Part of the Genetic Value Analysis
Value
The variance effective size, a single number; NA when there
are fewer than two living breeders.
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()