Special {sped}

Special Multigene Descent Probabilities

Description

Calculate particular multigene descent probabilities of particular interest.

Usage

alphas(individuals, pedigree)
betas(individuals, pedigree)
gammas(individuals, pedigree)
inbreeding(individuals, pedigree)

Arguments

individuals

an atomic vector of names of individuals. Must be of type integer or character.

pedigree

a matrix with three columns. Each row contains the name of an individual and its father and mother, in that order. Must be the same type as the preceding argument.

Details

We work relative to the pedigree defined by argument pedigree in which every individual has either two parents or none specified. Those with none specified are called founders. Any ancestors of founders are assumed to not be individuals in the pedigree, that is, we are assuming all unknown individuals are different from all known individuals.

Value

A matrix whose rows are probabilities relating to particular founders and whose columns are probabilities relating to particular individuals. The row and column labels say which founders and which individuals.

R function gammas gives the probability that a gene chosen at random from the individual comes from either gene of the founder.

R function betas gives the probability that both genes from the individual comes from the genes (not necessarily the same gene) of the founder.

R function alphas gives inbreeding of the individual relative to the founder: the probability that both genes from the individual comes from the same gene (either gene) of the founder.

R function inbreeding gives inbreeding coefficients of the individuals.

R function kinship returns a matrix whose entries are the kinship coefficients of the individuals.

References

Geyer, C.~J. (1988) Software for calculating gene survival and multigene descent probabilities and for pedigree manipulation and drawing. Technical Report No. 153, Department of Statistics, University of Washington. https://stat.uw.edu/sites/default/files/files/reports/1988/tr153.pdf.

Thompson, E. A. (1983) Gene extinction and allelic origins in complex genealogies (with discussion). Proceedings of the Royal Society of London. Series B, Biological Sciences, 219, 241–251. doi:10.1098/rspb.1983.0072.

Thompson, E. A. (1986) Ancestry of alleles and extinction of genes in populations with defined pedigrees. Zoo Biology, 5, 161–170. doi:10.1002/zoo.1430050210.

See Also

descent

Examples

# In alberta pedigree, probability that one gene picked at random
# from individual 1260 is descended from one gene in founder 52.
library(sped)

data(alberta)
gammas(c(1260, 1272), alberta)

data(thompson)
betas(c("U", "V", "Q", "R", "W"), thompson)
alphas(c("U", "V", "Q", "R", "W"), thompson)
inbreeding(c("U", "V", "Q", "R", "W"), thompson)
kinship(c("U", "V", "Q", "R", "W"), thompson)