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Title:

Probability Theory for Selecting Candidates in Plant Breeding

Version:

1.0.4.9

Description:

Use probability theory under the Bayesian framework for calculating the risk of selecting candidates in a multi-environment context. Contained are functions used to fit a Bayesian multi-environment model (based on the available presets), extract posterior values and maximum posterior values, compute the variance components, check the model’s convergence, and calculate the probabilities. For both across and within-environments scopes, the package computes the probability of superior performance and the pairwise probability of superior performance. Furthermore, the probability of superior stability and the pairwise probability of superior stability across environments is estimated. A joint probability of superior performance and stability is also provided.

URL:

https://github.com/saulo-chaves/ProbBreed,https://saulo-chaves.github.io/ProbBreed_site/,https://saulo-chaves.github.io/ProbBreed/

BugReports:

https://github.com/saulo-chaves/ProbBreed/issues

License:

AGPL (≥ 3)

Depends:

R (≥ 3.5.0)

Imports:

ggplot2, lifecycle, methods, Rcpp (≥ 0.12.0), RcppParallel(≥ 5.0.1), rlang, rstan (≥ 2.32.0), rstantools (≥ 2.4.0),stats, utils

LinkingTo:

StanHeaders (≥ 2.32.0), rstan (≥ 2.32.0), BH (≥1.72.0-2), Rcpp (≥ 0.12.0), RcppEigen (≥ 0.3.3.3.0),RcppParallel (≥ 5.0.1)

Suggests:

knitr, rmarkdown

Encoding:

UTF-8

UseLTO:

true

NeedsCompilation:

yes

RoxygenNote:

7.3.3

LazyData:

true

Biarch:

true

SystemRequirements:

GNU make

Packaged:

2025-12-15 14:52:08 UTC; saulo

Author:

Saulo Chaves

[aut, cre], Kaio Dias

[aut, cph], Matheus Krause

[aut]

Maintainer:

Saulo Chaves <saulochaves@usp.br>

Repository:

CRAN

Date/Publication:

2025-12-15 20:10:23 UTC

The 'ProbBreed' package.

Description

ProbBreed uses probability theory under the Bayesian framework for calculatingthe risk of selecting candidates in a multi-environment context.Contained are functions used to fit a Bayesian multi-environment model(based on the available presets), extract posterior values and maximum posterior values,compute the variance components, check the model’s convergence, and calculate the probabilities.For both across and within-environments scopes, the package computes the probability of superior performance and the pairwise probability of superior performance.Furthermore, the probability of superior stability and the pairwise probability of superior stability across environments is estimated.

Author(s)

Maintainer: Saulo Chavessaulochaves@usp.br (ORCID)

Authors:

Kaio Diaskaio.o.dias@ufv.br (ORCID) [copyright holder]
Matheus Krausemdkrause@iastate.edu (ORCID)

References

Stan Development Team (NA). RStan: the R interface to Stan. R package version 2.32.6. https://mc-stan.org

Dias, K. O. G, Santos J. P. R., Krause, M. D., Piepho H. -P., Guimarães, L. J. M.,Pastina, M. M., and Garcia, A. A. F. (2022). Leveraging probability conceptsfor cultivar recommendation in multi-environment trials.Theoretical andApplied Genetics, 133(2):443-455.doi:10.1007/s00122-022-04041-y

Bayesian model for multi-environment trials

Description

Fits a Bayesian multi-environment model usingrstan, theR interface toStan.

Usage

bayes_met(  data,  gen,  loc,  repl,  trait,  reg = NULL,  year = NULL,  res.het = FALSE,  iter = 2000,  cores = 1,  chains = 4,  pars = NA,  warmup = floor(iter/2),  thin = 1,  seed = sample.int(.Machine$integer.max, 1),  init = "random",  verbose = FALSE,  algorithm = c("NUTS", "HMC", "Fixed_param"),  control = NULL,  include = TRUE,  show_messages = TRUE,  ...)

