecovalence() internally)

• "Sij" (Deviations from the joint-regression analysis) and "R2" (R-squared from the joint-regression analysis, calling ge_reg() internally)

• "ASTAB" (AMMI Based Stability Parameter), "ASI" (AMMI Stability Index), "ASV" (AMMI-stability value), "AVAMGE" (Sum Across Environments of Absolute Value of GEI Modelled by AMMI ), "Da" (Annicchiarico's D Parameter values), "Dz" (Zhang's D Parameter), "EV" (Sums of the Averages of the Squared Eigenvector Values), "FA" (Stability Measure Based on Fitted AMMI Model), "MASV" (Modified AMMI Stability Value), "SIPC" (Sums of the Absolute Value of the IPC Scores), "Za" (Absolute Value of the Relative Contribution of IPCs to the Interaction), "WAAS" (Weighted average of absolute scores), calling ammi_indexes() internally

• "HMGV" (Harmonic mean of the genotypic value), "RPGV" (Relative performance of the genotypic values), "HMRPGV" (Harmonic mean of the relative performance of the genotypic values), by calling blup_indexes() internally

• ⁠"Pi_a", "Pi_f", "Pi_u"⁠ (Superiority indexes for all, favorable and unfavorable environments, respectively, calling superiority() internally)

• "Gai" (Geometric adaptability index, calling gai() internally)

• "S1" (mean of the absolute rank differences of a genotype over the n environments), "S2" (variance among the ranks over the k environments), "S3" (sum of the absolute deviations), "S6" (relative sum of squares of rank for each genotype), by calling Huehn() internally

• "N1", "N2", "N3", "N4" (Thennarasu"s statistics, calling Thennarasu() internally ).

Value

An object of class ge_stats which is a list with one data frame for each variable containing the computed indexes.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Annicchiarico, P. 1992. Cultivar adaptation and recommendation from alfalfa trials in Northern Italy. Journal of Genetic & Breeding, 46:269-278

Ajay BC, Aravind J, Abdul Fiyaz R, Bera SK, Kumar N, Gangadhar K, Kona P (2018). “Modified AMMI Stability Index (MASI) for stability analysis.” ICAR-DGR Newsletter, 18, 4–5.

Ajay BC, Aravind J, Fiyaz RA, Kumar N, Lal C, Gangadhar K, Kona P, Dagla MC, Bera SK (2019). “Rectification of modified AMMI stability value (MASV).” Indian Journal of Genetics and Plant Breeding (The), 79, 726–731. https://www.isgpb.org/article/rectification-of-modified-ammi-stability-value-masv.

Annicchiarico P (1997). “Joint regression vs AMMI analysis of genotype-environment interactions for cereals in Italy.” Euphytica, 94(1), 53–62. doi:10.1023/A:1002954824178

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

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

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

Farshadfar E (2008) Incorporation of AMMI stability value and grain yield in a single non-parametric index (GSI) in bread wheat. Pakistan J Biol Sci 11:1791–1796. doi:10.3923/pjbs.2008.1791.1796

Fox, P.N., B. Skovmand, B.K. Thompson, H.J. Braun, and R. Cormier. 1990. Yield and adaptation of hexaploid spring triticale. Euphytica 47:57-64. doi:10.1007/BF00040364.

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

Jambhulkar NN, Rath NC, Bose LK, Subudhi HN, Biswajit M, Lipi D, Meher J (2017). “Stability analysis for grain yield in rice in demonstrations conducted during rabi season in India.” Oryza, 54(2), 236–240. doi:10.5958/2249-5266.2017.00030.3

Kang, M.S., and H.N. Pham. 1991. Simultaneous Selection for High Yielding and Stable Crop Genotypes. Agron. J. 83:161. doi:10.2134/agronj1991.00021962008300010037x

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

Olivoto, T., A.D.C. Lúcio, J.A.G. da silva, V.S. Marchioro, V.Q. de Souza, and E. Jost. 2019a. 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

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

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

Raju BMK (2002). “A study on AMMI model and its biplots.” Journal of the Indian Society of Agricultural Statistics, 55(3), 297–322.

Rao AR, Prabhakaran VT (2005). “Use of AMMI in simultaneous selection of genotypes for yield and stability.” Journal of the Indian Society of Agricultural Statistics, 59, 76–82.

Sneller CH, Kilgore-Norquest L, Dombek D (1997). “Repeatability of yield stability statistics in soybean.” Crop Science, 37(2), 383–390. doi:10.2135/cropsci1997.0011183X003700020013x

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.

See Also

acv(), ammi_indexes(), ecovalence(), Fox(), gai(), ge_reg(), hmgv(), hmrpgv(), rpgv(), Huehn(), ge_polar(), Shukla(), superiority(), Thennarasu(), waas(), waasb()

Examples

library(metan)
model <- ge_stats(data_ge, ENV, GEN, REP, GY)
get_model_data(model, "stats")

Genotype-environment winners

Description

Computes the ranking for genotypes within environments and return the winners.

Usage

ge_winners(.data, env, gen, resp, type = "winners", better = NULL)

Arguments

Value

A tibble with two-way table with the winner genotype in each environment (default) or the genotype ranking for each environment (if type = "ranks").

