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Table 7 Parameterization of two-locus models under model framework (17) when m1, m2 ≥ 3.

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

Codings

Restrictions

Relationships

Allele

α 1 m 1 * = α 2 m 2 * =0

μ = G m 1 m 1 m 2 m 2 - ( G m 1 m 1 r s - G j m 1 r s - G k m 1 r s + G j k r s ) - ( G j k m 2 m 2 - G j k m 2 r - G j k m 2 s + G j k r s ) , j k m 1 ; r s m 2 α 1 j = G j k r s - G m 1 k r s , j = 1 , , m 1 - 1 ; k j , m 1 α 2 r = G j k r s - G j k m 2 s , r = 1 , , m 2 - 1 , r s , m 2 δ 1 j = G j j r s - G j k r s - G j l r s + G k l r s , j = 1 , , m 1 ; j k l δ 2 r = G j k r r - G j k r s - G j k r t + G j k s t , r = 1 , , m 2 ; r s t

F

2 α 1 m 1 * + δ 1 m 1 * = 0 2 α 2 m 2 * + δ 2 m 2 * = 0

τ = G m 1 m 1 m 2 m 2 + 1 2 j = 1 m 1 - 1 ( G j j m 2 m 2 - G m 1 m 1 m 2 m 2 ) + 1 2 r = 1 m 2 - 1 ( G m 1 m 1 r r - G m 1 m 1 m 2 m 2 ) a 1 j = G j j r s - G m 2 m 2 r s 2 , j = 1 , , m 1 - 1 a 2 r = G j k r r - G j k m 2 m 2 2 , r = 1 , , m 2 - 1 d 1 j = - G j j r s - G j k r s - G j l r s + G k l r s 2 , j = 1 , , m 1 ; j k l d 2 r = - G j k r r - G j k r s - G j k r t + G j k s t 2 , r = 1 , , m 2 ; r s t

Allele-count

α 1 m 1 * = α 2 m 2 * =0

π 0 = G m 1 m 1 m 2 m 2 - ( G m 1 m 1 r s - G j m 1 r s - G m 1 k r s + G j k r s ) - ( G j k m 2 m 2 - G j k r m 2 - G j k m 2 s + G j k r s ) , j k m 1 ; r s m 2 π 1 j = G j k r s - G m 1 k r s , j = 1 , , m 1 - 1 , k j , m 1 π 2 r = G j k r s - G j k m 2 s , r = 1 , , m 2 - 1 , r s , m 2 η 1 j = G j j r s - G j m 1 r s - G k m 1 r s + G j k r s , j = 1 , , m 1 - 1 ; k j , m 1 η 1 m 1 = G m 1 m 1 r s - G j m 1 r s - G k m 1 r s + G j k r s , j k m 1 η 2 r = G j k r r - G j k r m 2 - G j k s m 2 + G j k r s , r = 1 , , m 2 - 1 ; s r , m 2 η 2 m 2 = G j k m 2 m 2 - G j k m 2 r - G j k m 2 s + G j k r s , r s m 2

Allele-count

2 α 1 m 1 * + δ 1 m 1 * = 0 2 α 2 m 2 * + δ 2 m 2 * = 0

π 0 = G m 1 m 1 m 2 m 2 π 1 j = G j m 1 r s - G m 1 m 1 r s - G k m 1 r s + G j k r s 2 , j = 1 , , m 1 - 1 ; k j , m 1 π 1 m 1 = - G m 1 m 1 r s - G j m 1 r s - G k m 1 r s + G j k r s 2 , j k m 1 π 2 r = G j k r m 2 - G j k m 2 m 2 - G j k s m 2 + G j k r s 2 , r = 1 , , m 2 - 1 ; r s , m 2 π 2 m 2 = - G j k m 2 m 2 - G j k r m 2 - G j k s m 2 + G j k r s 2 , r s m 2 η 1 j = G j j r s - G m 1 m 1 r s , j = 1 , , m 1 - 1 η 2 r = G j k r r - G j k m 2 m 2 , r = 1 , , m 2 - 1