Arguments

data

A data frame in which to interpret the variables declared in the other arguments.

gen,loc

A string. The name of the columns that contain the evaluatedcandidates and locations (or environments, if you are working with factor combinations), respectively.

repl

A string, a vector, orNULL. If the trial is randomized in complete blocks design,repl will be a string representing the name of the column that corresponds to the blocks.If the trial is randomized in incomplete blocks design,repl will be a string vectorcontaining the name of the columns that correspond to the replicate and block effects onthe first and second positions, respectively (c(replicate, block)).If the data does not have replicates,repl must beNULL.

trait

A string. The analysed variable. Currently, only single-trait models are fitted.

reg

A string or NULL. The name of the column that contain information onregions or mega-environments.NULL (default) if not applicable.

year

A string or NULL. The name of the column that contain information onyears (or seasons).NULL (default) if not applicable.

res.het

Should the model consider heterogeneous residual variances?Defaults forFALSE. IfTRUE, the model will estimate oneresidual variance per location (or environmnet).

iter

A positive integer specifying the number of iterations for each chain (including warmup). The default is 2000.

cores

Number of cores to use when executing the chains in parallel,which defaults to 1 but we recommend setting themc.cores option to be as many processors as the hardware and RAM allow (up to the number of chains).

chains

A positive integer specifying the number of Markov chains. The default is 4.

pars

A vector of character strings specifying parameters of interest. The default isNA indicating all parameters in the model. Ifinclude = TRUE, only samples for parameters named inpars are stored in the fitted results. Conversely, ifinclude = FALSE, samples for all parametersexcept those named inpars are stored in the fitted results.

warmup

A positive integer specifying the number of warmup (aka burnin)iterations per chain. If step-size adaptation is on (which it is by default), this also controls the number of iterations for which adaptation is run (andhence these warmup samples should not be used for inference). The number of warmup iterations should be smaller thaniter and the default isiter/2.

thin

A positive integer specifying the period for saving samples. The default is 1, which is usually the recommended value.

seed

The seed for random number generation. The default is generated from 1 to the maximum integer supported byR on the machine. Even if multiple chains are used, only one seed is needed, with other chains having seeds derived from that of the first chain to avoid dependent samples.When a seed is specified by a number,as.integer will be applied to it. Ifas.integer producesNA, the seed is generated randomly. The seed can also be specified as a character string of digits, such as"12345", which is converted to integer.

init

Initial values specification. See the detailed documentation for the init argument instan.

verbose

TRUE orFALSE: flag indicating whether to print intermediate output from Stan on the console, which mightbe helpful for model debugging.

algorithm

One of sampling algorithms that are implemented in Stan. Current options are"NUTS" (No-U-Turn sampler, Hoffman and Gelman 2011, Betancourt 2017),"HMC" (static HMC), or"Fixed_param". The default and preferred algorithm is"NUTS".

control

A namedlist of parameters to control the sampler'sbehavior. See the details in the documentation for thecontrol argumentinstan.

include

Logical scalar defaulting toTRUE indicatingwhether to include or exclude the parameters given by thepars argument. IfFALSE, only entire multidimensionalparameters can be excluded, rather than particular elements of them.

show_messages

Either a logical scalar (defaulting toTRUE)indicating whether to print the summary of Informational Messages tothe screen after a chain is finished or a character string naming a pathwhere the summary is stored. Setting toFALSE is not recommendedunless you are very sure that the model is correct up to numerical error.

...

Additional arguments can bechain_id,init_r,test_grad,append_samples,refresh,enable_random_init. See the documentation instan.

Details

The function has nine available models, which will be fitted according to theoptions set in the arguments:

Entry-mean model : fitted whenrepl = NULL,reg = NULL andyear = NULL:
y = \mu + g + l + \varepsilon
Wherey is the phenotype,\mu is the intercept,g is the genotypiceffect,l is the location (or environment) effect, and\varepsilon isthe error (which contains the genotype-by-location interaction, in this case).
Randomized complete blocks design : fitted whenrepl is a single string.It will fit different models depending ifreg andyear areNULL:
- reg = NULL andyear = NULL :
  y = \mu + g + l + gl + r + \varepsilon
  wheregl is the genotype-by-location effect, andr is the replicate effect.
- reg = "reg" andyear = NULL :
  y = \mu + g + m + l + gl + gm + r + \varepsilon
  wherem is the region effect, andgm is the genotype-by-region effect.
- reg = NULL andyear = "year" :
  y = \mu + g + t + l + gl + gt + r + \varepsilon
  wheret is the year effect, andgt is the genotype-by-year effect.
- reg = "reg" andyear = "year" :
  y = \mu + g + m + t + l + gl + gm + gt + r + \varepsilon
Incomplete blocks design : fitted whenrepl is a string vector of size 2.It will fit different models depending ifreg andyear areNULL:
- reg = NULL andyear = NULL :
  y = \mu + g + l + gl + r + b + \varepsilon
  whereb is the block within replicates effect.
- reg = "reg" andyear = NULL :
  y = \mu + g + m + l + gl + gm + r + b + \varepsilon
- reg = NULL andyear = "year" :
  y = \mu + g + t + l + gl + gt + r + b + \varepsilon
- reg = "reg" andyear = "year" :
  y = \mu + g + m + t + l + gl + gm + gt + r + b + \varepsilon