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
ge_winners(data_ge, ENV, GEN, resp = everything())

# Assuming that for 'GY' lower values are better.
ge_winners(data_ge, ENV, GEN,
           resp = everything(),
           better = c("l, h"))

# Show the genotype ranking for each environment
ge_winners(data_ge, ENV, GEN,
           resp = everything(),
           type = "ranks")

Generate normal, correlated variables

Description

Given the mean and desired correlations, generate normal, correlated variables.

Usage

get_corvars(n = 10, mu, sigma, tol = 1e-06, seed = NULL)

Arguments

Value

A tibble containing the simulated data.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

sigma <- matrix(c(1,  .3,  0,
                  .3,   1, .9,
                  0,   .9,  1),3,3)
mu <- c(6,50,5)

df <- get_corvars(n = 10000, mu = mu, sigma = sigma, seed = 101010)
mean_by(df)
cor(df)

Generate a covariance matrix

Description

Given the variances and desired correlations, generate a covariance matrix

Usage

get_covmat(cormat, var)

Arguments

Value

A (co)variance matrix

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

cormat <-
matrix(c(1,  0.9, -0.4,
         0.9,  1,  0.6,
        -0.4, 0.6, 1),
      nrow = 3,
      ncol = 3)
get_covmat(cormat, var =  c(16, 25, 9))

Get a distance matrix

Description

Get the distance matrices from objects fitted with the function clustering(). This is especially useful to get distance matrices from several objects to be further analyzed using pairs_mantel().

Usage

get_dist(..., digits = 2)

Arguments

Value

A list of class clustering.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
d <- data_ge2 %>%
      mean_by(GEN) %>%
      column_to_rownames("GEN") %>%
      clustering()
get_dist(d)

Get data from a model easily

Description

Usage

get_model_data(x, what = NULL, type = "GEN", verbose = TRUE)

gmd(x, what = NULL, type = "GEN", verbose = TRUE)

sel_gen(x)

Arguments

Details

• get_model_data() Easily get data from some objects generated in the metan package such as the WAASB and WAASBY indexes (Olivoto et al., 2019a, 2019b) BLUPs, variance components, details of AMMI models and AMMI-based stability statistics.

• gmd() Is a shortcut to get_model_data.

• sel_gen() Extracts the selected genotypes by a given index.

Bellow are listed the options allowed in the argument what depending on the class of the object

Objects of class ammi_indexes:

• "ASV" AMMI stability value.

• "EV" Averages of the squared eigenvector values.

• "SIPC" Sums of the absolute value of the IPCA scores.

• "WAAS" Weighted average of absolute scores (default).

• "ZA" Absolute value of the relative contribution of IPCAs to the interaction.

Objects of class anova_ind:

• "MEAN"The mean value of the variable

• ⁠"DFG", "DFB", "DFCR", "DFIB_R", "DFE"⁠. The degree of freedom for genotypes, blocks (randomized complete block design), complete replicates, incomplete blocks within replicates (alpha-lattice design), and error, respectively.

• ⁠"MSG", "FCG", "PFG"⁠ The mean square, F-calculated and P-values for genotype effect, respectively.

• ⁠"MSB", "FCB", "PFB"⁠ The mean square, F-calculated and P-values for block effect in randomized complete block design.

• ⁠"MSCR", "FCR", "PFCR"⁠ The mean square, F-calculated and P-values for complete replicates in alpha lattice design.

• ⁠"MSIB_R", "FCIB_R", "PFIB_R"⁠ The mean square, F-calculated and P-values for incomplete blocks within complete replicates, respectively (for alpha lattice design only).

• "MSE" The mean square of error.

• "CV" The coefficient of variation.

• "h2" The broad-sence heritability

• "AS" The accucary of selection (square root of h2).

• "FMAX" The Hartley's test (the ratio of the largest MSE to the smallest MSE).

Objects of class anova_joint or gafem:

• "Y" The observed values.

• "h2" The broad-sense heritability.

• "Sum Sq" Sum of squares.

• "Mean Sq" Mean Squares.

• "F value" F-values.

• "Pr(>F)" P-values.

• ".fitted" Fitted values (default).

• ".resid" Residuals.

• ".stdresid" Standardized residuals.

• ".se.fit" Standard errors of the fitted values.

• "details" Details.

Objects of class Annicchiarico and Schmildt:

• "Sem_rp" The standard error of the relative mean performance (Schmildt).

• "Mean_rp" The relative performance of the mean.

• "rank" The rank for genotypic confidence index.

• "Wi" The genotypic confidence index.

Objects of class can_corr:

• "coefs" The canonical coefficients (default).

• "loads" The canonical loadings.

• "crossloads" The canonical cross-loadings.

• "canonical" The canonical correlations and hypothesis testing.

Objects of class colindiag:

• "cormat" The correlation matrix betwen predictors.

• "corlist" The correlations in a 'long' format

• "evalevet" The eigenvalue with associated eigenvectors

• "VIF" The Variance Inflation Factor

• "indicators" The colinearity indicators

Objects of class ecovalence:

• "Ecoval" Ecovalence value (default).

• "Ecov_perc" Ecovalence in percentage value.

