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|$\frac{1}{4}$|$\frac{1}{4}$|$\frac{1}{2}$|$\frac{1}{4}$|$\frac{1}{4}$|$\frac{3}{8}$|$\frac{1}{2}$|