Table 2. Expected frequencies of the 16 genotypes of markers A, B, C and D under the epistatic SDL genetic model in a backcross population.

Genotype	S1S2	S1s2	s1S2	s1s2	Observed count ni
ABCD	(1−r1)(1−r2)(1−rBC)(1−r3)(1−r4)/d	(1−r1)(1−r2)(1−rBC)r3r4v/d	r1r2(1−rBC)(1−r3)(1−r4)u/d	r1r2(1−rBC)r3r4x/d	n1
ABCd	(1−r1)(1−r2)(1−rBC)(1−r3)r4/d	(1−r1)(1−r2)(1−rBC)r3(1−r4)v/d	r1r2(1−rBC)(1−r3)r4u/d	r1r2(1−rBC)r3(1−r4)x/d	n2
ABcD	(1−r1)(1−r2)rBCr3(1−r4)/d	(1−r1)(1−r2)rBC(1−r3)r4v/d	r1r2rBCr3(1−r4)u/d	r1r2rBC(1−r3)r4x/d	n3
ABcd	(1−r1)(1−r2)rBCr3r4/d	(1−r1)(1−r2)rBC(1−r3)(1−r4)v/d	r1r2rBCr3r4u/d	r1r2rBC(1−r3)(1−r4)x/d	n4
AbCD	(1−r1)r2rBC(1−r3)(1−r4)/d	(1−r1)r2rBCr3r4v/d	r1(1−r2)rBC(1−r3)(1−r4)u/d	r1(1−r2)rBCr3r4x/d	n5
AbCd	(1−r1)r2rBC(1−r3)r4/d	(1−r1)r2rBCr3(1−r4)v/d	r1(1−r2)rBC(1−r3)(1−r4)u/d	r1(1−r2)rBCr3(1−r4)x/d	n6
AbcD	(1−r1)r2(1−rBC)r3(1−r4)/d	(1−r1)r2(1−rBC)(1−r3)r4v/d	r1(1−r2)(1−rBC)r3(1−r4)u/d	r1(1−r2)(1−rBC)(1−r3)r4x/d	n7
Abcd	(1−r1)r2(1−rBC)r3r4/d	(1−r1)r2(1−rBC)(1−r3)(1−r4)v/d	r1(1−r2)(1−rBC)r3r4u/d	r1(1−r2)(1−rBC)(1−r3)(1−r4)x/d	n8
aBCD	r1(1−r2)(1−rBC)(1−r3)(1−r4)/d	r1(1−r2)(1−rBC)r3r4v/d	(1−r1)r2(1−rBC)(1−r3)(1−r4)u/d	(1−r1)r2(1−rBC)r3r4x/d	n9
aBCd	r1(1−r2)(1−rBC)(1−r3)r4/d	r1(1−r2)(1−rBC)r3(1−r4)v/d	(1−r1)r2(1−rBC)(1−r3)r4u/d	(1−r1)r2(1−rBC)r3(1−r4)x/d	n10
aBcD	r1(1−r2)rBCr3(1−r4)/d	r1(1−r2)rBC(1−r3)r4v/d	(1−r1)r2rBCr3(1−r4)u/d	(1−r1)r2rBC(1−r3)r4x/d	n11
aBcd	r1(1−r2)rBCr3r4/d	r1(1−r2)rBC(1−r3)(1−r4)v/d	(1−r1)r2rBCr3r4u/d	(1−r1)r2rBC(1−r3)(1−r4)x/d	n12
abCD	r1r2rBC(1−r3)(1−r4)/d	r1r2rBCr3r4v/d	(1−r1)(1−r2)rBC(1−r3)(1−r4)u/d	(1−r1)(1−r2)rBCr3r4x/d	n13
abCd	r1r2rBC(1−r3)r4/d	r1r2rBCr3(1−r4)v/d	(1−r1)(1−r2)rBC(1−r3)r4u/d	(1−r1)(1−r2)rBCr3(1−r4)x/d	n14
abcD	r1r2(1−rBC)r3(1−r4)/d	r1r2(1−rBC)(1−r3)r4v/d	(1−r1)(1−r2)(1−rBC)r3(1−r4)u/d	(1−r1)(1−r2)(1−rBC)(1−r3)r4x/d	n15
abcd	r1r2(1−rBC)r3r4/d	r1r2(1−rBC)(1−r3)(1−r4)v/d	(1−r1)(1−r2)(1−rBC)r3r4u/d	(1−r1)(1−r2)(1−rBC)(1−r3)(1−r4)x/d	n16

d=[r_BC(r₂+r₃−2r₂r₃)+(1−r_BC)(1−r₂−r₃+2r₂r₃)](1+x)+[(1−r_BC)(r₂+r₃−2r₂r₃)+r_BC(1−r₂−r₃+2r₂r₃)](v+u).