• "rank" Rank for ecovalence.

Objects of class fai_blup: See the Value section of fai_blup() to see valid options for what argument.

Objects of class ge_acv:

• "ACV" The adjusted coefficient of variation (default).

• "ACV_R" The rank for adjusted coefficient of variation.

Objects of class ge_polar:

• "POLAR" The Power Law Residuals (default).

• "POLAR_R" The rank for Power Law Residuals.

Objects of class ge_reg:

• GEN: the genotypes.

• b0 and b1 (default): the intercept and slope of the regression, respectively.

• t(b1=1): the calculated t-value

• pval_t: the p-value for the t test.

• s2di the deviations from the regression (stability parameter).

• F(s2di=0): the F-test for the deviations.

• pval_f: the p-value for the F test;

• RMSE the root-mean-square error.

• R2 the determination coefficient of the regression.

Objects of class ge_effects:

• For objects of class ge_effects no argument what is required.

Objects of class ge_means:

• "ge_means" Genotype-environment interaction means (default).

• "env_means" Environment means.

• "gen_means" Genotype means.

Objects of class gge:

• "scores" The scores for genotypes and environments for all the analyzed traits (default).

• "exp_var" The eigenvalues and explained variance.

• "projection" The projection of each genotype in the AEC coordinates in the stability GGE plot

Objects of class gytb:

• "gyt" Genotype by yield*trait table (Default).

• "stand_gyt" The standardized (zero mean and unit variance) Genotype by yield*trait table.

• "si" The superiority index (sum standardized value across all yield*trait combinations).

Objects of class mgidi: See the Value section of mgidi() to see valid options for what argument.

Objects of class mtsi: See the Value section of mtsi() to see valid options for what argument.

**Objects of class path_coeff

• "coef" Path coefficients

• "eigenval" Eigenvalues and eigenvectors.

• "vif " Variance Inflation Factor

**Objects of class path_coeff_seq

• "resp_fc" Coefficients of primary predictors and response

• "resp_sc" Coefficients of secondary predictors and response

• "resp_sc2" contribution to the total effects through primary traits

• "fc_sc_coef" Coefficients of secondary predictors and primary predictors.

Objects of class Shukla:

• "rMean" Rank for the mean.

• "ShuklaVar" Shukla's stablity variance (default).

• "rShukaVar" Rank for Shukla's stablity variance.

• "ssiShukaVar" Simultaneous selection index.

Objects of class sh: See the Value section of Smith_Hazel() to see valid options for what argument.

Objects of class Fox:

• "TOP" The proportion of locations at which the genotype occurred in the top third (default).

Objects of class gai:

• "GAI" The geometric adaptability index (default).

• "GAI_R" The rank for the GAI values.

Objects of class superiority:

• "Pi_a" The superiority measure for all environments (default).

• "R_a" The rank for Pi_a.

• "Pi_f" The superiority measure for favorable environments.

• "R_f" The rank for Pi_f.

• "Pi_u" The superiority measure for unfavorable environments.

• "R_u" The rank for Pi_u.

Objects of class Huehn:

• "S1" Mean of the absolute rank differences of a genotype over the n environments (default).

• "S2" variance among the ranks over the k environments.

• "S3" Sum of the absolute deviations.

• "S6" Relative sum of squares of rank for each genotype.

• "S1_R", "S2_R", "S3_R", and "S6_R", the ranks for S1, S2, S3, and S6, respectively.

Objects of class Thennarasu:

• "N1" First statistic (default).

• "N2" Second statistic.

• "N3" Third statistic.

• "N4" Fourth statistic.

• "N1_R", "N2_R", "N3_R", and "N4_R", The ranks for the statistics.

Objects of class performs_ammi:

• ⁠"PC1", "PC2", ..., "PCn"⁠ The values for the nth interaction principal component axis.

• "ipca_ss" Sum of square for each IPCA.

• "ipca_ms" Mean square for each IPCA.

• "ipca_fval" F value for each IPCA.

• "ipca_pval" P-value for for each IPCA.

• "ipca_expl" Explained sum of square for each IPCA (default).

• "ipca_accum" Accumulated explained sum of square.

Objects of class waas, waas_means, and waasb:

• ⁠"PC1", "PC2", ..., "PCn"⁠ The values for the nth interaction principal component axis.

• "WAASB" The weighted average of the absolute scores (default for objects of class waas).

• "PctResp" The rescaled values of the response variable.

• "PctWAASB" The rescaled values of the WAASB.

• "wResp" The weight for the response variable.

• "wWAASB" The weight for the stability.

• "OrResp" The ranking regarding the response variable.

• "OrWAASB" The ranking regarding the WAASB.

• "OrPC1" The ranking regarding the first principal component axix.

• "WAASBY" The superiority index WAASBY.

• "OrWAASBY" The ranking regarding the superiority index.

Objects of class gamem and waasb:

• "blupge" Best Linear Unbiased Prediction for genotype-environment interaction (mixed-effect model, class waasb).

• "blupg" Best Linear Unbiased Prediction for genotype effect.

• "bluege" Best Linear Unbiased Estimation for genotype-environment interaction (fixed-effect model, class waasb).

• "blueg" Best Linear Unbiased Estimation for genotype effect (fixed model).

