On coding genotypes for genetic markers with multiple alleles in genetic association study of quantitative traits

Wang, Tao

doi:10.1186/1471-2156-12-82

BMC Genomic Data

Table 6 Parameterization of two-locus models under model framework (16).

From: On coding genotypes for genetic markers with multiple alleles in genetic association study of quantitative traits

Codings	Relationships
Allele	$\begin{gathered} μ = G_{m_{1} m_{1} m_{2} m_{2}} \\ α_{1 j} = G_{j m_{1} m_{2} m_{2}} - G_{m_{1} m_{1} m_{2} m_{2}}, j = 1, \dots, m_{1} - 1 \\ α_{2 r} = G_{m_{1} m_{1} r m_{2}} - G_{m_{1} m_{1} m_{2} m_{2}}, r = 1, \dots, m_{2} - 1 \\ δ_{1 j k} = G_{j k m_{2} m_{2}} - G_{j m_{1} m_{2} m_{2}} - G_{k m_{1} m_{2} m_{2}} + G_{m_{1} m_{1} m_{2} m_{2}}, j, k = 1, \dots, m_{1} - 1; j \leq k \\ δ_{2 r s} = G_{m_{1} m_{1} r s} - G_{m_{1} m_{1} r m_{2}} - G_{m_{1} m_{1} s m_{2}} + G_{m_{1} m_{1} m_{2} m_{2}}, r, s = 1, \dots, m_{2} - 1; r \leq s \end{gathered}$
F_∞	$\begin{gathered} τ = G_{m_{1} m_{1} m_{2} m_{2}} + \frac{1}{2} \sum_{j = 1}^{m_{1} - 1} (G_{j j m_{2} m_{2}} - G_{m_{1} m_{1} m_{2} m_{2}}) + \frac{1}{2} \sum_{r = 1}^{m_{2} - 1} (G_{m_{1} m_{1} r r} - G_{m_{1} m_{1} m_{2} m_{2}}) \\ a_{1 j} = \frac{G_{j j m_{2} m_{2}} - G_{m_{1} m_{1} m_{2} m_{2}}}{2}, j = 1, \dots, m_{1} - 1 \\ a_{2 r} = \frac{G_{m_{1} m_{1} r r} - G_{m_{1} m_{1} m_{2} m_{2}}}{2}, r = 1, \dots, m_{2} - 1 \\ d_{1 j j} = G_{j m_{1} m_{2} m_{2}} - \frac{G_{j j m_{2} m_{2}} + G_{m_{1} m_{1} m_{2} m_{2}}}{2}, j = 1, \dots, m_{1} - 1 \\ d_{1 j k} = G_{j k m_{2} m_{2}} - G_{j m_{1} m_{2} m_{2}} - G_{k m_{1} m_{2} m_{2}} + G_{m_{1} m_{1} m_{2} m_{2}}, j, k = 1, \dots, m_{1} - 1; j < k \\ d_{2 r r} = G_{m_{1} m_{1} r m_{2}} - \frac{G_{m_{1} m_{1} r r} + G_{m_{1} m_{1} m_{2} m_{2}}}{2}, r = 1, \dots, m_{2} - 1 \\ d_{2 r s} = G_{m_{1} m_{1} r s} - G_{m_{1} m_{1} r m_{2}} - G_{m_{1} m_{1} s m_{2}} + G_{m_{1} m_{1} m_{2} m_{2}}, r, s = 1, \dots, m_{2} - 1; r < s \end{gathered}$
Allele-count	$\begin{gathered} π_{0} = G_{m_{1} m_{1} m_{2} m_{2}} \\ π_{1 j} = G_{j m_{1} m_{2} m_{2}} - G_{m_{1} m_{1} m_{2} m_{2}}, j = 1, \dots, m_{1} - 1 \\ π_{2 r} = G_{m_{1} m_{1} r m_{2}} - G_{m_{1} m_{1} m_{2} m_{2}}, r = 1, \dots, m_{2} - 1 \\ η_{1 j j} = G_{j j m_{2} m_{2}} - G_{m_{1} m_{1} m_{2} m_{2}}, j = 1, \dots, m_{1} - 1 \\ η_{1 j k} = G_{j k m_{2} m_{2}} - G_{j m_{1} m_{2} m_{2}} - G_{k m_{1} m_{2} m_{2}} + G_{m_{1} m_{1} m_{2} m_{2}}, j, k = 1, \dots, m_{1} - 1; j < k \\ η_{2 r r} = G_{m_{1} m_{1} r r} - G_{m_{1} m_{1} m_{2} m_{2}}, r = 1, \dots, m_{2} - 1 \\ η_{2 r s} = G_{m_{1} m_{1} r s} - G_{m_{1} m_{1} r m_{2}} - G_{m_{1} m_{1} s m_{2}} + G_{m_{1} m_{1} m_{2} m_{2}}, r, s = 1, \dots, m_{2} - 1; r < s \end{gathered}$

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