Boxplots of Jacquard Coefficients

Description

Function BoxplotDelta produces boxplots of the Jacquard coefficients from a list structure containing nine matrices with the pairwise coefficients. The diagonals of J1 and J7 are plotted in separate boxplots.

Usage

BoxplotDelta(J, ind.sub = 1:nrow(J[[1]]), ...)

Arguments

Value

NULL

Author(s)

Jan Graffelman (jan.graffelman@upc.edu)

Examples

  data(DeltaSimulatedPedigree)
  BoxplotDelta(DeltaSimulatedPedigree)

Boxplots of Relateness parameters

Description

Function BoxplotTheta makes boxplots of relatedess parameters from a list object containing estimates of pairwise relatedness parameters.

Usage

BoxplotTheta(KS, ind.sub = 1:nrow(KS[[1]]), ...)

Arguments

Details

For individual inbreeding coefficients, two boxplots are made, the first based on the diagonal of T2, the second on the row means of T2. The remaining boxplots (kinship, T3 and T4) are all pairwise, and exclude self-pairs.

Value

NULL

Author(s)

Jan Graffelman (jan.graffelman@upc.edu)

References

Csuros, M. (2014) Non-identifiability of identity coefficients at biallelic loci. Theoretical Population Biology 92, pp. 22-29. doi:10.1016/j.tpb.2013.11.001.

Graffelman, J., Weir, B.S. and Goudet, J. (2024) Estimation of Jacquard's genetic identity coefficients with bi-allelic variants by constrained least-squares. Preprint at bioRxiv doi:10.1101/2024.03.25.586682.

See Also

CalculateTheta

Examples

data(DeltaSimulatedPedigree)
Theta <- CalculateTheta(DeltaSimulatedPedigree)
BoxplotTheta(Theta)

Calculate Moment Estimators for Relatedness Parameters

Description

Function CalculateMom computes moment estimators for a set of relatedness parameters (kinship, inbreeding, least one IBD out of three and T4) using the genotype data and the allele frequencies.

Usage

CalculateMom(Xgen, mafvec, ind.sub = 1:nrow(Xgen), verbose = TRUE)

Arguments

Value

A list object with four fields:

Author(s)

Jan Graffelman (jan.graffelman@upc.edu)

References

Csuros, M. (2014) Non-identifiability of identity coefficients at biallelic loci. Theoretical Population Biology 92, pp. 22-29. doi:10.1016/j.tpb.2013.11.001.

See Also

BoxplotTheta

Examples

data(SimulatedPedigree)
Xgen <- as.matrix(SimulatedPedigree[,6:ncol(SimulatedPedigree)])
mafvec <- mafvector(Xgen)
Theta.mom <- CalculateMom(Xgen[1:10,],mafvec)

Calculate Relatedness Paramenters from Jacquard Coefficients tA Capitalized Title (ideally limited to 65 characters)

Description

Function CalculateTheta calculates five identifiable relatedness parameters from a list structure containing nine matrices of Jacquard coefficients.

Usage

CalculateTheta(J, ind.sub = 1:nrow(J[[1]]))

Arguments

Details

CalculateTheta produces four matrices according to the expressions in Graffelman et al. (2024).

Value

A list object with four fields:

Author(s)

Jan Graffelman (jan.graffelman@upc.edu)

References

Csuros, M. (2014) Non-identifiability of identity coefficients at biallelic loci. Theoretical Population Biology 92, pp. 22-29. doi:10.1016/j.tpb.2013.11.001.

Graffelman, J., Weir, B.S. and Goudet, J. (2024) Estimation of Jacquard's genetic identity coefficients with bi-allelic variants by constrained least-squares. Preprint at bioRxiv doi:10.1101/2024.03.25.586682.

See Also

Jacquard.cls

Examples

data(DeltaSimulatedPedigree)
Theta <- CalculateTheta(DeltaSimulatedPedigree)

Extract estimates of Jacquard coefficients for a given pair

Description

Function DeltaPair extracts from the list object of all pairwise Jacquard coefficients the set of coefficients of a given pair (i,j).

Usage

DeltaPair(Delta, i, j, digits = 7)

Arguments

Value

A vector with nine elements

Author(s)

Jan Graffelman (jan.graffelman@upc.edu)

See Also

PairwiseList,Jacquard.cls

Examples

 data(DeltaSimulatedPedigree)
 DeltaPair(DeltaSimulatedPedigree,1,2)

Estimates of Jacquard Coefficients for Simulated SNP data according to a Pedigree

Description

A list object containing nine matrices with pairwise Jacquard coefficients

Usage

data("DeltaSimulatedPedigree")

Format

A list with nine fields.

Details

DeltaSimulatedPedigree can be generated by applying function Jacquard.cls to the data in SimulatedPedigree.

References

Graffelman, J., Weir, B.S. and Goudet, J. (2024) Estimation of Jacquard's genetic identity coefficients with bi-allelic variants by constrained least-squares. Preprint at bioRxiv doi:10.1101/2024.03.25.586682.

Examples

data(DeltaSimulatedPedigree)

Joint Genotype Counts according to a Pedigree

Description

Contains a list object with nine fields, consisting of nine lower triangular matrices with the joint genotype counts for 111 individuals.

Usage

data("GTC")

Format

A list with nine fields.

References

Goudet, J. (2022) JGTeach: JG Teaching material. R package version 0.1.9. https://github.com/jgx65

Graffelman, J., Weir, B.S. and Goudet, J. (2024) Estimation of Jacquard's genetic identity coefficients with bi-allelic variants by constrained least-squares. Preprint at bioRxiv doi:10.1101/2024.03.25.586682.

