xoprob {xoi}

Distribution of number of crossovers

Description

Calculates the probability of 0, 1, 2, or >2 crossovers for a chromosome of a given length, for the gamma model.

Usage

xoprob(
  nu,
  L = 103,
  max.conv = 25,
  integr.tol = 0.00000001,
  max.subd = 1000,
  min.subd = 10
)

Arguments

nu

The interference parameter in the gamma model.

L

Length of the chromosome (in cM).

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.

integr.tol

Tolerance for convergence of numerical integration.

max.subd

Maximum number of subdivisions in numerical integration.

min.subd

Minimum number of subdivisions in numerical integration.

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 the start of the chromosome to the first crossover is g^*(x;\nu) = 1 - F^*(x;\nu) where F^* is the cdf of f^*.

We calculate the desired probabilities by numerical integration.

Value

A vector of length 4, giving the probabilities of 0, 1, 2, or >2 crossovers, respectively, on a chromosome of length L cM.

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(), firstden(), gammacoi()

Examples

xoprob(1, L=103)
xoprob(4.3, L=103)