AGHmatrix (version 3.0.1)

Amatrix: Construction of Relationship Matrix A

Description

Constructs an additive relationship matrix (A) from pedigree data in a three-column format. The calculation depends on the specified ploidy level (must be an even number). If ploidy = 4, the matrix can incorporate a user-defined proportion (w) of parental gametes that are IBD (Identical by Descent) due to double reduction.

When ploidy = 2 and dominance = FALSE, the diploid additive numerator relationship matrix is built using Henderson's (1976) method. If dominance = TRUE, a diploid dominance numerator relationship matrix is computed following Cockerham (1954). The recursive approach is detailed in Mrode (2005).

For ploidy > 2 and dominance = FALSE, an autopolyploid additive relationship matrix is computed based on Kerr et al. (2012). If slater = TRUE and ploidy = 4, Slater's (2013) method is used instead.

Usage

Amatrix(
  data = NULL,
  ploidy = 2,
  w = 0,
  verify = TRUE,
  dominance = FALSE,
  slater = FALSE,
  ASV = FALSE,
  ...
)

Value

A square matrix representing the relationship between individuals in the pedigree.

Arguments

data

Pedigree data frame in a 3-column format. Unknown values should be set to 0.

ploidy

An even number representing the ploidy level (default is 2).

w

Proportion of parental gametes that are IBD due to double reduction (default is 0). Applicable only when ploidy = 4.

verify

Logical; if TRUE (default), the pedigree file is checked for conflicting entries.

dominance

Logical; if TRUE, computes the dominance relationship matrix (valid only for ploidy = 2).

slater

Logical; if TRUE and ploidy = 4, computes the additive autotetraploid relationship matrix using Slater (2013).

ASV

Logical; if TRUE, transforms the matrix into the average semivariance (ASV) defined as \(K = K / (\text{trace}(K) / (\text{nrow}(K) - 1))\). See Feldmann et al. (2022), Formula 2.

...

Additional arguments passed to datatreat().

Author

Rodrigo R Amadeu,

Thiago de Paula Oliveira,

References

Cockerham, C.C. (1954). An extension of the concept of partitioning hereditary variance for analysis of covariances among relatives when epistasis is present. Genetics, 39, 859–882.

Feldmann, M.J., et al. (2022). Average semivariance directly yields accurate estimates of the genomic variance in complex trait analyses. G3 (Bethesda), 12(6).

Henderson, C.R. (1976). A simple method for computing the inverse of a numerator relationship matrix used in prediction of breeding values. Biometrics, 32, 69–83.

Kerr, R.J., et al. (2012). Use of the numerator relationship matrix in genetic analysis of autopolyploid species. Theoretical and Applied Genetics, 124, 1271–1282.

Mrode, R.A. (2014). Linear Models for the Prediction of Animal Breeding Values (3rd ed.). CABI.

Slater, A.T., et al. (2013). Improving the analysis of low heritability complex traits for enhanced genetic gain in potato. Theoretical and Applied Genetics, 127, 809–820.

Examples

data(ped.mrode)
# Additive relationship matrix for diploids (Henderson 1976):
Amatrix(ped.mrode, ploidy = 2)

# Dominance relationship matrix for diploids (Cockerham 1954):
Amatrix(ped.mrode, ploidy = 2, dominance = TRUE)

# Additive relationship matrix for autotetraploids (Kerr 2012):
Amatrix(ped.mrode, ploidy = 4)

# Additive relationship matrix for autooctaploids (Kerr 2012):
Amatrix(ped.mrode, ploidy = 8)

# Additive relationship matrix for autotetraploids with double reduction 
# (Kerr 2012):
Amatrix(ped.mrode, ploidy = 4, w = 0.1)

# Additive relationship matrix for autotetraploids with double reduction 
# using Slater (2013):
Amatrix(ped.mrode, ploidy = 4, w = 0.1, slater = TRUE)

# Additive relationship matrix for autohexaploids with double reduction 
# (Kerr 2012):
Amatrix(ped.mrode, ploidy = 6, w = 0.1)