Examples

data(GTC)

Estimation of Jacquard coefficients by Constrained Least Squares

Description

Function Jacquard.cls estimates the nine condensed Jacquard coefficients of a pair of individuals using their joint genotype probabilities and the allele frequencies using constrained least squares.

Usage

Jacquard.cls(Xlist, mafvec = NULL, eps = 1e-06, delta.init = runif(9), Mavg = NULL,
             inner.iter = 1000, outer.iter = 1000, verbose = TRUE)

Arguments

Details

Function Jacquard.cls relies on the solver solnp from the Rsolnp package.

Value

A list object with fields:

Author(s)

Jan Graffelman (jan.graffelman@upc.edu)

References

Graffelman, J., Weir, B.S. and Goudet, J. (2024) Estimation of Jacquard's genetic identity coefficients with bi-allelic variants by constrained least-squares. Preprint at bioRxiv doi:10.1101/2024.03.25.586682.

Ghalanos, A. and Theussl, S. (2015) Rsolnp: General Non-linear Optimization Using Augmented Lagrange Multiplier Method. R package version 1.16. https://cran.r-project.org/package=Rsolnp

See Also

JointGenotypeCounts

Examples

data(SimulatedPedigree)
Xgen <- as.matrix(SimulatedPedigree[,6:ncol(SimulatedPedigree)])

data(GTC)

mafvec <- mafvector(Xgen)

ii <- 1:3

GTCsubset <- list(length = 9)
for (k in 1:9) {
  GTCsubset[[k]] <- matrix(numeric(3^2), ncol = 3)
  GTCsubset[[k]] <- GTC[[k]][ii,ii]
}

output <- Jacquard.cls(GTCsubset,mafvec=mafvec,
                       eps=1e-06)
Delta.cls <- output$delta
print(Delta.cls)
print(output$convergence)

# A particular estimate of a Jacquard coefficient for a particular pair can
# be extracted from Delta.cls
#
# E.g., Delta\_9 of the first pair of individuals (1,2) can be extracted by
#

D9_12 <- Delta.cls[[9]][1,2]

Calculate joint pairwise Genotype Counts

Description

Function JointGenotypeCounts counts for each pair of individuals in the database their nine joint genotype counts

Usage

JointGenotypeCounts(X.gen, one.is.minor = TRUE)

Arguments

Value

A list object with nine fields containing:

Author(s)

Jan Graffelman (jan.graffelman@upc.edu)

References

Graffelman, J., Weir, B.S. and Goudet, J. (2024) Estimation of Jacquard's genetic identity coefficients with bi-allelic variants by constrained least-squares. Preprint at bioRxiv. doi:10.1101/2024.03.25.586682

Examples

data(SimulatedPedigree)
JC <- JointGenotypeCounts(SimulatedPedigree[1:3,1:100])
print(JC)

Create matrix of conditional joint genotype probabilities

Description

Function MakeM creates the matrix of conditional joint genotype probabilities for biallelic markers for a given allele frequency.

Usage

MakeM(p)

Arguments

Value

a 9 by 9 matrix

Author(s)

Jan Graffelman (jan.graffelman@upc.edu)

References

Csuros, M. (2014) Non-identifiability of identity coefficients at biallelic loci. Theoretical Population Biology 92, pp. 22–29. doi: 10.1016/j.tpb.2013.11.001

Graffelman, J., Weir, B.S. and Goudet, J. (2024) Estimation of Jacquard's genetic identity coefficients with bi-allelic variants by constrained least-squares. Under review.

Examples

set.seed(123)
p <- runif(1)
M <- MakeM(p)

Create a Pairwise List of Jacquard Coefficients

Description

Function PairwiseList processes the list structure of Jacquard coefficients and converts it into to table of pairs of individuauls with their Jacquard coefficients.

Usage

PairwiseList(X, digits = 3)

Arguments

Value

A matrix

Author(s)

Jan Graffelman (jan.graffelman@upc.edu)

See Also

Jacquard.cls

Examples

data(DeltaSimulatedPedigree)

ii <- 1:3

SubSet <- list(length = 9)
for (k in 1:9) {
  SubSet[[k]] <- matrix(numeric(3^2), ncol = 3)
  SubSet[[k]] <- DeltaSimulatedPedigree[[k]][ii,ii]
}

List <- PairwiseList(SubSet)

print(List)

Simulated SNP data according to a Pedigree

Description

A matrix containing 111 individuals (rows), pedigree information (first five columns) and 20.000 single nucleotide polymorphisms (remaining columns) coded in (0,1,2) format and simulated according to a pedigree of 20 unrelated founders with six posterior generations.

Usage

data("SimulatedPedigree")

Format

A data frame containing 111 rows and 20.005 columns.

Details

The SNP data was generated using the JGTeach package. The genotype counts in the object SimulatedPedigree represent the counts of the minor allele.

References

Goudet, J. (2022) JGTeach: JG Teaching material. R package version 0.1.9. https://github.com/jgx65

Graffelman, J., Weir, B.S. and Goudet, J. (2024) Estimation of Jacquard's genetic identity coefficients with bi-allelic variants by constrained least-squares. Preprint at bioRxiv doi:10.1101/2024.03.25.586682.

Examples

data(SimulatedPedigree)

Calculate the Minor Allele Frequency (MAF) for a matrix with (0,1,2) genotype data

Description

Function mafvector calculates genotype counts columnwise and determines the minor allele frequency for each column.

Usage

mafvector(X)

Arguments

Details

mafvector calculates the frequency of the minor allele irrespective of the coding; i.e., irrespective of whether the genotype data represent major or minor allele counts. Missing values are discarded for the calculation of the MAF.

Value

a vector

Author(s)

Jan Graffelman (jan.graffelman@upc.edu)

Examples

  data(SimulatedPedigree)
  p <- mafvector(SimulatedPedigree[,1:10])
  print(p)