Calculate the demographic sex-ratio effective population size

Part of the Genetic Value Analysis

Usage

calcNeSexRatio(ped)

Arguments

ped

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

Value

The sex-ratio effective size, a single non-negative number; 0 when either breeding sex is absent among the living breeders.

Details

The sex-ratio effective size, Ne = 4 * nMale * nFemale / (nMale + nFemale), is the effective population size implied by an unequal breeding sex ratio, where nMale and nFemale are the numbers of current living breeders that are known male and known female. It quantifies the diversity lost when many of one sex are bred to few of the other (as in a harem colony): it equals the census count when the sexes are balanced and falls toward four times the rarer sex as the ratio skews.

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). Only animals with a known sex ("M" or "F") are counted; unknown and hermaphrodite breeders are excluded. When either sex is absent among the living breeders (nMale == 0 or nFemale == 0, including no living breeders at all), the result is 0: a single breeding sex contributes no diversity from sex balance.

Like all effective-size estimators this idealizes a Wright-Fisher population (constant size, discrete generations, random union of gametes within each sex); a managed colony departs from those assumptions, so read the result as a sex-ratio 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

calcGeneDiversity

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

Examples

ped <- data.frame(
  id = c("s1", "d1", "d2", "k1", "k2"),
  sire = c(NA, NA, NA, "s1", "s1"),
  dam = c(NA, NA, NA, "d1", "d2"),
  sex = c("M", "F", "F", "M", "F"),
  exit = c(NA, NA, NA, NA, NA),
  stringsAsFactors = FALSE
)
calcNeSexRatio(ped) # 4 * 1 * 2 / (1 + 2) = 2.666667
#> [1] 2.666667