• "data" The data used.

• "details" The details of the trial.

• "genpar" Genetic parameters (default).

• "gcov" The genotypic variance-covariance matrix.

• "pcov" The phenotypic variance-covariance matrix.

• "gcor" The genotypic correlation matrix.

• "pcor" The phenotypic correlation matrix.

• "h2" The broad-sense heritability.

• "lrt" The likelihood-ratio test for random effects.

• "vcomp" The variance components for random effects.

• "ranef" Random effects.

Objects of class blup_ind

• ⁠"HMGV","HMGV_R"⁠ For harmonic mean of genotypic values or its ranks.

• ⁠"RPGV", RPGV_Y"⁠ For relative performance of genotypic values or its ranks.

• ⁠"HMRPGV", "HMRPGV_R"⁠ For harmonic mean of relative performance of genotypic values or its ranks.

• ⁠"WAASB", "WAASB_R"⁠ For the weighted average of absolute scores from the singular or its ranks. value decomposition of the BLUPs for GxE interaction or its ranks.

Value

A tibble showing the values of the variable chosen in argument what.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

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

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

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

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

Fox, P.N., B. Skovmand, B.K. Thompson, H.J. Braun, and R. Cormier. 1990. Yield and adaptation of hexaploid spring triticale. Euphytica 47:57-64. doi:10.1007/BF00040364

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

Olivoto, T., A.D.C. Lúcio, J.A.G. da silva, V.S. Marchioro, V.Q. de Souza, and E. Jost. 2019a. 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

Olivoto, T., A.D.C. Lúcio, J.A.G. da silva, B.G. Sari, and M.I. Diel. 2019b. Mean performance and stability in multi-environment trials II: Selection based on multiple traits. Agron. J. 111:2961-2969. doi:10.2134/agronj2019.03.0221

Purchase, J.L., H. Hatting, and C.S. van Deventer. 2000. Genotype vs environment interaction of winter wheat (Triticum aestivum L.) in South Africa: II. Stability analysis of yield performance. South African J. Plant Soil 17:101-107. doi:10.1080/02571862.2000.10634878

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

Sneller, C.H., L. Kilgore-Norquest, and D. Dombek. 1997. Repeatability of Yield Stability Statistics in Soybean. Crop Sci. 37:383-390. doi:10.2135/cropsci1997.0011183X003700020013x

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

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

Zali, H., E. Farshadfar, S.H. Sabaghpour, and R. Karimizadeh. 2012. Evaluation of genotype vs environment interaction in chickpea using measures of stability from AMMI model. Ann. Biol. Res. 3:3126-3136.

See Also

ammi_indexes(), anova_ind(), anova_joint(), ecovalence(), Fox(), gai(), gamem(), gafem(), ge_acv(), ge_polar() ge_means(), ge_reg(), mgidi(), mtsi(), mps(), mtmps(), performs_ammi(), blup_indexes(), Shukla(), superiority(), waas(), waasb()

Examples

library(metan)


#################### WAASB index #####################
# Fitting the WAAS index
AMMI <- waasb(data_ge2,
              env = ENV,
              gen = GEN,
              rep = REP,
              resp = c(PH, ED, TKW, NKR))

# Getting the weighted average of absolute scores
gmd(AMMI, what = "WAASB")


#################### BLUP model #####################
# Fitting a mixed-effect model
# Genotype and interaction as random
blup <- gamem_met(data_ge2,
                  env = ENV,
                  gen = GEN,
                  rep = REP,
                  resp = c(PH, ED))

# Getting p-values for likelihood-ratio test
gmd(blup, what = "lrt")

# Getting the variance components
gmd(blup, what = "vcomp")

Genotype plus genotype-by-environment model

Description

Produces genotype plus genotype-by-environment model based on a multi-environment trial dataset containing at least the columns for genotypes, environments and one response variable or a two-way table.

Usage

gge(
  .data,
  env,
  gen,
  resp,
  centering = "environment",
  scaling = "none",
  svp = "environment",
  by = NULL,
  ...
)

Arguments

Value

The function returns a list of class gge containing the following objects

• coordgen The coordinates for genotypes for all components.

• coordenv The coordinates for environments for all components.

• eigenvalues The vector of eigenvalues.

• totalvar The overall variance.

• labelgen The name of the genotypes.

• labelenv The names of the environments.

• labelaxes The axes labels.

• ge_mat The data used to produce the model (scaled and centered).

• centering The centering method.

• scaling The scaling method.

• svp The singular value partitioning method.

• d The factor used to generate in which the ranges of genotypes and environments are comparable when singular value partitioning is set to 'genotype' or 'environment'.

• grand_mean The grand mean of the trial.

• mean_gen A vector with the means of the genotypes.

• mean_env A vector with the means of the environments.

• scale_var The scaling vector when the scaling method is 'sd'.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Yan, W., and M.S. Kang. 2003. GGE biplot analysis: a graphical tool for breeders, geneticists, and agronomists. CRC Press.

