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.
trans_polygenic(n_loci, annotate = FALSE)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).
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.
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.
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.
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.
trans_polygenic(4, annotate = TRUE)
apply(trans_polygenic(4), 1, sum)
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