Calculates the coincidence function for the Stahl model.
Usage
stahlcoi(nu, p = 0, L = 103, x, n = 400, max.conv = 25)
Arguments
nu
The interference parameter in the gamma model.
p
The proportion of chiasmata coming from the no-interference
mechanism.
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
The Stahl model is an extension to the gamma model, in which chiasmata occur
according to two independent mechanisms. A proportion p come from a
mechanism exhibiting no interference, and a proportion 1-p come from a
mechanism in which chiasma locations follow a gamma model with interference
parameter nu.
Let f(x;nu,lambda) denote the density of a gamma
random variable with parameters shape=nu and
rate=lambda.
The coincidence function for the Stahl model is C(x;nu,p) = [p + sum_(k=1 to infty)
f(x;k*nu,2*(1-p)nu)]/2C(x;nu,p) = [p + sum_(k=1 to
infty) f(x;k*nu,2*(1-p)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.