Examples

library(metan)
mod <- gge(data_ge, ENV, GEN, GY)
plot(mod)

# GGE model for all numeric variables
mod2 <- gge(data_ge2, ENV, GEN, resp = everything())
plot(mod2, var = "ED")

# If we have a two-way table with the mean values for
# genotypes and environments

table <- make_mat(data_ge, GEN, ENV, GY) %>% round(2)
table
make_long(table) %>%
gge(ENV, GEN, Y) %>%
plot()

Genotype by trait biplot

Description

Produces a genotype-by-trait biplot model. From a genotype by environment by trait three-way table, genotype-by-trait tables in any single environment, across all environments, or across a subset of the environments can be generated and visually studied using biplots. The model for biplot analysis of genotype by trait data is the singular value decomposition of trait-standardized two-way table.

Usage

gtb(.data, gen, resp, centering = "trait", scaling = "sd", svp = "trait")

Arguments

Value

The function returns a list of class gge that is compatible with the function plot() used in gge().

• coordgen The coordinates for genotypes for all components.

• coordenv The coordinates for traits for all components.

• eigenvalues The vector of eigenvalues.

• totalvar The overall variance.

• labelgen The name of the genotypes.

• labelenv The names of the traits.

• labelaxes The axes labels.

• gt_mat The data used to produce the model (scaled and centered).

• centering The centering method.

• scaling The scaling method.

• svp The singular value partitioning method.

• d The factor used to generate in which the ranges of genotypes and traits are comparable when singular value partitioning is set to 'genotype' or 'trait'.

• grand_mean The grand mean of the trial.

• mean_gen A vector with the means of the genotypes.

• mean_env A vector with the means of the traits.

• scale_var The scaling vector when the scaling method is 'sd'.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Yan, W., and M.S. Kang. 2003. GGE biplot analysis: a graphical tool for breeders, geneticists, and agronomists. CRC Press.

Examples

library(metan)
# GT biplot for all numeric variables
mod <- gtb(data_ge2, GEN, resp = contains("E"))
plot(mod)

Genotype by yield*trait biplot

Description

Produces a Genotype by Yield*Trait biplot (GTY) proposed by Yan and Fregeau-Reid (2018).

Usage

gytb(
  .data,
  gen,
  yield,
  traits = everything(),
  ideotype = NULL,
  weight = NULL,
  prefix = "Y",
  centering = "trait",
  scaling = "sd",
  svp = "trait"
)

Arguments

Value

The function returns a list of class gge that is compatible with the function plot() used in gge().

• data The Genotype by yield\*trait (GYT) data.

• ge_mat The Genotype by yield\*trait (GYT) data (scaled and centered).

• coordgen The coordinates for genotypes for all components.

• coordenv The coordinates for traits for all components.

• eigenvalues The vector of eigenvalues.

• totalvar The overall variance.

• labelgen The name of the genotypes.

• labelenv The names of the traits.

• labelaxes The axes labels.

• centering The centering method.

• scaling The scaling method.

• svp The singular value partitioning method.

• d The factor used to generate in which the ranges of genotypes and traits are comparable when singular value partitioning is set to 'genotype' or 'trait'.

• grand_mean The grand mean of the trial.

• mean_gen A vector with the means of the genotypes.

• mean_env A vector with the means of the traits.

• scale_var The scaling vector when the scaling method is 'sd'.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Yan, W., & Fregeau-Reid, J. (2018). Genotype by Yield\*Trait (GYT) Biplot: a Novel Approach for Genotype Selection based on Multiple Traits. Scientific Reports, 8(1), 1-10. doi:10.1038/s41598-018-26688-8

Examples

library(metan)
# GYT biplot for all numeric traits of 'data_g'
# KW (kernel weight) considered as 'yield',
mod <- gytb(data_g, GEN, KW)
plot(mod)

Missing value imputation

Description

Impute the missing entries of a matrix with missing values using different algorithms. See Details section for more details

Usage

impute_missing_val(
  .data,
  naxis = 1,
  algorithm = "EM-SVD",
  tol = 1e-10,
  max_iter = 1000,
  simplified = FALSE,
  verbose = TRUE
)

Arguments

Details

EM-AMMI algorithm

The EM-AMMI algorithm completes a data set with missing values according to both main and interaction effects. The algorithm works as follows (Gauch and Zobel, 1990):

1. The initial values are calculated as the grand mean increased by main effects of rows and main effects of columns. That way, the matrix of observations is pre-filled in.

2. The parameters of the AMMI model are estimated.

3. The adjusted means are calculated based on the AMMI model with naxis principal components.

4. The missing cells are filled with the adjusted means.

5. The root mean square error of the predicted values (RMSE_p) is calculated with the two lasts iteration steps. If RMSE_p > tol, the steps 2 through 5 are repeated. Declare convergence if RMSE_p < tol. If max_iter is achieved without convergence, the algorithm will stop with a warning.

EM-SVD algorithm

The EM-SVD algorithm impute the missing entries using a low-rank Singular Value Decomposition approximation estimated by the Expectation-Maximization algorithm. The algorithm works as follows (Troyanskaya et al., 2001).

