. 2017 May 26;206(4):2085–2103. doi: 10.1534/genetics.116.198424

Table 2. Allele-pair matching proportions.

Matching of two distinct alleles within individual j in population i

{\tilde{M}}_{j}^{i} = (1 / 2) \sum_{u} X_{j u}^{i} (X_{j u}^{i} - 1), ℰ ({\tilde{M}}_{j}^{i}) = M + (1 - M) F_{j}^{i}

Average within-individual matching in population i

{\tilde{M}}_{I}^{i} = (1 / n_{i}) \sum_{j = 1}^{n_{i}} {\tilde{M}}_{j}^{i}, ℰ ({\tilde{M}}_{I}^{i}) = M + (1 - M) F_{I}^{i}

Average over populations of within-individual matching

{\tilde{M}}^{I} = (1 / r) \sum_{i = 1}^{r} {\tilde{M}}_{I}^{i}, ℰ ({\tilde{M}}^{I}) = M + (1 - M) F^{I}

Matching of one allele from each of individuals

j, j^{'}

in population i

{\tilde{M}}_{j j^{'}}^{i} = (1 / 4) \sum_{u} X_{j u}^{i} X_{j^{'} u}^{i}, ℰ ({\tilde{M}}_{j j^{'}}^{i}) = M + (1 - M) θ_{j j^{'}}^{i}

Average between-individual matching in population i

{\tilde{M}}_{S}^{i} = 1 / [n_{i} (n_{i} - 1)] \sum_{j = 1}^{n_{i}} \sum_{j^{'} = 1, j^{'} \neq j}^{n_{i}} {\tilde{M}}_{j j^{'}}^{i}, ℰ ({\tilde{M}}_{S}^{i}) = M + (1 - M) θ_{S}^{i}

Average over populations of between-individual within-population matching

{\tilde{M}}^{S} = (1 / r) \sum_{i = 1}^{r} {\tilde{M}}_{S}^{i}, ℰ ({\tilde{M}}^{S}) = M + (1 - M) θ^{S}

Matching of two distinct alleles, ignoring genotypes, within population i

{\tilde{M}}_{W}^{i} = [2 n_{i} / (2 n_{i} - 1)] \sum_{u} {\tilde{p}}_{i u}^{2} - [1 / (2 n_{i} - 1)], ℰ ({\tilde{M}}_{W}^{i}) = M + (1 - M) θ_{W}^{i}

Average over populations of within-population allele matching, ignoring genotypes

{\tilde{M}}^{W} = (1 / r) \sum_{i = 1}^{1} {\tilde{M}}_{W}^{i}, ℰ ({\tilde{M}}^{W}) = M + (1 - M) θ^{W}

Matching of an allele from individual j in population i with an allele from individual

j^{'}

in population

i^{'} .

{\tilde{M}}_{j j^{'}}^{i i^{'}} = (1 / 4) \sum_{u} X_{j u}^{i} X_{j^{'} u}^{i^{'}}, ℰ ({\tilde{M}}_{j j^{'}}^{i i^{'}}) = M + (1 - M) θ_{j j^{'}}^{i i^{'}}

Matching of one allele from each of populations

i, i^{'}

{\tilde{M}}_{B}^{i i^{'}} = [1 / (n_{i} n_{j^{'}})] \sum_{j = 1}^{n_{i}} \sum_{j^{'} = 1}^{n_{i^{'}}} {\tilde{M}}_{j j^{'}}^{i i^{'}} = \sum_{u} {\tilde{p}}_{i u} {\tilde{p}}_{i^{'} u}, ℰ ({\tilde{M}}_{B}^{i i^{'}}) = M + (1 - M) θ_{B}^{i i^{'}}

Average over pairs of populations of between-population-pair matching

{\tilde{M}}^{B} = {1 / [r (r - 1)]} \sum_{i = 1}^{r} \sum_{i^{'} = 1, i^{'} \neq i}^{r} {\tilde{M}}_{B}^{i i'}, ℰ ({\tilde{M}}^{B}) = M + (1 - M) θ^{B}