The models described above have predefined priors:

x \sim \mathcal{N} \left( 0, S^{[x]} \right)

\sigma \sim \mathcal{HalfCauchy}\left( 0, S^{[\sigma]} \right)

wherex can be any effect but the error, and\sigma is the standarddeviation of the likelihood. Ifres.het = TRUE, then\sigma_k \sim \mathcal{HalfCauchy}\left( 0, S^{\left[ \sigma_k \right]} \right).The hyperpriors are set as follows:

S^{[x]} \sim \mathcal{HalfCauchy}\left( 0, \phi \right)

where\phi is the known global hyperparameter defined such as\phi = max(y) \times 10.

More details about the usage ofbayes_met and other functions oftheProbBreed package can be found athttps://saulo-chaves.github.io/ProbBreed_site/.Solutions to convergence or mixing issues can be found athttps://mc-stan.org/misc/warnings.html.

Value

An object of S4 classstanfit representingthe fitted results. Slotmode for this objectindicates if the sampling is done or not.

Methods

sampling: signature(object = "stanmodel")Call a sampler (NUTS, HMC, or Fixed_param depending on parameters) to draw samples from the model defined by S4 classstanmodel given the data, initial values, etc.

Examples

mod = bayes_met(data = maize,                gen = "Hybrid",                loc = "Location",                repl = c("Rep","Block"),                trait = "GY",                reg = "Region",                year = NULL,                res.het = TRUE,                iter = 2000, cores = 2, chain = 4)

Bayesian Probabilistic Selection Index (BPSI)

Description

This function estimates the genotype's merit for multiple traits using theprobabilities of superior performance across environments.

Usage

bpsi(problist, increase = NULL, lambda = NULL, int, save.df = FALSE)

Arguments

problist

A list of object of classprobsup, obtained from theprob_sup function

increase

Optional logical vector with size corresponding to the number of traitsofproblist, in the same order.TRUE if the selection is for increasing the trait value,FALSE otherwise.If not declared,bpsi will consider the information provided inprob_sup

lambda

A numeric representing the weight of each trait. Defaults to 1 (equal weights).The trait with more economic interest should be greater.

int

A numeric representing the selection intensity (between 0 and 1), considering the selection index.

save.df

Logical. Should the data frames be saved in the work directory?TRUE for saving,FALSE (default) otherwise.

Details

Bayesian Probabilistic Selection Index

BPSI_i = \sum_{m=1}^{t} \frac{\gamma_{pt} -\gamma_{it} }{(1/\lambda_t)}

where\gamma_p is the probability of superior performance of the worst genotype for the traitt,\gamma is the probability of superior performance of genotypei for traitt,t is the total number of traits evaluated,\left(m = 1, 2, ..., t \right),and\lambda is the weight for each traitt.

More details about the usage ofbpsi can be found athttps://tiagobchagas.github.io/BPSI/.

Value

The function returns an object of classbpsi, which contains two lists,one with the BPSI- Bayesian Probabilistic Selection Index, and another with the originaldata-with across-environments probabilities of superior performance for each trait.

Author(s)

José Tiago Barroso Chagas

References

Chagas, J. T. B., Dias, K. O. G., Carneiro, V. Q., Oliveira, L. M. C., Nunes, N. X.,Pereira Júnior, J. D., Carneiro, P. C. S., & Carneiro, J. E. S. (2025).Bayesian probabilistic selection index in the selection of common bean families.Crop Science, 65(3).doi:10.1002/CSC2.70072

