xoi (version 0.72)

stahlcoi: Coincidence function for the Stahl model

Description

Calculates the coincidence function for the Stahl model.

Usage

stahlcoi(nu, p = 0, L = 103, x = NULL, n = 400, max.conv = 25)

Value

A data frame with two columns: x is the distance (between 0 and L, in cM) at which the coicidence was calculated and coincidence.

Arguments

nu

The interference parameter in the gamma model.

p

The proportion of chiasmata coming from the no-interference mechanism.

L

Maximal distance (in cM) at which to calculate the density. Ignored if x is specified.

x

If specified, points at which to calculate the density.

n

Number of points at which to calculate the density. The points will be evenly distributed between 0 and L. Ignored if x is specified.

max.conv

Maximum limit for summation in the convolution. This should be greater than the maximum number of chiasmata on the 4-strand bundle.

Author

Karl W Broman,

Details

The Stahl model is an extension to the gamma model, in which chiasmata occur according to two independent mechanisms. A proportion \(p\) come from a mechanism exhibiting no interference, and a proportion 1-\(p\) come from a mechanism in which chiasma locations follow a gamma model with interference parameter \(\nu\).

Let \(f(x;\nu,\lambda)\) denote the density of a gamma random variable with parameters shape=\(\nu\) and rate=\(\lambda\).

The coincidence function for the Stahl model is \(C(x;\nu,p) = [p + \sum_{k=1}^{\infty} f(x;k\nu, \)\( 2(1-p)\nu)]/2\).

References

Copenhaver, G. P., Housworth, E. A. and Stahl, F. W. (2002) Crossover interference in Arabidopsis. Genetics 160, 1631--1639.

Housworth, E. A. and Stahl, F. W. (2003) Crossover interference in humans. Am J Hum Genet 73, 188--197.

See Also

gammacoi(), location.given.one(), first.given.two(), distance.given.two(), ioden(), firstden(), xoprob()

Examples

f1 <- stahlcoi(1, p=0, L=200)
plot(f1, type="l", lwd=2, las=1,
     ylim=c(0,1.25), yaxs="i", xaxs="i", xlim=c(0,200))

f2 <- stahlcoi(2.6, p=0, L=200)
lines(f2, col="blue", lwd=2)

f2s <- stahlcoi(2.6, p=0.1, L=200)
lines(f2s, col="blue", lwd=2, lty=2)

f3 <- stahlcoi(4.3, p=0, L=200)
lines(f3, col="red", lwd=2)

f3s <- stahlcoi(4.3, p=0.1, L=200)
lines(f3s, col="red", lwd=2, lty=2)

f4 <- stahlcoi(7.6, p=0, L=200)
lines(f4, col="green", lwd=2)

f4s <- stahlcoi(7.6, p=0.1, L=200)
lines(f4s, col="green", lwd=2, lty=2)