Table 1 The IBD states among the four genes of two individuals
IBD StateaState Descriptions
B1B2PartitionEwensProbabilityb
abcdz(a1, a2, a3, a4)Jacquardk
1111(a, b, c, d)(0,0,0,1)Δ1
1122(a, b)(c, d)(0,2,0,0)Δ2
1112(a, b, c)(d)(1,0,1,0)Δ3
1121(a, b, d)(c)(1,0,1,0)
1123(a, b)(c)(d)(2,1,0,0)Δ4
1211(a, c, d)(b)(1,0,1,0)Δ5
1222(a)(b, c, d)(1,0,1,0)
1233(a)(b)(c, d)(2,1,0,0)Δ6
1212(a, c)(b, d)(0,2,0,0)Δ7k2
1221(a, d)(b, c)(0,2,0,0)
1213(a, c)(b)(d)(2,1,0,0)Δ8c
1231(a, d)(b)(c)(2,1,0,0)
1223(a)(b, c)(d)(2,1,0,0)
1232(a)(b, d)(c)(2,1,0,0)
1234(a)(b)(c)(d)(4,0,0,0)Δ9k0
• The two gametes of individual B1 are denoted a and b, and the two gametes of B2 are c and d.

• a The pattern is defined by the labeling developed by Nadot and Vayssiex (1973).

• b The total probability of each subset of genotypically equivalent states is given on the first row. For example, Δ3 is the combined probability of states (11 12) and (11 21).

• c Note that Cotterman (1940) and some later authors use 2k1 instead of k1 for this probability.