1. Initialize all NA values to the column means.

2. Compute the first naxis terms of the SVD of the completed matrix

3. Replace the previously missing values with their approximations from the SVD

4. The root mean square error of the predicted values (RMSE_p) is calculated with the two lasts iteration steps. If RMSE_p > tol, the steps 2 through 3 are repeated. Declare convergence if RMSE_p < tol. If max_iter is achieved without convergence, the algorithm will stop with a warning.

colmeans algorithm

The colmeans algorithm simply impute the missing entires using the column mean of the respective entire. Thus, there is no iteractive process.

Value

An object of class imv with the following values:

• .data The imputed matrix

• pc_ss The sum of squares representing variation explained by the principal components

• iter The final number of iterations.

• Final_RMSE The maximum change of the estimated values for missing cells in the last step of iteration.

• final_axis The final number of principal component axis.

• convergence Logical value indicating whether the modern converged.

References

Gauch, H. G., & Zobel, R. W. (1990). Imputing missing yield trial data. Theoretical and Applied Genetics, 79(6), 753-761. doi:10.1007/BF00224240

Troyanskaya, O., Cantor, M., Sherlock, G., Brown, P., Hastie, T., Tibshirani, R., . Altman, R. B. (2001). Missing value estimation methods for DNA microarrays. Bioinformatics, 17(6), 520-525.

Examples

library(metan)
mat <- (1:20) %*% t(1:10)
mat
# 10% of missing values at random
miss_mat <- random_na(mat, prop = 10)
miss_mat
mod <- impute_missing_val(miss_mat)
mod$.data

Check for common errors in multi-environment trial data

Description

inspect() scans a data.frame object for errors that may affect the use of functions in metan. By default, all variables are checked regarding the class (numeric or factor), missing values, and presence of possible outliers. The function will return a warning if the data looks like unbalanced, has missing values or possible outliers.

Usage

inspect(.data, ..., plot = FALSE, threshold = 15, verbose = TRUE)

Arguments

Value

A tibble with the following variables:

• Variable The name of variable

• Class The class of the variable

• Missing Contains missing values?

• Levels The number of levels of a factor variable

• Valid_n Number of valid n (omit NAs)

• Outlier Contains possible outliers?

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
inspect(data_ge)

# Create a toy example with messy data
df <- data_ge2[-c(2, 30, 45, 134), c(1:5)] %>% as.data.frame()
df[c(1, 20, 50), 5] <- NA
df[40, 4] <- "2..814"

inspect(df)

Data for examples

Description

Data for examples

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Coerce to an object of class lpcor

Description

Functions to check if an object is of class lpcor

Usage

is.lpcor(x)

Arguments

Value

A logical value TRUE or FALSE.

Examples

library(metan)
library(dplyr)
mt_num <- mtcars %>% select_if(., is.numeric)
lpdata <- as.lpcor(cor(mt_num[1:5]),
                   cor(mt_num[1:5]),
                   cor(mt_num[2:6]),
                   cor(mt_num[4:8]))
is.lpcor(lpdata)

Check if a data set is balanced

Description

Check if a data set coming from multi-environment trials is balanced, i.e., all genotypes are in all environments.

Usage

is_balanced_trial(.data, env, gen, resp)

Arguments

Value

A logical value

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

unb <- data_ge %>%
        remove_rows(1:3) %>%
        droplevels()
is_balanced_trial(data_ge, ENV, GEN, GY)
is_balanced_trial(unb, ENV, GEN, GY)

Fast way to create line plots

Description

• plot_lines() Creates a line plot based on one quantitative factor and one numeric variable. It can be used to show the results of a one-way trial with quantitative treatments.

• plot_factlines() Creates a line plot based on: one categorical and one quantitative factor and one numeric variable. It can be used to show the results of a two-way trial with qualitative-quantitative treatment structure.

Usage

plot_lines(
  .data,
  x,
  y,
  fit,
  level = 0.95,
  confidence = TRUE,
  xlab = NULL,
  ylab = NULL,
  n.dodge = 1,
  check.overlap = FALSE,
  col = "red",
  alpha = 0.2,
  size.shape = 1.5,
  size.line = 1,
  size.text = 12,
  fontfam = "sans",
  plot_theme = theme_metan()
)

plot_factlines(
  .data,
  x,
  y,
  group,
  fit,
  level = 0.95,
  confidence = TRUE,
  xlab = NULL,
  ylab = NULL,
  n.dodge = 1,
  check.overlap = FALSE,
  legend.position = "bottom",
  grid = FALSE,
  scales = "free",
  col = TRUE,
  alpha = 0.2,
  size.shape = 1.5,
  size.line = 1,
  size.text = 12,
  fontfam = "sans",
  plot_theme = theme_metan()
)

Arguments

Value

An object of class ⁠gg, ggplot⁠.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

See Also

plot_bars() and plot_factbars()

Examples

library(metan)
# One-way line plot
df1 <- data.frame(group = "A",
                  x = c(0, 100, 200, 300, 400),
                  y = c(3.2, 3.3, 4.0, 3.8, 3.4))
plot_lines(df1, x, y, fit = 2)

# Two-way line plot
df2 <- data.frame(group = "B",
                  x = c(0, 100, 200, 300, 400),
                  y = c(3.2, 3.3, 3.7, 3.9, 4.1))
facts <- rbind(df1, df2)

p1 <- plot_factlines(facts, x, y, group = group, fit = 1)
p2 <- plot_factlines(facts,
                     x = x,
                     y = y,
                     group = group,
                     fit = c(2, 1),
                     confidence = FALSE)
arrange_ggplot(p1, p2)

Linear and Partial Correlation Coefficients

Description

Estimates the linear and partial correlation coefficients using as input a data frame or a correlation matrix.