Examples

mod = bayes_met(data = soy_pat,                gen = "gen",                loc = "env",                repl = NULL,                trait = "PH",                reg = NULL,                year = NULL,                res.het = TRUE,                iter = 2000, cores = 2, chain = 4)mod2 = bayes_met(data = soy_pat,                 gen = "gen",                 loc = "env",                 repl = NULL,                 trait = "GY",                 reg = NULL,                 year = NULL,                 res.het = TRUE,                 iter = 2000, cores = 2, chain = 4)mod3 = bayes_met(data = soy_pat,                 gen = "gen",                 loc = "env",                 repl =  NULL,                 trait = "NDM",                 reg = NULL,                 year = NULL,                 res.het = TRUE,                 iter = 2000, cores = 2, chain = 4)models=list(mod,mod2,mod3)names(models) <- c("PH","GY","NDM")increase = c(FALSE,TRUE,FALSE)names(increase) <- names(models)probs = list()for (i in names(models)) {  outs <- extr_outs(model = models[[i]],                    probs = c(0.05, 0.95),                    verbose = TRUE)  probs[[i]] <- prob_sup(    extr = outs,    int = .2,    increase = increase[[i]],    save.df = FALSE,    verbose = TRUE  )}index = bpsi(  problist = probs,  increase = increase,  int = 0.1,  lambda = c(1, 2, 1),  save.df = FALSE)

Extract outputs from`stanfit` objects obtained frombayes_met

Description

Extracts outputs of the Bayesian model fittedusingbayes_met(), and provides some diagnostics.

Usage

extr_outs(model, probs = c(0.025, 0.975), verbose = FALSE)

Arguments

model

An object of classstanfit, obtained usingbayes_met()

probs

A vector with two elements representing the probabilities(in decimal scale) that will be considered for computing the quantiles.

verbose

A logical value. IfTRUE, the function will indicate thecompleted steps. Defaults toFALSE

Details

More details about the usage ofextr_outs and other functions oftheProbBreed package can be found athttps://saulo-chaves.github.io/ProbBreed_site/.

Value

The function returns an object of classextr, which is a list with:

variances : a data frame containing the variance components ofthe model effects, their standard deviation, naive standard error and highestposterior density interval.
post : a list with the posterior of the effects, and the datagenerated by the model.
map : a list with the maximum posterior values of each effect
ppcheck : a matrix containing the p-values of maximum, minimum,median, mean and standard deviation; effective number of parameters, WAIC2value, Rhat and effective sample size.

Examples

mod = bayes_met(data = maize,                gen = "Hybrid",                loc = "Location",                repl = c("Rep","Block"),                trait = "GY",                reg = "Region",                year = NULL,                res.het = TRUE,                iter = 2000, cores = 2, chain = 4)outs = extr_outs(model = mod,                 probs = c(0.05, 0.95),                 verbose = TRUE)

Maize real dataset

Description

This dataset belongs to value of cultivation and use maize trials ofEmbrapa Maize and Sorghum, and was used by Dias et al. (2022).It contains the grain yield of 32 single-cross hybrids and four commercial checks(36 genotypes in total) evaluated in 16 locations acrossfive regions or mega-environments. These trials were laid out in incomplete blocksdesign, using a block size of 6 and two replications per trial.

Usage

maize

Format

`maize`

A data frame with 823 rows and 6 columns:

Location: 16 locations
Region: 5 regions
Rep: 2 replicates
Block: 6 blocks
Hybrid: 36 genotypes
GY: Grain yield (phenotypes)

Source

Dias, K. O. G, Santos, J. P. R., Krause, M. D., Piepho, H. -P., Guimarães, L. J. M.,Pastina, M. M., and Garcia, A. A. F. (2022). Leveraging probability conceptsfor cultivar recommendation in multi-environment trials.Theoretical andApplied Genetics, 133(2):443-455.doi:10.1007/s00122-022-04041-y

Plots for the`bpsi` object

Description

Build plots using the outputs stored in thebpsi object.

Usage

## S3 method for class 'bpsi'plot(x, ..., category = "BPSI")

Arguments

x

An object of classbpsi.

...

currently not used

category

A string indicating which plot to build. There are currently twotypes of visualizations. Set "Ranks" for bar plots along each trait and "BPSI" (default) for circular bar plots multitrait.

