Founder Equivalents:
Founder equivalents estimates the expected number of equally contributing founders that would be required to produce the observed genetic diversity in the current population.

fe = 1 / Σ(pi2)

Where pi is the proportion of the genes of the living, descendant population contributed by founder i.

Founder Genome Equivalents:
Founder genome equivalents estimates the expected number of equally contributing founders that would be required to produce the observed genetic diversity in the current population if no alleles had been lost to drift.

fg = 1 / Σ(pi2/ri)

Where pi is the proportion of the genes of the living, descendant population contributed by founder i, and ri is the allelic retention for founder i (estimated by gene drop).

Because the retention values ri are estimated by gene drop, fg is a Monte Carlo estimate reported with a sampling standard error (shown as the +/- next to FG); that standard error shrinks roughly in proportion to one over the square root of the number of gene-drop iterations. At small iteration counts fg also carries a slight finite-sample bias that the standard error does not capture.

Lacy RC. 1989. Analysis of founder representation in pedigrees: founder equivalents and founder genome equivalents. Zoo Biol 8:111-123.

Gene Diversity (GD):
Gene diversity is the expected heterozygosity retained relative to the founding gene pool -- the fraction of the founders' allelic variation that still survives in the current population.

GD = 1 − 1 / (2 × fg)

Where fg is the founder genome equivalents above. GD is a proportion, not a count of individuals: 0 means none of the founding diversity is retained, and it approaches (but never reaches) 1 as fg grows. It is computed over the same analysis set as the founder statistics above.

Gene diversity is derived here from the founder genome equivalents above, following Lacy RC. 1989. Analysis of founder representation in pedigrees: founder equivalents and founder genome equivalents. Zoo Biol 8:111-123.

Sex-Ratio Effective Population Size (Sex-Ratio Ne):
The sex-ratio effective size is the effective population size implied by an unequal breeding sex ratio -- the diversity lost when many of one sex are bred to few of the other, as in a harem colony.

Ne = 4 × Nm × Nf / (Nm + Nf)

Where Nm and Nf are the numbers of current living breeders known to be male and female. It equals the census count when the sexes are balanced and falls toward four times the rarer sex as the ratio skews; it is 0 when either breeding sex is absent. This estimate is taken over the current living breeders -- the living animals that appear as a sire or dam -- which is a different (usually smaller) population than the analysis set summarized by the founder statistics above.

Crow JF, Kimura M. 1970. An Introduction to Population Genetics Theory. Harper and Row, New York.

Variance Effective Population Size (Variance Ne):
The variance effective size measures the diversity lost to unequal family sizes -- usually the dominant reducer of effective size in a managed colony, where a few breeders produce most of the offspring.

Ne = (N × k − 1) / (k − 1 + V / k)

Where N is the number of current living breeders (of every sex), k is their mean number of lifetime offspring, and V is the variance of those offspring counts. This is the general Crow & Kimura (1970) form; it makes no constant-size assumption and reduces to the classic (4N − 2) / (V + 2) when the mean family size is at replacement (k = 2). It is undefined -- shown as N/A -- when fewer than two living breeders are present.

Crow JF, Kimura M. 1970. An Introduction to Population Genetics Theory. Harper and Row, New York.

Both effective-size estimates idealize a Wright-Fisher population (constant size, discrete generations, random union of gametes), so read each as an index of one source of diversity loss rather than a literal head count. They are two of several ways to estimate effective size; an estimate based on the rate of increase in coancestry may be added in a future version.

Genome Uniqueness (GU):
Genome uniqueness estimates, for each animal, the proportion of gene-drop simulations in which it carries a copy of a rare founder allele (present in at most a chosen threshold number of other animals, default 1) -- animals with high genome uniqueness are more likely to carry genetic material that would otherwise be lost from the colony.

GUi = (rarei / (2 × iterations)) × 100

Where rarei is the number of simulated allele copies for animal i that are rare, summed across all gene-drop iterations, and iterations is the number of gene-drop simulations run. Because it is a Monte Carlo estimate, GU is reported with a sampling standard error (the guSE column) that shrinks roughly in proportion to one over the square root of the number of iterations.

Genome uniqueness is calculated using a gene-drop simulation according to MacCluer JW, et al. (1986) and Ballou JD, Lacy RC. (1995).

Mean Kinship (MK):
Mean kinship summarizes how related an animal is to the rest of the living colony -- animals with low mean kinship carry genetic material that is comparatively underrepresented, making them of higher value for breeding.

MKi = Σfij / N

Where fij is the pairwise kinship coefficient between animal i and every animal j (including i itself), and N is the number of animals in the kinship matrix. Ballou JD, Lacy RC. 1995. Identifying genetically important individuals for management of genetic variation in pedigreed populations, p 77-111. In: Ballou JD, Gilpin M, Foose TJ, editors. Population management for survival and recovery. New York (NY): Columbia University Press.