Usage

lpcor(.data, ..., by = NULL, n = NULL, method = "pearson")

Arguments

Value

If .data is a grouped data passed from dplyr::group_by() then the results will be returned into a list-column of data frames, containing:

• linear.mat The matrix of linear correlation.

• partial.mat The matrix of partial correlations.

• results Hypothesis testing for each pairwise comparison.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
partial1 <- lpcor(iris)

# Alternatively using the pipe operator %>%
partial2 <- iris %>% lpcor()

# Using a correlation matrix
partial3 <- cor(iris[1:4]) %>%
            lpcor(n = nrow(iris))

# Select all numeric variables and compute the partial correlation
# For each level of Species

partial4 <- lpcor(iris, by = Species)

Mahalanobis Distance

Description

Compute the Mahalanobis distance of all pairwise rows in .means. The result is a symmetric matrix containing the distances that may be used for hierarchical clustering.

Usage

mahala(.means, covar, inverted = FALSE)

Arguments

Value

A symmetric matrix with the Mahalanobis' distance.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
library(dplyr)
# Compute the mean for genotypes
means <- mean_by(data_ge, GEN) %>%
         column_to_rownames("GEN")

# Compute the covariance matrix
covmat <- cov(means)

# Compute the distance
dist <- mahala(means, covmat)

# Dendrogram
dend <- dist %>%
        as.dist() %>%
        hclust() %>%
        as.dendrogram()
plot(dend)

Mahalanobis distance from designed experiments

Description

Compute the Mahalanobis distance using data from an experiment conducted in a randomized complete block design or completely randomized design.

Usage

mahala_design(
  .data,
  gen,
  rep,
  resp,
  design = "RCBD",
  by = NULL,
  return = "distance"
)

Arguments

Value

A symmetric matrix with the Mahalanobis' distance. If .data is a grouped data passed from dplyr::group_by() then the results will be returned into a list-column of data frames.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
maha <- mahala_design(data_g,
                      gen = GEN,
                      rep = REP,
                      resp = everything(),
                      return = "covmat")

# Compute one distance for each environment (all numeric variables)
maha_group <- mahala_design(data_ge,
                           gen = GEN,
                           rep = REP,
                           resp = everything(),
                           by = ENV)

# Return the variance-covariance matrix of residuals
cov_mat <- mahala_design(data_ge,
                        gen = GEN,
                        rep = REP,
                        resp = c(GY, HM),
                        return = 'covmat')

Two-way table to a 'long' format

Description

Helps users to easily convert a two-way table (genotype vs environment) to a 'long' format data. The data in mat will be gathered into three columns. The row names will compose the first column. The column names will compose the second column and the third column will contain the data that fills the two-way table.

Usage

make_long(mat, gen_in = "rows")

Arguments

Value

A tibble with three columns: GEN (genotype), ENV (environment), and Y (response) variable.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)

set.seed(1)
mat <- matrix(rnorm(9, 2530, 350), ncol = 3)
colnames(mat) <- paste("E", 1:3, sep = "")
rownames(mat) <- paste("G", 1:3, sep = "")

make_long(mat)

gen_cols <- t(mat)
make_long(gen_cols, gen_in = "cols")

Make a two-way table

Description

This function help users to easily make a two-way table from a "long format" data.

Usage

make_mat(.data, row, col, value, fun = mean)

Arguments

Value

A two-way table with the argument row in the rows, col in the columns, filled by the argument value.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Examples

library(metan)
matrix <- data_ge %>% make_mat(row = GEN, col = ENV, val = GY)
matrix

# standart error of mean

data_ge %>% make_mat(GEN, ENV, GY, sem)

Mantel test

Description

Performs a Mantel test between two correlation/distance matrices. The function calculates the correlation between two matrices, the Z-score that is is the sum of the products of the corresponding elements of the matrices and a two-tailed p-value (null hypothesis: \[r = 0\]).

Usage

mantel_test(mat1, mat2, nboot = 1000, plot = FALSE)

Arguments

Value

• mantel_r The correlation between the two matrices.

• z_score The Z-score.

• p-value The quantile of the observed Z-score. in the permutation distribution.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

See Also

pairs_mantel()

Examples

library(metan)
# Test if the correlation of traits (data_ge2 dataset)
# changes between A1 and A2 levels of factor ENV
A1 <- corr_coef(data_ge2 %>% subset(ENV == "A1"))[["cor"]]
A2 <- corr_coef(data_ge2 %>% subset(ENV == "A2"))[["cor"]]
mantel_test(A1, A2, plot = TRUE)

Data for examples

Description

This dataset contains the means for grain yield of 10 genotypes cultivated in 5 environments. The interaction effects for this data is found in int.effects()

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

Multi-Environment Trial Analysis

Description

metan provides functions for performing the most used analyses in the evaluation of multi-environment trials, including, but not limited to:

• ANOVA-based stability statistics;

• AMMI-based stability indexes;

• BLUP-based stability indexes;

• Cross-validation procedures for AMMI-family and BLUP models;

• GGE biplot analysis;

• Estimation using AMMI considering different numbers of interaction principal component axes;

• Graphics tools for generating biplots;

• Nonparametric stability statistics;

• Variance components and genetic parameters in mixed-effect models;

• Within-environment analysis of variance;

metan also provides functions for biometrical analysis such as path analysis, canonical correlation, partial correlation, clustering analysis, as well as tools for summarizing and plotting data.