Author(s)

José Tiago Barroso Chagas

References

Chagas, J. T. B., Dias, K. O. das G., Quintão Carneiro, V., de Oliveira, L. M. C., Nunes, N. X., Júnior, J. D. P., Carneiro, P. C. S., & Carneiro, J. E. de S. (2025).Bayesian probabilistic selection index in the selection of common bean families.Crop Science, 65(3).doi:10.1002/CSC2.70072

Examples

mod = bayes_met(data = soy_pat,                gen = "gen",                loc = "env",                repl = NULL,                trait = "PH",                reg = NULL,                year = NULL,                res.het = TRUE,                iter = 2000, cores = 2, chain = 4)mod2 = bayes_met(data = soy_pat,                 gen = "gen",                 loc = "env",                 repl = NULL,                 trait = "GY",                 reg = NULL,                 year = NULL,                 res.het = TRUE,                 iter = 2000, cores = 2, chain = 4)mod3 = bayes_met(data = soy_pat,                 gen = "gen",                 loc = "env",                 repl =  NULL,                 trait = "NDM",                 reg = NULL,                 year = NULL,                 res.het = TRUE,                 iter = 2000, cores = 2, chain = 4)models=list(mod,mod2,mod3)names(models) <- c("PH","GY","NDM")increase = c(FALSE,TRUE,FALSE)names(increase) <- names(models)probs = list()for (i in names(models)) {  outs <- extr_outs(model = models[[i]],                    probs = c(0.05, 0.95),                    verbose = TRUE)  probs[[i]] <- prob_sup(    extr = outs,    int = .2,    increase = increase[[i]],    save.df = FALSE,    verbose = TRUE  )}index = bpsi(  problist = probs,  increase = increase,  int = 0.1,  lambda = c(1, 2, 1),  save.df = FALSE)plot(index, category = "BPSI")plot(index, category = "Ranks")

Plots for the`extr` object

Description

Build plots using the outputs stored in theextr object.

Usage

## S3 method for class 'extr'plot(x, ..., category = "ppdensity")

Arguments

x

An object of classextr.

...

Passed toggplot2::geom_histogram, whencategory = histogram. Useful to change thenumber of bins.

category

A string indicating which plot to build. See options in the Details section.

Details

The available options are:

ppdensity : Density plots of the empirical and sampled data, useful to assess themodel's convergence.
density : Density plots of the model's effects.
histogram : Histograms of the model's effects.
traceplot: Trace plot showing the changes in the effects' values across iterations and chains.

Examples

mod = bayes_met(data = maize,                gen = "Hybrid",                loc = "Location",                repl = c("Rep","Block"),                trait = "GY",                reg = "Region",                year = NULL,                res.het = TRUE,                iter = 2000, cores = 2, chain = 4)outs = extr_outs(model = mod,                 probs = c(0.05, 0.95),                 verbose = TRUE)plot(outs, category = "ppdensity")plot(outs, category = "density")plot(outs, category = "histogram")plot(outs, category = "traceplot")

Plots for the`probsup` object

Description

Build plots using the outputs stored in theprobsup object.

Usage

## S3 method for class 'probsup'plot(x, ..., category = "perfo", level = "across")

Arguments

x

An object of classprobsup.

...

currently not used

category

A string indicating which plot to build. See options in the Details section.

level

A string indicating the information level to be used for buildingthe plots. Options are"across" for focusing on the probabilities across environments,or"within" to focus on the within-environment effects. Defaults to"across".

Details

The available options are:

hpd : a caterpillar plot representing the marginal genotypic value ofeach genotype, and their respective highest posterior density interval (95% represented by thethick line, and 97.5% represented by the thin line). Available only iflevel = "across".
perfo : iflevel = "across", a lollipop plot illustrating the probabilities of superior performance.Iflevel = "within", a heatmap with the probabilities of superior performance withinenvironments. If a model withreg and/oryear is fitted, multiple plots are produced.
stabi: a lollipop plot with the probabilities of superior stability.If a model withreg and/oryear is fitted, multiple plots are produced.Available only iflevel = "across". Unavailable if an entry-mean model was used inbayes_met.
pair_perfo : iflevel = "across", a heatmap representing the pairwise probability of superiorperformance (the probability of genotypes at thex-axis being superior.to those on they-axis). Iflevel = "within", a list of heatmaps representing the pairwise probability of superiorperformance within environments. If a model withreg and/oryear is fitted, multiple plots (and multiple lists) are produced.Should this option is set, it is mandatory to store the outputs in an object.(e.g.,pl <- plot(obj, category = "pair_perfo", level = "within")) so they can be visualized one at a time.The optionlevel = "within" is unavailable if an entry-mean model was used inbayes_met.
pair_stabi: a heatmap with the pairwise probabilities of superior stability(the probability of genotypes at thex-axis being more stable than those on they-axis).If a model withreg and/oryear is fitted, multiple plots are produced. Available only iflevel = "across".Unavailable if an entry-mean model was used inbayes_met.
joint: a lollipop plot with the joint probabilities of superior performance and stability. Unavailable if an entry-mean model was used inbayes_met.

