twohk function

One and Two Gene Models Using Linearized Posterior

Fits all one and two gene models (without interactions aka 'epistasis') in an intercross, backcross, or recombinant inbred line. Uses a linear approximation to the likelihood, i.e. the expected allele states are used.

twohk(varcov, ana.obj, ...)

Arguments

• varcov: An object produced by make.varcov

• ana.obj: An analysis.object --- see make.analysis.obj

• ...: Additional arguments override the default choices of candidate loci (locs), prior for locus (locs.prior), or method specified by ana.obj: locs A vector indexing the loci to use. locs.prior

  The prior mass to associate with each locus. Typically, these sum to one, but sometimes they might each be set to one (as in computing lod scores). combo.prior Only valid for ana.obj$method=="F2". The prior probability for each term or combination of terms for the phenotypic effect at a locus. Typically, there will be three of these - one for the 'additive' term (linear in number of alleles from one parent strain), the 'dominance' term (quadratic in allele number), or both terms. The default sets them all to 1/3.

Details

The marginal posterior (integrating over regression parameters and dispersion) is calculated for each one and two gene model under the assumed correctness of the regression model using expected genotypes given marker values. This amounts to linearizing the likelihood with respect to the (possibly unknown) locus states. For models where the loci are fully informative markers this is the true posterior.

Returns

A list with components: - loc.1: The marginal posterior for each one gene model relative to a no gene model. For twohkf2 this is a matrix of 3 columns; the first for models with additive terms, the second for dominance terms, and the third for both. The sum over all three columns yields the marginal posterior for the locus.

• loc.2: The marginal posterior for each locus --- obtained by summing over all two gene models that include that locus--- relative to a no gene model. For twohkf2 this is a matrix of 3 columns; the first for models with additive terms, the second for dominance terms, and the third for both.

• coefs.1: The regression coefficients for the genetic effect for each locus. For twohkf2, this is a matrix with two rows; the first is for the 'additive effect' and the second is for the 'dominance' effect.

• coefs.2: The marginal posterior mean of regression coefficients for the genetic effect for each locus - obtained by averaging over all two gene models that include that locus according to the posterior masses. For twohkf2, this is a matrix with two rows; the first is for the 'additive effect' and the second is for the 'dominance' effect.

References

Haley C.S. and Knott S.A. (1992) A simple regression method for mapping quantitative trait loci in line crosses using flanking markers. Heredity 69 ,315-324.

Author(s)

Charles C. Berry cberry@ucsd.edu

Examples

data(little.ana.bc)
little.vc<-make.varcov(little.ana.bc$data[,little.ana.bc$reg.names],
  little.ana.bc$data$bc.phenotype)
little.2<- twohk(little.vc,little.ana.bc,rparm=1)
print( c(odds.1=sum(little.2$loc.1),odds.2=sum(little.2$loc.2)) )
par(mfrow=c(3,2))
little.pe <- 2 * little.2$loc.2 / sum(little.2$loc.2)   #locus-wise posterior expectation
plot(little.ana.bc,little.pe,type="h",ylab="E(genes")
rm(little.2,little.vc,little.pe,little.ana.bc)