Package 'PopVar'

Description

Internal functions generally not to be called by the user.

Usage

par_position(crossing.table, par.entries)

par_name(crossing.mat, par.entries)

tails(GEBVs, tail.p)

maf_filt(G)

XValidate_nonInd(
  y.CV = NULL,
  G.CV = NULL,
  models.CV = NULL,
  frac.train.CV = NULL,
  nCV.iter.CV = NULL,
  burnIn.CV = NULL,
  nIter.CV = NULL
)

XValidate_Ind(
  y.CV = NULL,
  G.CV = NULL,
  models.CV = NULL,
  nFold.CV = NULL,
  nFold.CV.reps = NULL,
  burnIn.CV = NULL,
  nIter.CV = NULL
)

calc_marker_effects(
  M,
  y.df,
  models = c("rrBLUP", "BayesA", "BayesB", "BayesC", "BL", "BRR"),
  nIter,
  burnIn
)

Arguments

Description

Predicts the genotypic mean, genetic variance, and usefulness criterion (superior progeny mean) in a set of multi-parent populations using marker effects and a genetic map. If more than two traits are specified, the function will also return predictions of the genetic correlation in the population and the correlated response to selection.

Usage

mppop.predict(
  G.in,
  y.in,
  map.in,
  crossing.table,
  parents,
  n.parents = 4,
  tail.p = 0.1,
  self.gen = 10,
  DH = FALSE,
  models = c("rrBLUP", "BayesA", "BayesB", "BayesC", "BL", "BRR"),
  n.core = 1,
  ...
)

mppop_predict2(
  M,
  y.in,
  marker.effects,
  map.in,
  crossing.table,
  parents,
  n.parents = 4,
  tail.p = 0.1,
  self.gen = 10,
  DH = FALSE,
  models = c("rrBLUP", "BayesA", "BayesB", "BayesC", "BL", "BRR"),
  n.core = 1,
  ...
)

Arguments

Details

Predictions are based on the deterministic equations specified by Allier et al. (2019).

In the case of four-way crosses (i.e. 4 parents), the function assumes that the first two parents are mated, producing a $F_1$ offspring; then, the next two parents are mated, producing another $F_1$ offspring. The two $F_1$ offspring are then mated and inbreeding or doubled haploid induction (if specified) proceeds from there. For example, say cross i uses parents P1, P2, P3, and P4. P1 and P2 are first mated, producing O1; then, P3 and P4 are mated, producing O2; then, O1 and O2 are mated, producing a segregating family.

The mppop.predict function takes similarly formatted arguments as the pop.predict function in the PopVar package. For the sake of simplicity, we also include the mppop_predict2 function, which takes arguments in a format more consistent with other genomewide prediction packages/functions.

If you select a model other than "rrBLUP", you must specify the following additional arguments:

• nIter: See pop.predict.

• burnIn: See pop.predict.

Value

A data.frame containing predictions of $\mu$, $V_G$, and $\mu_{sp}$ for each trait for each potential multi-parent cross. When multiple traits are provided, the correlated responses and correlation between all pairs of traits is also returned.

References

Allier, A., L. Moreau, A. Charcosset, S. Teyssèdre, and C. Lehermeier, 2019 Usefulness Criterion and Post-selection Parental Contributions in Multi-parental Crosses: Application to Polygenic Trait Introgression. G3 (Bethesda) 9: 1469–1479. https://doi.org/https://doi.org/10.1534/g3.119.400129

Examples

# Load data
data("think_barley")

# Vector with 8 parents
parents <- sample(y.in_ex$Entry, 8)

# Create a crossing table with four parents per cross
cross_tab <- as.data.frame(t(combn(x = parents, m = 4)))
names(cross_tab) <- c("parent1", "parent2", "parent3", "parent4")

out <- mppop_predict2(M = G.in_ex_mat, y.in = y.in_ex, map.in = map.in_ex, 
                      crossing.table = cross_tab, models = "rrBLUP")

Description

pop.predict uses phenotypic and genotypic data from a set of individuals known as a training population (TP) and a set of candidate parents, which may or may not be included in the TP, to predict the mean ($\mu$), genetic variance (V_G), and superior progeny values ($\mu$_sp) of the half-diallel, or a defined set of pairwise bi-parental crosses between parents. When multiple traits are provided pop.predict will also predict the correlated responses and correlation between all pairwise traits. See Mohammadi, Tiede, and Smith (2015) for further details.