Examples

mod = bayes_met(data = maize,                gen = "Hybrid",                loc = "Location",                repl = c("Rep","Block"),                trait = "GY",                reg = "Region",                year = NULL,                res.het = TRUE,                iter = 2000, cores = 2, chain = 4)outs = extr_outs(model = mod,                 probs = c(0.05, 0.95),                 verbose = TRUE)results = prob_sup(extr = outs,                   int = .2,                   increase = TRUE,                   save.df = FALSE,                   verbose = FALSE)plot(results, category = "hpd")plot(results, category = "perfo", level = "across")plot(results, category = "perfo", level = "within")plot(results, category = "stabi")plot(results, category = "pair_perfo", level = "across")plwithin = plot(results, category = "pair_perfo", level = "within")plot(results, category = "pair_stabi")plot(results, category = "joint")

Print an object of class`bpsi`

Description

Print abpsi object in R console

Usage

## S3 method for class 'bpsi'print(x, ...)

Arguments

x

An object of classbpsi

...

currently not used

Author(s)

José Tiago Barroso Chagas

Print an object of class`extr`

Description

Print aextr object in R console

Usage

## S3 method for class 'extr'print(x, ...)

Arguments

x

An object of classextr

...

currently not used

Print an object of class`probsup`

Description

Print aprobsup object in R console

Usage

## S3 method for class 'probsup'print(x, ...)

Arguments

x

An object of classprobsup

...

currently not used

Probabilities of superior performance and stability

Description

This function estimates the probabilities of superior performance and stabilityacross environments, and probabilities of superior performance within environments.

Usage

prob_sup(extr, int, increase = TRUE, save.df = FALSE, verbose = FALSE)

Arguments

extr

An object of classextr, obtained from theextr_outs function

int

A numeric representing the selection intensity(between 0 and 1)

increase

Logical.TRUE (default) if the selection is for increasing the trait value,FALSE otherwise.

save.df

Logical. Should the data frames be saved in the work directory?TRUE for saving,FALSE (default) otherwise.

verbose

A logical value. IfTRUE, the function will indicate thecompleted steps. Defaults toFALSE.

Details

Probabilities provide the risk of recommending a selection candidate for a targetpopulation of environments or for a specific environment.prob_supcomputes the probabilities of superior performance and the probabilities of superior stability:

Probability of superior performance

Let\Omega represent the subset of selected genotypes based on theirperformance across environments. A given genotypej will belong to\Omegaif its genotypic marginal value (\hat{g}_j) is high or low enough compared toits peers.prob_sup leverages the Monte Carlo discretized samplingfrom the posterior distribution to emulate the occurrence ofS trials. Then,the probability of thej^{th} genotype belonging to\Omega is theratio of success (\hat{g}_j \in \Omega) events and the total number of sampled events,as follows:

Pr\left(\hat{g}_j \in \Omega \vert y \right) = \frac{1}{S}\sum_{s=1}^S{I\left(\hat{g}_j^{(s)} \in \Omega \vert y\right)}

whereS is the total number of samples\left(s = 1, 2, ..., S \right),andI\left(g_j^{(s)} \in \Omega \vert y\right) is an indicator variable that can assumetwo values: (1) if\hat{g}_j^{(s)} \in \Omega in thes^{th} sample,and (0) otherwise.S is conditioned to the number of iterations and chainspreviously set atbayes_met.

Similarly, the within-environment probability of superior performance can be applied toindividual environments. Let\Omega_k represent the subset of superiorgenotypes in thek^{th} environment, so that the probability of thej^{th} \in \Omega_k can calculated as follows:

Pr\left(\hat{g}_{jk} \in \Omega_k \vert y\right) = \frac{1}{S} \sum_{s=1}^S I\left(\hat{g}_{jk}^{(s)} \in \Omega_k \vert y\right)

whereI\left(\hat{g}_{jk}^{(s)} \in \Omega_k \vert y\right) is an indicator variablemapping success (1) if\hat{g}_{jk}^{(s)} exists in\Omega_k, andfailure (0) otherwise, and\hat{g}_{jk}^{(s)} = \hat{g}_j^{(s)} + \widehat{ge}_{jk}^{(s)}.Note that when computing within-environment probabilities, we are accounting forthe interaction of thej^{th} genotype with thek^{th}environment.

