kappaIBD: IBD (kappa) coefficients

In ribd: Pedigree-based Relatedness Coefficients

IBD (kappa) coefficients

Description

Computes the three IBD coefficients summarising the relationship between two non-inbred individuals. Both autosomal and X chromosomal versions are implemented. The pedigree founders (other than the individuals in question) are allowed to be inbred; see pedtools::founderInbreeding() for how to set this up, and see Examples below.

Usage

kappaIBD(x, ids = labels(x), inbredAction = 1, simplify = TRUE, Xchrom = FALSE)

Arguments

x	A pedigree in the form of a ped object (or a list of such).
ids	A character (or coercible to character) containing ID labels of two or more pedigree members.
inbredAction	An integer telling the program what to do if either of the ids individuals are inbred. Possible values are: 0 = do nothing; 1 = print a warning message (default); 2 = raise an error. In the first two cases the coefficients are reported as NA.
simplify	Simplify the output (to a numeric of length 3) if ids has length 2. Default: TRUE.
Xchrom	A logical, indicating if the autosomal (default) or X-chromosomal kappa coefficients should be computed.

Details

For non-inbred individuals a and b, their autosomal IBD coefficients (\kappa0, \kappa1, \kappa2) are defined as follows:

\kappa_i = P(a and b share exactly i alleles IBD at a random autosomal locus)

The autosomal kappa coefficients are computed from the kinship coefficients. When a and b are both nonfounders, the following formulas hold:

• \kappa2 = \phi_MM * \phi_FF + \phi_MF * \phi_FM

• \kappa1 = 4 * \phi_ab - 2 * \kappa2

• \kappa0 = 1 - \kappa1 - \kappa2

Here \phi_MM denotes the kinship coefficient between the mothers of a and b, and so on. If either a or b is a founder, then \kappa2 = 0, while the other two formulas remain as above.

The X-chromosomal IBD coefficients are defined similarly to the autosomal case. Here \kappa2 is undefined when one or both individuals are male, which greatly simplifies the calculations when males are involved. The formulas are (with \phi_ab referring to the X-chromosomal kinship coefficient):

• Both male: (\kappa0, \kappa1, \kappa2) = (1-\phi_ab, \phi_ab, NA)

• One male, one female: (\kappa0, \kappa1, \kappa2) = (1-2*\phi_ab, 2*\phi_ab, NA)

• Two females: Similar formulas as in the autosomal case.

Value

If ids has length 2 and simplify = TRUE: A numeric vector of length 3: (\kappa0, \kappa1, \kappa2).

Otherwise: A data frame with one row for each pair of individuals, and 5 columns. The first two columns contain the ID labels, and columns 3-5 contain the IBD coefficients.

Unless inbredAction = 2, the coefficients of pairs involving inbred individuals (X-inbred females if Xchrom = T) are reported as NA. Furthermore, the X-chromosomal \kappa2 is NA whenever at least one of the two individuals is male.

See Also

kinship(), identityCoefs()

Examples

### Siblings
x = nuclearPed(2)
kappaIBD(x)

k = kappaIBD(x, 3:4)
stopifnot(identical(k, c(.25, .5, .25)))

### Quad half first cousins
x = quadHalfFirstCousins()
k = kappaIBD(x, ids = leaves(x))
stopifnot(identical(k, c(17/32, 14/32, 1/32)))

### Paternal half brothers with 100% inbred father
# Genetically indistinguishable from an (outbred) father-son relationship
x = halfSibPed()
ids = 4:5

# Set founder inbreeding
fou = commonAncestors(x, ids) # robust to label change
founderInbreeding(x, fou) = 1

k = kappaIBD(x, ids)
stopifnot(identical(k, c(0, 1, 0)))

### X-chromosomal kappa
y = nuclearPed(2, sex = 2)
kappaIBD(y, Xchrom = TRUE)

ribd documentation built on Aug. 10, 2023, 5:08 p.m.