twoLocusJacquard {IBDsim}

Estimating two-locus Jacquard coefficients

Description

Estimates by simulation the two-locus version of Jacquard's condensed identity coefficients for a pairwise relationship.

Usage

twoLocusJacquard(x, ind1, ind2, rho=NULL, cM=NULL, Nsim, verbose=TRUE,...)

Arguments

x

A pedigree in the form of a linkdat object.

ind1, ind2

Numeric ID labels of the two individuals.

rho

NULL, or a number in the interval [0, 0.5]: the recombination fraction between the two loci. If non-NULL, it is converted to centiMorgan using Haldanes map function: cM = -50*log(1-2*rho).

cM

NULL, or a non-negative number: the distance in centiMorgan between the two loci. The numeric Inf is allowed, and corresponds to unlinked loci.

Nsim

The number of simulations to be performed.

verbose

A logical.

...

Further arguments to be passed on to IBDsim.

Details

As in the case of IBD coefficients (see twoLocusIBD), we can generalise Jacquard's identity coefficients to two loci: Given any pair of individuals, and any pair of autosomal loci, we define the two-locus Jacquard coefficient \Delta[i,j] (where 1 \le i,j \le 9) by

\Delta[i,j] = Pr(Jacquard state \Sigma[i] at locus 1, and state \Sigma[j] at locus 2).

Value

A numerical 9*9 matrix. The entry in row a and column b is the estimate of \Delta[a-1, b-1] defined above.

Author(s)

Magnus Dehli Vigeland

See Also

jacquard, oneLocusIBD, twoLocusIBD, oneLocusJacquard

Examples

### Siblings whose parents are full siblings.
x = fullSibMating(generations=2)
Nsim = 100 # (increase to improve accuracy) 

# Estimate of the 9 identity coefficients
j_est = oneLocusJacquard(x, ind1=5, ind2=6, Nsim=Nsim, seed=123)

### Two-locus Jacquard coefficients
# Completely linked loci
rho = 0 
j2_linked = twoLocusJacquard(x, ind1=5, ind2=6, rho=rho, Nsim=Nsim, seed=123)
stopifnot(identical(diag(j2_linked), j_est))

# Completely unlinked
rho = 0.5
j2_unlinked = twoLocusJacquard(x, ind1=5, ind2=6, rho=rho, Nsim=Nsim, seed=123)
stopifnot(identical(j2_unlinked, outer(j_est, j_est)))