#### Calculating Coefficient of Inbreeding

- The coefficient of inbreeding is commonly symbolized as Fx (called, “F of x”)
- The basic formulae for Fx is Σ(1/2)n where n symbolizes no. of nodes in the path

**Pedigree Problem 1:**

Animals 1 and 2 are common to the sire and dam of X. Assume that they are each heterozygous at the hypothetical A locus and share no alleles with each other. Because the members of a homologous pair of chromosomes segregate from each other at meiosis, the probability that an individual will pass one of the two alleles at a locus to an offspring is 1/2. Since each passage of an allele from an individual to an offspring is an independent event, the probability that a given allele will be passed through n generations is (1/2) n. In this case of a brother-sister mating, we wish to compute the coefficient of inbreeding of animal x. There are two ancestors that are common to the sire and dam of animal x, animal 1 and animal 2.

**Solutions:**

Probability that the allele A1 will be transmitted to x through animal 3 = (1/2)=1/4

Probability that A1 will be transmitted to x through 4 = (1/2)² = 1/4

Probability that x will receive A1 from both 3 and 4 = (1/4)(1/4) = 1/16

Likewise, the probability that x will receive A2 from both 3 and 4 = 1/16

Probability that x will receive A2 from both 3 and 4 = 1/16

Probability that x will receive A3 from both 3 and 4 = 1/16

Probability that x will receive A4 from both 3 and 4 = 1/16

Probability that x will be homozygous for A1 ,A2 ,A3 , or A4 (add the individual probabilities) =4/16 = 1/4

The coefficient of inbreeding of = x = ¼

**Pedigree Problem 2:**

In this case of a father-daughter mating, there is only one ancestor that is common to the sire and dam of animal x: the father, animal 1. The alleles and present in animal 2 are irrelevant to the calculation of the inbreeding coefficient of animal x because he could not have received either of them from both his sire and his dam.

Probability that the allele A1 will be transmitted to x through animal 3= (1/2)²=1/4

Probability that A1 will be transmitted to x from 1 directly = 1/2

Probability that x will receive A1 from both parents = (1/2)(1/4) = 1/8

Likewise, the probability that x will receive A2 from both parents = 1/8

Probability that x will be homozygous for either A1 or A2 = FX = 2/8 = 1/4

Note that is the same for brother X sister as for parent X offspring matings, although in the latter case, there is only one common ancestor.

**Pedigree Problem 3:**

In this mating between first cousins, there are two ancestors that are common to both the sire and the dam of animal x: animals 1 and 2.

Probability that animal x will receive A1 through animal 6 = (1/2)³ = 1/8

Probability that A1 will be transmitted to x through 5 = (1/2)³ = 1/8

Probability that x is homozygous for A1 = (1/8)(1/8) = 1/64

Probability that x will be homozygous for A1,A2 ,A3 or A4 = FX = 4/64 = 1/16

**Pedigree Problem 4:**

Number of Nodes = 5

Inbreeding Coefficient = f= (1/2)^{n}

f= (1/2)^{5}

=0.03125 = 1/32

The progeny of first 1/2 cousins have an inbreeding coefficient of 1/32.

**Pedigree Problem 5: Full first cousins**

There are now two paths:

IAC**E**DBI

IAC**F**DBI

Nodes/path = 5

F = (1/2)^{N1 }+ (1/2)^{N2 }

= (1/2)^{5} + (1/2)^{5}

= 0.03125 + 0.03125

= 1/16

The progeny of first cousins have an inbreeding coefficient of 1/16.

**Also Study:**

**Inbreeding in Humans | Inbreeding in Animals | Inbreeding in Plants**

**How To Calculate Breeding Value**