calcNeVariance: Calculate the variance effective population size

In nprcgenekeepr: Genetic Tools for Colony Management

Calculate the variance effective population size

Description

Part of the Genetic Value Analysis

Usage

calcNeVariance(ped)

Arguments

ped	Pedigree data.frame with id, sire, and dam; exit is used to identify living animals when present.

Details

The variance effective size measures the diversity lost to unequal family sizes – typically the dominant reducer of effective size in a harem colony, where a few breeders produce most of the offspring. It is the mean-adjusted Crow & Kimura (1970) form

N_e = \frac{N \bar{k} - 1}{\bar{k} - 1 + V_k / \bar{k}}

where N is the number of current living breeders, \bar{k} the mean number of lifetime offspring among them, and V_k the variance of those offspring counts. This general form makes no constant-size assumption and reduces to the classic (4N - 2) / (Vk + 2) at exact replacement (\bar{k} = 2); it is preferred over that bare form, which assumes \bar{k} \approx 2 and misstates the effective size when the mean family size departs from replacement.

The breeders are the current living breeders of ped (living animals that appear as a sire or dam, excluding auto-generated unknown parents), independent of which animals are selected as probands – a different population than the analysis-set founder statistics (calcFE, calcFG, calcGeneDiversity). Unlike the sex-ratio effective size (calcNeSexRatio), breeders of every sex are counted. When fewer than two living breeders are present the variance is undefined and the result is NA.

Like all effective-size estimators this idealizes a Wright-Fisher population (constant size, discrete generations, random union of gametes); a managed colony departs from those assumptions, so read the result as a family-size-variance index rather than a literal head count.

Value

The variance effective size, a single number; NA when there are fewer than two living breeders.

References

Crow, J. F. and Kimura, M. (1970) An Introduction to Population Genetics Theory. Harper and Row, New York.

See Also

calcNeSexRatio, calcGeneDiversity

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

Examples

ped <- data.frame(
  id = c("s1", "d1", "k1", "k2", "k3"),
  sire = c(NA, NA, "s1", "s1", "s1"),
  dam = c(NA, NA, "d1", "d1", "d1"),
  sex = c("M", "F", "M", "F", "F"),
  exit = c(NA, NA, NA, NA, NA),
  stringsAsFactors = FALSE
)
calcNeVariance(ped) # 2 breeders, equal families: (2*3-1)/(3-1) = 2.5

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