         NOTE - \code{pop.predict} writes and reads files to disk so it is highly recommended to set your working directory

Usage

pop.predict(
  G.in = NULL,
  y.in = NULL,
  map.in = NULL,
  crossing.table = NULL,
  parents = NULL,
  tail.p = 0.1,
  nInd = 200,
  map.plot = FALSE,
  min.maf = 0.01,
  mkr.cutoff = 0.5,
  entry.cutoff = 0.5,
  remove.dups = TRUE,
  impute = "EM",
  nSim = 25,
  frac.train = 0.6,
  nCV.iter = 100,
  nFold = NULL,
  nFold.reps = 1,
  nIter = 12000,
  burnIn = 3000,
  models = c("rrBLUP", "BayesA", "BayesB", "BayesC", "BL", "BRR"),
  return.raw = FALSE,
  saveAt = tempdir()
)

Arguments

Details

pop.predict can be used to predict the mean ($\mu$), genetic variance (V_G), superior progeny values ($\mu$$_sp$), as well as the predicted correlated response and correlations between all pairwise traits. The methodology and procedure to do so has been described in Bernardo (2014) and Mohammadi, Tiede, and K.P. Smith (2015). Users familiar with genome-wide prediction, association mapping, and/or linkage mapping will be familiar with the required inputs of pop.predict. G.in includes all of the entries (taxa) in the TP as well as additional entries to be considered as parent candidates. Entries included in G.in that do have a phenotype for any or all traits in y.in are considered TP entries for those respective traits. G.in is filtered according to min.maf, mkr.cutoff, entry.cutoff, and remove.dups; remaining missing marker data is imputed using the EM algorithm (Poland et al., 2012) when possible, and the marker mean otherwise, both implemented in A.mat. For each trait, the TP (i.e. entries with phenotype) is used to:

1. Perform CV to select a regression model. NOTE - Using the model with the highest CV accuracy is expected to result in the most accurate marker effect estimates (Bernardo, 2014). This expectation, however, is yet to be empirically validated and the user is encouraged to investigate the various models in order to make an educated decision about which one to ultimately use.

2. Estimate marker effects using the model resulting in the highest CV accuracy

Models include ridge regression BLUP implemented in mixed.solve (Endelman, 2011) and BayesA, BayesB, BayesC$\pi$, Bayesian lasso (BL), and Bayesian ridge regression (BRR) implemented in BGLR (de los Compos and Rodriguez, 2014). Information from the map.in is then used to simulate chromosomal recombination expected in a recombinant inbred line (i.e. F-infinity) (Broman et al., 2003) population (size=nInd). A function then converts the recombined chromosomal segments of the generic RIL population to the chromosomal segments of the population's respective parents and GEBVs of the simulated progeny are calculated. The simulation and conversion process is repeated s times, where s = nSim, to calculate dispersion statistics for $\mu$ and V_G; the remainder of the values in the predictions output are means of the s simulations. During each iteration the correlation (r) and correlated response of each pairwise combination of traits is also calculated and their mean across n simulations is returned. The correlated response of trait.B when predicting trait.A is the mean of trait.B for the ($\mu$$_sp$) of trait.A, and vice-versa; a correlated response for the bottom tail.p and upper $1-tail.p$ is returned for each trait.

     A dataset \code{\link{think_barley.rda}} is provided as an example of the proper formatting of input files and also for users to become familiar with \code{pop.predict}.

Value

A list containing:

• predictions A list of dataframes containing predictions of ($\mu$), (V_G), and ($\mu$_sp). When multiple traits are provided the correlated responses and correlation between all pairwise traits is also included. More specifically, for a given trait pair the correlated response of the secondary trait with both the high and low superior progeny of the primary trait is returned since the favorable values cannot be known by PopVar.