The pairwise probabilities of superior performance can also be calculated acrossor within environments. This metric assesses the probability of thej^{th}genotype being superior to another experimental genotype or a commercial check.The calculations are as follows, across and within environments, respectively:

Pr\left(\hat{g}_{j} > \hat{g}_{j^\prime} \vert y\right) = \frac{1}{S} \sum_{s=1}^S I\left(\hat{g}_{j}^{(s)} > \hat{g}_{j^\prime}^{(s)} \vert y\right)

Pr\left(\hat{g}_{jk} > \hat{g}_{j^\prime k} \vert y\right) = \frac{1}{S} \sum_{s=1}^S I\left(\hat{g}_{jk}^{(s)} > \hat{g}_{j^\prime k}^{(s)} \vert y\right)

These equations are set for when the selection direction is positive. Ifincrease = FALSE,> is simply switched by<.

Probability of superior stability

This probability makes a direct analogy with themethod of Shukla (1972): a stable genotype is the one that has a lowgenotype-by-environment interaction variance[var(\widehat{ge})].Using the same probability principles previously described, the probabilityof superior stability is given as follows:

Pr \left[var \left(\widehat{ge}_{jk}\right) \in \Omega \vert y \right] = \frac{1}{S} \sum_{s=1}^S I\left[var \left(\widehat{ge}_{jk}^{(s)} \right) \in \Omega \vert y \right]

whereI\left[var \left(\widehat{ge}_{jk}^{(s)} \right) \in \Omega \vert y \right] indicates ifvar\left(\widehat{ge}_{jk}^{(s)}\right) exists in\Omega (1) or not (0).Pairwise probabilities of superior stability are also possible in this context:

Pr \left[var \left(\widehat{ge}_{jk} \right) < var\left(\widehat{ge}_{j^\prime k} \right) \vert y \right] = \frac{1}{S} \sum_{s=1}^S I \left[var \left(\widehat{ge}_{jk} \right)^{(s)} < var \left(\widehat{ge}_{j^\prime k} \right)^{(s)} \vert y \right]

Note thatj will be superior toj^\prime if it has alowervariance of the genotype-by-environment interaction effect. This is true regardlessifincrease is set toTRUE orFALSE.

The joint probability independent events is the product of the individual probabilities.The estimated genotypic main effects and the variances of GEI effects are independentby design, thus the joint probability of superior performance and stability as follows:

Pr \left[\hat{g}_j \in \Omega \cap var \left(\widehat{ge}_{jk} \right) \in \Omega \right] = Pr \left(\hat{g}_j \in \Omega \right) \times Pr \left[var \left(\widehat{ge}_{jk} \right) \in \Omega \right]

The estimation of these probabilities are strictly related to some key questions thatconstantly arises in plant breeding:

What is the risk of recommending a selection candidate for a target population of environments?
What is the probability of a given selection candidate having good performance ifrecommended to a target population of environments? And for a specific environment?
What is the probability of a given selection candidate having better performancethan a cultivar check in the target population of environments? And in specific environments?
How probable is it that a given selection candidate performs similarly across environments?
What are the chances that a given selection candidate is more stablethan a cultivar check in the target population of environments?
What is the probability that a given selection candidate having asuperior and invariable performance across environments?

More details about the usage ofprob_sup, as well as the other function oftheProbBreed package can be found athttps://saulo-chaves.github.io/ProbBreed_site/.

Value

The function returns an object of classprobsup, which contains two lists,one with theacross-environments probabilities, and another with thewithin-environments probabilities.If an entry-mean model was used inProbBreed::bayes_met, only theacross list will be available.

Theacross list has the following elements:

g_hpd: Highest posterior density (HPD) of the posterior genotypic main effects.
perfo: the probabilities of superior performance.
pair_perfo: the pairwise probabilities of superior performance.
stabi: a list with the probabilities of superior stability. It contains the data framesgl,gm (whenreg is notNULL) andgt (whenyear is notNULL). Unavailable if an entry-mean model was used inbayes_met.
pair_stabi: a list with the pairwise probabilities of superior stability. It contains the data framesgl,gm (whenreg is notNULL) andgt (whenyear is notNULL). Unavailable if an entry-mean model was used inbayes_met.
joint_prob: the joint probabilities of superior performance and stability. Unavailable if an entry-mean model was used inbayes_met.

