ioden: Distance between crossovers

Description

Calculates the density of the distance from a given crossover to the next crossover, for the gamma model.

Usage

ioden(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 density was calculated and f is the density.

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.

Author

Karl W Broman, broman@wisc.edu

Details

Let $f (x; ν)$ denote the density of a gamma random variable with parameters shape= $ν$ and rate= $2 ν$ , and let $f_{k} (x; ν)$ denote the density of a gamma random variable with parameters shape= $k ν$ and rate= $2 ν$ .

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

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.

Examples

Run this code


f1 <- ioden(1, L=200, n=201)
plot(f1, type="l", lwd=2, las=1,
     ylim=c(0,0.014), yaxs="i", xaxs="i", xlim=c(0,200))

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

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

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

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