Table 2 Formulas of genealogical measures in GENLIB
From: GENLIB: an R package for the analysis of genealogical data
Completeness | \( {C}_g = \frac{A_g}{2^g} \) | A g : number of known ancestors at generation g F g : number of founders at generation g T g : number of expected ancestors at generation g (=2 g) N f : generation of founder f (summation over all generations g or over all founders f) |
Implex index | \( {I}_g = \frac{Distinct\ {A}_g}{2^g} \) | |
Mean genealogical depth | \( D={\displaystyle \sum_gg\frac{F_g}{T_g}={\displaystyle \sum_f{N}_f}\frac{1}{2^{N_f}}} \) | |
Variance of mean genealogical depth | \( {\displaystyle \sum_g}g2\frac{F_g}{T_g}-D2 \) | |
Kinship | \( {\varphi}_{ij} = {\displaystyle \sum_a}\left(1+{f}_a\right){\frac{1}{2}}^{g_{ai}+{g}_{aj}+1} \) | g ai (g aj ) : number of generations between subject i (j) and ancestor a, common to i and j (summation over all ancestors a) |
Inbreeding | f i = φ kl | k, l : the parents of i |
Genetic Contribution | \( GC\left(s,a\right)={\displaystyle \sum_p}{\left(\frac{1}{2}\right)}^{g_p} \) | g p : number of generations between subject s and ancestor a through path p (summation over all possible paths p) |