calcFGSE: Calculate the standard error of founder genome equivalents

In nprcgenekeepr: Genetic Tools for Colony Management

Calculate the standard error of founder genome equivalents

Description

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

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.

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.

See Also

calcFG, calcFEFG, calcRetention, calcGUSE, reportGV

Other genetic value analysis: calcA(), calcFE(), calcFEFG(), calcFG(), calcGU(), calcGUSE(), calcGeneDiversity(), calcNeSexRatio(), calcNeVariance(), calcRetention()

Examples

library(nprcgenekeepr)
data("lacy1989Ped")
data("lacy1989PedAlleles")
calcFGSE(lacy1989Ped, lacy1989PedAlleles)

nprcgenekeepr documentation built on July 26, 2026, 5:06 p.m.