stahlcoi {xoi}

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)

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.

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.

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.

Author(s)

Karl W Broman, [e-mail]

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)