firstden: Distance to a crossover

In kbroman/xoi: Tools for Analyzing Crossover Interference

Distance to a crossover

Description

Calculates the density of the distance from an arbitrary point to the next crossover, for the gamma model.

Usage

firstden(nu, L = 103, x = NULL, n = 400, max.conv = 25)

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 convolutions to get inter-crossover distance distribution from the inter-chiasma distance distributions. This should be greater than the maximum number of chiasmata on the 4-strand bundle.

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 distribution of the distance from one crossover to the next is f^*(x;\nu) = \sum_{k=1}^{\infty} f_k(x;\nu)/2^k.

The distribution of the distance from an arbitrary point to the first crossover is g^*(x;\nu) = 1 - F^*(x;\nu) where F^* is the cdf of f^*.

Value

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

Author(s)

Karl W Broman, [e-mail]

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

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

Examples

f1 <- firstden(1, L=200, n=201)
plot(f1, type="l", lwd=2, las=1,
     ylim=c(0,0.012), yaxs="i", xaxs="i", xlim=c(0,200))

f2 <- firstden(2.6, L=200, n=201)
lines(f2, col="blue", lwd=2)

f3 <- firstden(4.3, L=200, n=201)
lines(f3, col="red", lwd=2)

f4 <- firstden(7.6, L=200, n=201)
lines(f4, col="green", lwd=2)

kbroman/xoi documentation built on May 1, 2023, 9:35 p.m.