A complete guide may be found at https://tiagoolivoto.github.io/metan/

Multitrait Genotype-Ideotype Distance Index

Description

Computes the multi-trait genotype-ideotype distance index, MGIDI, (Olivoto and Nardino, 2020), used to select genotypes in plant breeding programs based on multiple traits.The MGIDI index is computed as follows: \[MGIDI_i = \sqrt{\sum\limits_{j = 1}^f(F_{ij} - {F_j})^2}\]

where \(MGIDI_i\) is the multi-trait genotype-ideotype distance index for the ith genotype; \(F_{ij}\) is the score of the ith genotype in the jth factor (i = 1, 2, ..., g; j = 1, 2, ..., f), being g and f the number of genotypes and factors, respectively, and \(F_j\) is the jth score of the ideotype. The genotype with the lowest MGIDI is then closer to the ideotype and therefore should presents desired values for all the analyzed traits.

Usage

mgidi(
  .data,
  use_data = "blup",
  SI = 15,
  mineval = 1,
  ideotype = NULL,
  weights = NULL,
  use = "complete.obs",
  verbose = TRUE
)

Arguments

Value

An object of class mgidi with the following items:

• data The data used to compute the factor analysis.

• cormat The correlation matrix among the environments.

• PCA The eigenvalues and explained variance.

• FA The factor analysis.

• KMO The result for the Kaiser-Meyer-Olkin test.

• MSA The measure of sampling adequacy for individual variable.

• communalities The communalities.

• communalities_mean The communalities' mean.

• initial_loadings The initial loadings.

• finish_loadings The final loadings after varimax rotation.

• canonical_loadings The canonical loadings.

• scores_gen The scores for genotypes in all retained factors.

• scores_ide The scores for the ideotype in all retained factors.

• gen_ide The distance between the scores of each genotype with the ideotype.

• MGIDI The multi-trait genotype-ideotype distance index.

• contri_fac The relative contribution of each factor on the MGIDI value. The lower the contribution of a factor, the close of the ideotype the variables in such factor are.

• contri_fac_rank, contri_fac_rank_sel The rank for the contribution of each factor for all genotypes and selected genotypes, respectively.

• complementarity The complementarity matrix, which is the Euclidean distance between selected genotypes based on the contribution of each factor on the MGIDI index (waiting reference).

• sel_dif The selection differential for the variables.

• stat_gain A descriptive statistic for the selection gains. The minimum, mean, confidence interval, standard deviation, maximum, and sum of selection gain values are computed. If traits have negative and positive desired gains, the statistics are computed for by strata.

• sel_gen The selected genotypes.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

References

Olivoto, T., and Nardino, M. (2020). MGIDI: toward an effective multivariate selection in biological experiments. Bioinformatics. doi:10.1093/bioinformatics/btaa981

Examples

library(metan)

# simulate a data set
# 10 genotypes
# 5 replications
# 4 traits
df <-
 g_simula(ngen = 10,
          nrep = 5,
          nvars = 4,
          gen_eff = 35,
          seed = c(1, 2, 3, 4))

# run a mixed-effect model (genotype as random effect)
mod <-
  gamem(df,
        gen = GEN,
        rep = REP,
        resp = everything())
# BLUPs for genotypes
gmd(mod, "blupg")

# Compute the MGIDI index
# Default options (all traits with positive desired gains)
# Equal weights for all traits
mgidi_ind <- mgidi(mod)
gmd(mgidi_ind, "MGIDI")

# Higher weight for traits V1 and V4
# This will increase the probability of selecting H7 and H9
# 30% selection pressure
mgidi_ind2 <-
   mgidi(mod,
         weights = c(1, .2, .2, 1),
         SI = 30)
gmd(mgidi_ind2, "MGIDI")

# plot the contribution of each factor on the MGIDI index
p1 <- plot(mgidi_ind, type = "contribution")
p2 <- plot(mgidi_ind2, type = "contribution")
p1 + p2

# Negative desired gains for V1
# Positive desired gains for V2, V3 and V4
mgidi_ind3 <-
  mgidi(mod,
       ideotype = c("h, h, h, l"))


# Extract the BLUPs for each genotype
(blupsg <- gmd(mod, "blupg"))

# Consider the following ideotype that will be close to H4
# Define a numeric ideotype for the first three traits, and the lower values
# for the last trait
ideotype <- c("129.46, 76.8, 89.7, l")

mgidi_ind4 <-
  mgidi(mod,
       ideotype = ideotype)

# Note how the strenghts of H4 are related to FA1 (V1 and V2)
plot(mgidi_ind4, type = "contribution", genotypes = "all")

Mean performance and stability in multi-environment trials

Description

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