xoprob: Distribution of number of crossovers
In kbroman/xoi: Tools for Analyzing Crossover Interference

xoprob

R Documentation

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.