geno_freq_polygenic: Genotype frequencies for the hypergeometric polygenic model

In clipp: Calculating Likelihoods by Pedigree Paring

Genotype frequencies for the hypergeometric polygenic model

Description

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

Usage

geno_freq_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 vector suitable to be used as the geno_freq argument of pedigree_loglikelihood. When TRUE, the function adds a names attribute to this vector to indicate which element corresponds to which genotype.

Details

The hypergeometric polygenic model (Cannings et al., 1978; Lange, 2002) is a computationally feasible genetic model that approximates the combined effect of a given number (n_loci) of unlinked biallelic genetic loci. This model is often used to model the effect of such loci on a trait when the alleles at these loci either increase the trait by a certain, locus-independent amount (if a 'positive' allele) or decrease the trait by the same amount (if a 'negative' allele), with 'positive' and 'negative' alleles equally likely at each locus. In this case, the only relevant aspect of the 3 ^ n_loci possible joint genotypes is the total number of 'positive' alleles, so the possible genotypes of the hypergeometric polygenic model are taken to be 0:(2*n_loci). The transmission probabilities and genotype frequencies of the hypergeometric polygenic model approximate these quantities for the combination of the n_loci biallelic genetic loci described above. Under this model, the polygenic genotype for each person is approximately normally distributed, and these genotypes are correlated within families with correlation coefficients (in non-inbred families) equal to the kinship coefficients (Lange, 2002).

Setting annotate to TRUE names each element of the output vector with the corresponding genotype. The annotate option must be set to FALSE if the output of this function is to be used as the geno_freq argument of pedigree_loglikelihood.

Value

A vector of strictly positive numbers (the genotype frequencies) that sum to 1, named with the genotype names 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

geno_freq_polygenic(4, annotate = TRUE)
sum(geno_freq_polygenic(4))

clipp documentation built on July 12, 2022, 9:05 a.m.