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Calculate the standard error of founder genome equivalents

Source: R/calcFGSE.R
calcFGSE.Rd

Part of the Genetic Value Analysis

Usage

calcFGSE(ped, alleles)

Arguments

ped

the pedigree information in datatable format. Pedigree (req. fields: id, sire, dam, gen, population). The pedigree must have no partial parentage (every animal has both parents known or both unknown); calcFGSE stops with an error otherwise.

alleles

dataframe containing an AlleleTable: an id column, a parent column, and one column per gene-drop iteration. Produced by geneDrop(); the same input calcFG takes.

Value

A single numeric value: the Monte Carlo sampling standard error of the colony founder-genome-equivalent estimate, on the same scale as calcFG. NA (with a warning) when a contributing founder has zero retention.

Details

Founder genome equivalents (calcFG) is a Monte Carlo estimate: FG = 1 / sum(p^2 / r), where the founder contributions p are deterministic but the mean allelic retention values r (calcRetention) are averages over the gene-drop iterations, so FG carries sampling error that shrinks as the number of iterations grows. Unlike genome uniqueness (a mean, whose standard error is a column variance), FG is a nonlinear function of r, so its standard error is obtained by the delta method (first-order linearization).

With S = sum(p_f^2 / r_f) and FG = 1 / S, the gradient is dFG/dr_f = FG^2 * p_f^2 / r_f^2. Writing R for the founder-by- iteration retention matrix (each column an independent gene drop), the influence series y_k = sum_f (dFG/dr_f) * R[f, k] has sd(y) / sqrt(K) equal to the full delta-method standard error, including the within-iteration covariance among founders. This influence form is used because it folds in that covariance automatically and never forms the founder-by-founder covariance matrix.

Founders are matched between p and r by name (not position), so the result is correct even when the founders are not in sorted pedigree order.

A contributing founder (p > 0) that is retained in zero of the iterations (r == 0) makes FG undefined (the same degeneracy that calcFG now reports as NA); in that case this function returns NA with a warning advising more iterations. Founders that do not contribute to the current population (p == 0) are dropped, so the standard error refers to exactly the founder set FG is computed from.

See also

calcFG, calcFEFG, calcRetention, calcGUSE, reportGV

Examples

library(nprcgenekeepr)
data("lacy1989Ped")
data("lacy1989PedAlleles")
calcFGSE(lacy1989Ped, lacy1989PedAlleles)
#> [1] 0.006213056