nprcgenekeepr (version 2.0.0)

calcNeVariance: Calculate the variance effective population size

Description

Part of the Genetic Value Analysis

Usage

calcNeVariance(ped)

Value

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

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.

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