trans_polygenic {clipp}

The transmission matrix for the hypergeometric polygenic model

Description

A function to calculate the transmission matrix for the hypergeometric polygenic model of (Cannings et al., 1978), see also Section 8.9 of (Lange, 2002) for a nice description of this model.

Usage

trans_polygenic(n_loci, annotate = FALSE)

Arguments

n_loci

A positive integer, interpreted as the number of biallelic genetic loci that contribute to the polygene. The polygene will have 2*n_loci + 1 genotypes, so n_loci is typically fairly small, e.g. 4.

annotate

A logical flag. When FALSE (the default), the function returns a matrix suitable to be used as the trans argument of pedigree_loglikelihood. When TRUE, the function annotates this matrix (and converts it to a data frame) to make the output more easily understood by humans.

Details

This function calculates the genetic transmission probabilities (i.e. the conditional probability of a person's genotype, given his or her biological parents' genotypes) for the hypergeometric polygenic model, which is described in geno_freq_polygenic.

When annotate is FALSE, a matrix of transmission probabilities is returned, with rows corresponding to the possible joint parental genotypes and columns corresponding to the possible offspring genotypes. Setting annotate to TRUE shows which rows and columns correspond to which genotypes, by adding offspring genotypes as column names and adding columns gm and gf containing (respectively) the mother's and father's genotypes. Note that if the output of this function is to be used as the trans argument of pedigree_loglikelihood then the annotate option must be set to FALSE.

Value

Either a matrix of genetic transmission probabilities suitable to be used as the trans argument of pedigree_loglikelihood (if annotate is FALSE), or a data frame that is an annotated version of this matrix (if annotate is TRUE).

References

Cannings C, Thompson E, Skolnick M. Probability functions on complex pedigrees. Advances in Applied Probability, 1978;10(1):26-61.

Lange K. Mathematical and Statistical Methods for Genetic Analysis (second edition). Springer, New York. 2002.

Examples

trans_polygenic(4, annotate = TRUE)
apply(trans_polygenic(4), 1, sum)