qtl (version 0.85-4)

argmax.geno: Reconstruct underlying genotypes

Description

Uses the Viterbi algorithm to identify the most likely sequence of underlying genotypes, given the observed multipoint marker data, using a model for genotyping errors.

Usage

argmax.geno(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 genotypes are to be reconstructed, though for step = 0, genotypes are reconstructed only at the marker locations.

off.end

Distance (in cM) at which to carry the genotype reconstructions 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 reconstructed genotypes 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, argmax, is added. This is a matrix of size [n.ind x n.pos], where n.pos is the number of positions at which the reconstructed genotypes were desired, containing the most likely sequences of underlying genotypes.

Details

We use the Viterbi algorithm to calculate $\arg \max_v \Pr(g = v | O)$ where $g$ is the underlying sequence of genotypes and $O$ is the observed marker genotypes.

This done by calculating $\gamma_k(v_k) = \max_{v_1, \ldots, v_{k-1}} \Pr(g_1 = v_1, \ldots, g_k = v_k, O_1, \ldots, O_k)$ for $k = 1, \ldots, n$ and then tracing back through the sequence.

Calculations are done within the C function argmax_geno.

Attributes "error.prob", "step", and "off.end" are set to the values of the corresponding arguments, for later reference.

Note: the results of argmax.geno() depend greatly on the choice of the value of the argument step. This is a sad truth of the result of the Viterbi algoriothm. Further note that if several sequences are all most likely, our method of choosing a random such is flawed.

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, calc.genoprob

Examples

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