| geno_freq_polygenic {clipp} | R Documentation |
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
|
annotate |
A logical flag. When |
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))