Thewithin list has the following elements:

perfo: a list of data frames containing the probabilities of superior performancewithin locations (gl), regions (gm) and years (gt).
pair_perfo: lists with the pairwise probabilities of superior performancewithin locations (gl), regions (gm) and years (gt).

References

Shukla, G. K. (1972) Some statistical aspects of partioning genotype environmentalcomponentes of variability.Heredity, 29:237-245.doi:10.1038/hdy.1972.87

Examples

mod = bayes_met(data = maize,                gen = "Hybrid",                loc = "Location",                repl = c("Rep","Block"),                trait = "GY",                reg = "Region",                year = NULL,                res.het = TRUE,                iter = 2000, cores = 2, chain = 4)outs = extr_outs(model = mod,                 probs = c(0.05, 0.95),                 verbose = TRUE)results = prob_sup(extr = outs,                   int = .2,                   increase = TRUE,                   save.df = FALSE,                   verbose = FALSE)

Soybean real dataset

Description

This dataset belongs to the USDA Northern Region Uniform Soybean Tests,and it is a subset of the data used by Krause et al. (2023). It contains theempirical best linear unbiased estimates of genotypic means of the seed yieldfrom 39 experimental genotypes evaluated in 14 locations. The original data, available at the packageSoyURT, has 4,257 experimental genotypes evaluated at 63 locations and31 years resulting in 591 location-year combinations (environments) with39,006 yield values.

Usage

soy

Format

`soy`

A data frame with 823 rows and 3 columns:

Loc: 14 locations
Gen: 39 experimental genotypes
Y: 435 EBLUEs (phenotypes)

Source

Krause, M. D., Dias, K. O. G., Singh A. K., Beavis W. D. (2023). Using soybeanhistorical field trial data to study genotype by environmentvariation and identify mega-environments with the integrationof genetic and non-genetic factors.Agronomy Journal,117(1):170023.doi:10.1002/agj2.70023

Soybean Pan-African Trials data set

Description

This data set belongs to the Soybean Pan-African Trials (PAT). This subset hasthe best linear unbiased estimates of grain yield (GY), plant height (PH) andnumber of days to maturity (NDM) of 65 soybean genotypes evaluated over 19 environments.The complete data set is available at Araújo et al. (2025) (check references).It contains the empirical best linear unbiased estimates ofgrain yield (GY), plant height (PH) and number of days to maturity (NDM)from 65 experimental genotypes evaluated in 19 locations.

Usage

soy_pat

Format

`soy_pat`

A data frame with 540 rows and 5 columns:

Env: 19 environments
Gen: 65 experimental genotypes
Plant_Height: 395 BLUEs - Plant height measurements
Grain_Yield: 525 BLUEs - Grain yield measurements
Days_to_Maturity: 312 BLUEs - Number of days to maturity

Source

Araújo, M. S., Chaves, S., Ferreira, G. N. C., Chigeza, G.,Leles, E. P., Santos, M. F. S., Diers, B. W., Goldsmith, P.,and Pinheiro, J. B. (2025). High-resolution soybean trial data supporting theexpansion of agriculture in Africa.Scientific Data, 12:1908.doi:10.1038/s41597-025-06190-3

Movatterモバイル変換

The 'ProbBreed' package.

Description

Author(s)

References

See Also

Bayesian model for multi-environment trials

Description

Usage

Arguments

Details

Value

Methods

See Also

Examples

Bayesian Probabilistic Selection Index (BPSI)

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Extract outputs fromstanfit objects obtained frombayes_met

Description

Usage

Arguments

Details

Value

See Also

Examples

Maize real dataset

Description

Usage

Format

maize

Source

Plots for thebpsi object

Description

Usage

Arguments

Author(s)

References

See Also

Examples

Plots for theextr object

Description

Usage

Arguments

Details

See Also

Examples

Plots for theprobsup object

Description

Usage

Arguments

Details

See Also

Examples

Print an object of classbpsi

Description

Usage

Arguments

Author(s)

See Also

Print an object of classextr

Description

Usage

Arguments

See Also

Print an object of classprobsup

Description

Usage

Arguments

See Also

Probabilities of superior performance and stability

Description

Usage

Extract outputs from`stanfit` objects obtained frombayes_met

`maize`

Plots for the`bpsi` object

Plots for the`extr` object

Plots for the`probsup` object

Print an object of class`bpsi`

Print an object of class`extr`

Print an object of class`probsup`

`soy`

`soy_pat`