• preds.per.sim If return.raw is TRUE then a dataframe containing the results of each simulation is returned. This is useful for calculating dispersion statistics for traits not provided in the standard predictions dataframe.

• CVs A dataframe of CV results for each trait/model combination specified.

• models.chosen A matrix listing the statistical model chosen for each trait.

• markers.removed A vector of markers removed during filtering for MAF and missing data.

• entries.removed A vector of entries removed during filtering for missing data and duplicate entries.

References

 Bernardo, R. 2014. Genomewide Selection of Parental Inbreds: Classes of Loci and Virtual Biparental Populations. Crop Sci. 55:2586-2595.
 
 Broman, K. W., H. Wu, S. Sen and G.A. Churchill. 2003. R/qtl: QTL mapping in experimental crosses. Bioinformatics 19:889-890.
 
 Endelman, J. B. 2011. Ridge regression and other kernels for genomic selection with R package rrBLUP. Plant Genome 4:250-255. doi: 10.3835/plantgenome2011.08.0024

 Gustavo de los Campos and Paulino Perez Rodriguez, (2014). BGLR: Bayesian Generalized Linear Regression. R package version 1.0.3. http://CRAN.R-project.org/package=BGLR
 
 Mohammadi M., T. Tiede, and K.P. Smith. 2015. PopVar: A genome-wide procedure for predicting genetic variance and correlated response in bi-parental breeding populations. Crop Sci. \emph{Accepted}.
 
 Munoz-Amatriain, M., M. J. Moscou, P. R. Bhat, J. T. Svensson, J. Bartos, P. Suchankova, H. Simkova, T. R. Endo, R. D. Fenton, S. Lonardi, A. M. Castillo, S. Chao, L. Cistue, A. Cuesta-Marcos, K. L. Forrest, M. J. Hayden, P. M. Hayes, R. D. Horsley, K. Makoto, D. Moody, K. Sato, M. P. Valles, B. B. H. Wulff, G. J. Muehlbauer, J. Dolezel, and T. J. Close. 2011 An improved consensus linkage map of barley based on flow-sorted chromosomes and single nucleotide polymorphism markers. Plant Gen. 4:238-249.
 
 Poland, J., J. Endelman, J. Dawson, J. Rutkoski, S. Wu, Y. Manes, S. Dreisigacker, J. Crossa, H. Sanches-Villeda, M. Sorrells, and J.-L. Jannink. 2012. Genomic Selection in Wheat Breeding using Genotyping-by-Sequencing. Plant Genome 5:103-113.

Examples

## Not run: 

# Load data
data("think_barley")

## The following examples only use the model 'rrBLUP' for the sake of testing. Functions
## BGLR package write temporary files to the disk.
##
## Ex. 1 - Predict a defined set of crosses
## This example uses CV method 1 (see Details of x.val() function)
ex1.out <- pop.predict(G.in = G.in_ex, y.in = y.in_ex, 
   map.in = map.in_ex, crossing.table = cross.tab_ex,
   nSim=5, nCV.iter=2, models = "rrBLUP")
ex1.out$predictions  ## Predicted parameters
ex1.out$CVs          ## CV results
       
## Ex. 2 - Use only rrBLUP and Bayesian lasso (BL) models
ex3.out <- pop.predict(G.in = G.in_ex, y.in = y.in_ex,
   map.in = map.in_ex, crossing.table = cross.tab_ex,
   models = c("rrBLUP"), nSim=5, nCV.iter=10)  

## Ex. 3 - Same as Ex. 3, but return all raw SNP and prediction data for each simulated population
ex4.out <- pop.predict(G.in = G.in_ex, y.in = y.in_ex,
   map.in = map.in_ex, crossing.table = cross.tab_ex,
   models = c("rrBLUP"), nSim=5, nCV.iter=2, return.raw = TRUE)  

## End(Not run)

Description

Generates predictions of the genetic variance and genetic correlation in bi-parental populations using a set of deterministic equations instead of simulations.

