Calculates the probability of 0, 1, 2, or >2 crossovers for a chromosome of a given length, for the gamma model.
xoprob(
nu,
L = 103,
max.conv = 25,
integr.tol = 0.00000001,
max.subd = 1000,
min.subd = 10
)A vector of length 4, giving the probabilities of 0, 1, 2, or >2
crossovers, respectively, on a chromosome of length L cM.
The interference parameter in the gamma model.
Length of the chromosome (in cM).
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.
Tolerance for convergence of numerical integration.
Maximum number of subdivisions in numerical integration.
Minimum number of subdivisions in numerical integration.
Karl W Broman, broman@wisc.edu
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.
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.
location.given.one(), first.given.two(),
distance.given.two(), joint.given.two(),
ioden(), firstden(), gammacoi()
xoprob(1, L=103)
xoprob(4.3, L=103)
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