Coefficient of Relationship

i.b.d.: identical by descent

Consider relatives A and B

What is the probability that for any gene the alleles are i.b.d.?

Probability # identical
$c_2$ both
$c_1$ one
$c_0$ neither

$c_2 + c_1 + c_0 = 1$

$a= 1 + \delta a + e$

From Haldan and Jayacar(1962) tables of r (coefficient of relationship) are presented.

f: coefficient of relationship or of inbreeding; the probability that if A has produced a gamete carrying a rare gene, the first tested gamete of B will carry the same gene.

$\phi$ is for sex linked genes in gametes

For diploid genotypes F and $\Phi$ are used

Relation Symbol Converse f F $\phi_{11}$ $\phi_{12}$ $\phi_{21}$ $\phi_{22}$ $\Phi$
Degree 1
Parent Child $\frac{1}{4}$ 0 0 $\frac{1}{2}$ $\frac{1}{2}$ $\frac{1}{4}$ 0
Degree 2
Mother’s Parent Daughter’s Child $\frac{1}{8}$ 0 $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{4}$ $\frac{1}{8}$ 0
Father’s Parent Son’s Child $\frac{1}{8}$ 0 0 0 0 $\frac{1}{4}$ 0
Maternal half sib W S $\frac{1}{8}$ 0 $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{4}$ $\frac{1}{8}$ 0
Paternal half sib H S $\frac{1}{8}$ 0 0 0 0 $\frac{1}{4}$ 0
Full sib M S $\frac{1}{4}$ $\frac{1}{4}$ $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{4}$ $\frac{3}{8}$ $\frac{1}{2}$