Table 2 Formulas used to calculate marker generated kinship matrices
From: PyAGH: a python package to fast construct kinship matrices based on different levels of omic data
Type of effect | Original kinship matrix | Kinship matrix |
|---|---|---|
Dominance(d) | \({K}_{d}^{*}=\sum_{k=1}^{m}{W}_{k}{W}_{k}^{T}\) | \({K}_{d}=(\frac{1}{mean[diag\left({K}_{d}^{*}\right)]}) {K}_{d}^{*}\) |
Additive × additive (aa) | \({K}_{aa}^{*}=\sum_{k=1}^{m-1}\sum_{{k}^{^{\prime}}=k+1}^{m}({Z}_{k}\#{Z}_{{k}^{^{\prime}}}){({Z}_{k}\#{Z}_{{k}^{^{\prime}}})}^{T}\) | \({K}_{aa}=(\frac{1}{mean[diag\left({K}_{aa}^{*}\right)]}) {K}_{aa}^{*}\) |
Dominance × dominance (dd) | \({K}_{dd}^{*}=\sum_{k=1}^{m-1}\sum_{{k}^{^{\prime}}=k+1}^{m}({W}_{k}\#{W}_{{k}^{^{\prime}}}){({W}_{k}\#{W}_{{k}^{^{\prime}}})}^{T}\) | \({K}_{dd}=(\frac{1}{mean[diag\left({K}_{dd}^{*}\right)]}) {K}_{dd}^{*}\) |
Additive × dominance (ad) | \({K}_{ad}^{*}=\sum_{k=1}^{m-1}\sum_{{k}^{^{\prime}}=k+1}^{m}({Z}_{k}\#{W}_{{k}^{^{\prime}}}){({Z}_{k}\#{W}_{{k}^{^{\prime}}})}^{T}\) | \({K}_{ad}=(\frac{1}{mean[diag\left({K}_{ad}^{*}\right)]}) {K}_{ad}^{*}\) |
Dominance × additive (da) | \({K}_{dd}^{*}=\sum_{k=1}^{m-1}\sum_{{k}^{^{\prime}}=k+1}^{m}({W}_{k}\#{Z}_{{k}^{^{\prime}}}){({W}_{k}\#{Z}_{{k}^{^{\prime}}})}^{T}\) | \({K}_{da}=(\frac{1}{mean[diag\left({K}_{da}^{*}\right)]}) {K}_{da}^{*}\) |