xoi (version 0.72)

gammacoi: Coincidence function for the gamma model

Description

Calculates the coincidence function for the gamma model.

Usage

gammacoi(nu, 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.

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

Let \(f(x;\nu)\) denote the density of a gamma random variable with parameters shape=\(\nu\) and rate=\(2\nu\), and let \(f_k(x;\nu)\) denote the density of a gamma random variable with parameters shape=\(k \nu\) and rate=\(2\nu\).

The coincidence function for the gamma model is \(C(x;\nu) = \sum_{k=1}^{\infty} f_k(x;\nu)/2\).

References

Broman, K. W. and Weber, J. L. (2000) Characterization of human crossover interference. Am. J. Hum. Genet. 66, 1911--1926.

Broman, K. W., Rowe, L. B., Churchill, G. A. and Paigen, K. (2002) Crossover interference in the mouse. Genetics 160, 1123--1131.

McPeek, M. S. and Speed, T. P. (1995) Modeling interference in genetic recombination. Genetics 139, 1031--1044.

See Also

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

Examples

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

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

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

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