qtl (version 0.85-4)

calc.genoprob: Calculate conditional genotype probabilities

Description

Uses the hidden Markov model technology to calculate the probabilities of the true underlying genotypes given the observed multipoint marker data, using a model for genotyping errors.

Usage

calc.genoprob(cross, step=0, off.end=0, error.prob=0, 
              map.function=c("haldane","kosambi","c-f"))

Arguments

cross

An object of class cross. See read.cross for details.

step

Maximum number of cM between positions at which the genotype probabilities are calculated, though for step = 0, calculate probabilites only at the marker locations.

off.end

Distance (in cM) at which to carry the genotype probability calculations past the p and q terminal markers on each chromosome.

error.prob

Assumed genotyping error rate used in the calculation of the penetrance Pr(observed genotype | true genotype).

map.function

Indicates whether to use the Haldane, Kosambi or Carter-Falconer map function when converting genetic distances into recombination fractions.

Value

• The cross object in the input is returned with the genotype probabilities added. Recall that the cross$geno component is a list whose elements correspond to chromosomes and which are themselves lists with components data and map. For each chromosomes, an additional component, prob, is added. This is an array of size [n.ind x n.pos x n.gen] where n.pos is the number of positions at which the probabilities were calculated and n.gen = 3 for an intercross, = 2 for a backcross, and = 4 for a 4-way cross.

Details

Calculations are done within the C function calc_genoprob.

Let $O_i$ denote the observed marker genotype at position $i$, and $g_i$ denote the corresponding true underlying genotype.

We use the forward-backward equations to calculate $alpha_{iv} = \log Pr(O_1, \ldots, O_i, g_i = v)$ and $beta_{iv} = \log Pr(O_{i+1}, \ldots, O_n | g_i = v)$

We then obtain $Pr(g_i | O_1, \ldots, O_n) = \exp(alpha_{iv} + beta_{iv}) / s$ where $s = \sum_v \exp(alpha_{iv} + beta_{iv})$

In the case of the 4-way cross, with a sex-specific map, we assume a constant ratio of female:male recombination rates within the inter-marker intervals.

Attributes "error.prob", "step", and "off.end" are set to the values of the corresponding arguments, for later reference (especially by the function cacl.errorlod).

References

K Lange (1999) Numerical analysis for statisticians Springer-Verlag, New York. Sec 23.3.

LR Rabiner (1989) A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE 77:257-286.

See Also

sim.geno, argmax.geno, calc.errorlod

Examples

data(fake.f2)
fake.f2 <- calc.genoprob(fake.f2,step=2,off.end=5)
<testonly>data(fake.bc)</testonly>
<testonly>fake.bc <- calc.genoprob(fake.bc,step=0,off.end=0)</testonly>