Coincidence function for the gamma model

Share:

Description

Calculates the coincidence function for the gamma model.

Usage

1
gammacoi(nu, L = 103, x, 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 convolution. 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 coincidence function for the gamma model is C(x;nu) = sum_(k=1 to infty) f_k(x;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, kbroman@biostat.wisc.edu

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

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
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)