6 Identity by Descent in the Mapping of Genetic Traits
133
Table 6.2 The 15 IBD partitions at a locus, among the four gametes of two individuals. For two
individuals A and B, the paternal (p) and maternal m gametes are denoted and depicted as in
Fig. 6.3 with individual A above and B below
State
Partition
Ewens’ {a i }
Probability
Kinship
1
{A p , A m , B p , B m }
a 4 = 1
6β 3
1
2
{A p , A m }, {B p , B m }
a 2 = 2
β 2 (1 − β)
0
3
{A p , A m , B p }, {B m }
a 1 = a 3 = 1
2β 2 (1 − β)
1/2
4
{A p , A m , B m }, {B p }
a 1 = a 3 = 1
2β 2 (1 − β)
1/2
5
{A p , A m }, {B p }, {B m }
a 2 = 1, a 1 = 2
β(1 − β) 2
0
6
{A p , B p , B m }, {A m }
a 1 = a 3 = 1
2β 2 (1 − β)
1/2
7
{A p }, {A m , B p , B m }
a 1 = a 3 = 1
2β 2 (1 − β)
1/2
8
{A p }, {A m }, {B p , B m }
a 2 = 1, a 1 = 2
β(1 − β) 2
0
9
{A p , B p }, {A m , B m }
a 2 = 2
β 2 (1 − β)
1/2
10
{A p , B m }, {A m , B p }
a 2 = 2
β 2 (1 − β)
1/2
11
{A p , B p }, {A m }, {B m }
a 2 = 1, a 1 = 2
β(1 − β) 2
1/4
12
{A p , B m }, {A m }, {B p }
a 2 = 1, a 1 = 2
β(1 − β) 2
1/4
13
{A p }, {A m , B p }, {B m }
a 2 = 1, a 1 = 2
β(1 − β) 2
1/4
14
{A p }, {A m , B m }, {B p }
a 2 = 1, a 1 = 2
β(1 − β) 2
1/4
15
{A p }, {A m }, {B p }, {B m }
a 1 = 4
(1 − β) 3
0
The classical coefficient of kinship between two individuals A and B is the
probability that gametes segregating from each of A and B are IBD at any point in
the genome. The final column of Table 6.2 gives this probability conditional on the
IBD state among the four gametes of A and B. Note there are only four possibilities.
If there is no IBD between the individuals (states 2, 5, 8, and 15), the value is 0.