Usage

pop.predict2(
  G.in,
  y.in,
  map.in,
  crossing.table,
  parents,
  tail.p = 0.1,
  self.gen = Inf,
  DH = FALSE,
  models = c("rrBLUP", "BayesA", "BayesB", "BayesC", "BL", "BRR"),
  ...
)

pop_predict2(
  M,
  y.in,
  marker.effects,
  map.in,
  crossing.table,
  parents,
  tail.p = 0.1,
  self.gen = Inf,
  DH = FALSE,
  models = c("rrBLUP", "BayesA", "BayesB", "BayesC", "BL", "BRR"),
  ...
)

Arguments

Details

Predictions are based on the deterministic equations specified by Zhong and Jannink (2007), Allier et al. (2019), and Neyhart et al. (2019).

If you select a model other than "rrBLUP", you must specify the following additional arguments:

• nIter: See pop.predict.

• burnIn: See pop.predict.

Value

A data.frame containing predictions of $\mu$, $V_G$, and $\mu_{sp}$ for each trait for each potential bi-parental cross. When multiple traits are provided, the correlated responses and correlation between all pairs of traits is also returned.

Functions

• pop_predict2():

References

Zhong, S., and J.-L. Jannink, 2007 Using quantitative trait loci results to discriminate among crosses on the basis of their progeny mean and variance. Genetics 177: 567–576. https://doi.org/10.1534/ genetics.107.075358

Allier, A., L. Moreau, A. Charcosset, S. Teyssèdre, and C. Lehermeier, 2019 Usefulness Criterion and Post-selection Parental Contributions in Multi-parental Crosses: Application to Polygenic Trait Introgression. G3 9: 1469–1479. doi: 10.1534/g3.119.400129

Neyhart, J.L., A.J. Lorenz, and K.P. Smith, 2019 Multi-trait Improvement by Predicting Genetic Correlations in Breeding Crosses. G3 9: 3153-3165. doi: 10.1534/g3.119.400406

Examples

# Load data
data("think_barley")

# Use example data to make predictions
out <- pop.predict2(G.in = G.in_ex_imputed, y.in = y.in_ex, map.in = map.in_ex, 
                    crossing.table = cross.tab_ex)
                    
# Provide a vector of parents to predict all possible crosses (some parents
# have missing phenotypic data)
out <- pop.predict2(G.in = G.in_ex_imputed, y.in = y.in_ex, map.in = map.in_ex, 
                    parents = y.in_ex$Entry[1:5])
                    
# Make predictions for 5 crosses with various levels of inbreeding
out_list <- lapply(X = 1:10, FUN = function(self.gen) {
  out <- pop.predict2(G.in = G.in_ex_imputed, y.in = y.in_ex, map.in = map.in_ex, 
                      crossing.table = cross.tab_ex[1:5,], self.gen = self.gen)
  out$self.gen <- self.gen
  out })
               
# Plot predictions of grain yield genetic variance over levels of inbreeding
dat <- do.call("rbind", lapply(out_list, subset, trait == "Yield"))
plot(pred_varG ~ self.gen, data = dat, type = "b", 
     subset = parent1 == parent1[1] & parent2 == parent2[1])






# Load data
data("think_barley")

# Use example data to make predictions
out <- pop_predict2(M = G.in_ex_mat, y.in = y.in_ex, map.in = map.in_ex, 
                    crossing.table = cross.tab_ex)
                    
# Provide a vector of parents to predict all possible crosses (some parents
# have missing phenotypic data)
out <- pop_predict2(M = G.in_ex_mat, y.in = y.in_ex, map.in = map.in_ex, 
                    parents = y.in_ex$Entry[1:10])

Description

A sample dataset, previously described in Sallam et al. (2014) is provided as an example of the proper formatting of input files and also for users to become familiar with PopVar; the think_barley dataset is useful in demonstrating both pop.predict and x.val. Note that a number of entries are missing data for one or both traits, which is representative of a real breeding scenario where phenotypic data may not be available for all parent candidates.

Format

The names of the example files are:

G.in_ex

A set of 245 barley lines genotyped with 742 SNP markers

G.in_ex_mat

A n x p matrix of n = 245 barley lines genotyped with p = 742 SNP markers

G.in_ex_imputed

A n x p matrix of n = 245 barley lines and p = 742 imputed SNP marker genotypes

y.in_ex

Phenotypes of four traits for a portion of the 245 barley lines, Fusarium head blight (FHB), deoxynivalenol (DON) in ppm, grain yield in bushels/acre, and plant height in cm.

map.in_ex

Genetic map (i.e. chromosome assignment and genetic distance (cM) between markers) of the 742 SNP markers based on Munoz-Amatriain et al., 2011

cross.tab_ex

A table of user-defined crosses

References

Sallam, A.H., J.B. Endelman, J-L. Jannink, and K.P. Smith. 2015. Assessing Genomic Selection Prediction Accuracy in a Dynamic Barley Breeding Population. Plant Gen. 8(1)

Description

x.val performs cross-validation (CV) to estimate the accuracy of genome-wide prediction (otherwise known as genomic selection) for a specific training population (TP), i.e. a set of individuals for which phenotypic and genotypic data is available. Cross-validation can be conducted via one of two methods within x.val, see Details for more information.

         NOTE - \code{x.val}, specifically \code{\link[BGLR]{BGLR}} writes and reads files to disk so it is highly recommended to set your working directory

Usage

x.val(
  G.in = NULL,
  y.in = NULL,
  min.maf = 0.01,
  mkr.cutoff = 0.5,
  entry.cutoff = 0.5,
  remove.dups = TRUE,
  impute = "EM",
  frac.train = 0.6,
  nCV.iter = 100,
  nFold = NULL,
  nFold.reps = 1,
  return.estimates = FALSE,
  CV.burnIn = 750,
  CV.nIter = 1500,
  models = c("rrBLUP", "BayesA", "BayesB", "BayesC", "BL", "BRR"),
  saveAt = tempdir()
)

Arguments

Details

Two CV methods are available within PopVar:

• CV method 1: During each iteration a training (i.e. model training) set will be randomly sampled from the TP of size $N*(frac.train)$, where N is the size of the TP, and the remainder of the TP is assigned to the validation set. The accuracies of individual models are expressed as average Pearson's correlation coefficient (r) between the genome estimated breeding value (GEBV) and observed phenotypic values in the validation set across all nCV.iter iterations. Due to its amendibility to various TP sizes, CV method 1 is the default CV method in pop.predict.

• CV method 2: nFold independent validation sets are sampled from the TP and predicted by the remainder. For example, if $nFold = 10$ the TP will be split into 10 equal sets, each containing $1/10$-th of the TP, which will be predicted by the remaining $9/10$-ths of the TP. The accuracies of individual models are expressed as the average (r) between the GEBV and observed phenotypic values in the validation set across all nFold folds. The process can be repeated nFold.reps times with nFold new independent sets being sampled each replication, in which case the reported prediction accuracies are averages across all folds and replications.

Value

A list containing:

• CVs A dataframe of CV results for each trait/model combination specified

• If return.estimates is TRUE the additional items will be returned:

  • models.used A list of the models chosen to estimate marker effects for each trait

  • mkr.effects A vector of marker effect estimates for each trait generated by the respective prediction model used

  • betas A list of beta values for each trait generated by the respective prediction model used

Examples

## The following examples only use the model 'rrBLUP' for the sake of testing. Functions
## BGLR package write temporary files to the disk.

## CV using method 1 with 25 iterations
CV.mthd1 <- x.val(G.in = G.in_ex, y.in = y.in_ex, nCV.iter = 25, models = "rrBLUP")
CV.mthd1$CVs

## CV using method 2 with 5 folds and 3 replications
x.val(G.in = G.in_ex, y.in = y.in_ex, nFold = 5, nFold.reps = 3, models = "rrBLUP")