Chapter 4: Relationship and inbreeding

Definitions

Calculation of relationship and inbreeding coefficients

Examples

Segregation of recessive by inbreeding

The tabular method

Definition, Relationship

• Related individuals are individuals with common ancestors, this can for instance be a common father

• The relationship coefficient axy is equal to the probability of identical genes in two animals due to common ancestors

Definition, Inbreeding

• Inbreeding occurs after mating of related individuals

• The degree of inbreeding Fx is the probability of identical homozygosity due to common ancestors

Formulas: Relationship- and inbreeding coefficient

The relationship coefficient

axy = (½)n (1 + FA),

where n is the number of generations between X and Y from the common ancestor A, level of inbreeding is FA

The inbreeding coefficient

Fx = ½ amf (m = mother, f = father)

axx = 1+ Fx

Example: Double first cousin breeding

Simple forms of relationship

Simple forms of relationship, continued

Practical application of relationship and inbreeding coefficients

• Important in the control of inbreeding on individual basis

• Inbreeding should normally be avoided, and should not be more than 10%

•By breeding value estimation the relationships coefficients are important for weighing the information from related animals

Segregation of identical homozygotes by full sib breeding

Segregation of the recessive by inbreeding: Example

The gene frequeny for a recessive disease is

q = 0,01 and p = 0,99

Which corresponds to the genotype frequencies

f(rr) = q2 = 0,012 = 0,0001f(Rr) = 2pq = 20,010,99 = 0,0198 f(RR) = p2 = 0,992 = 0,9801

Segregation of the recessive,

continuedP

F1

F2

P(mothers father or mothers mother is heterozygot) = 2(2pq) = 20,198P(x is rr mothers father or mothers mother is heterozygot) = 1/16

Segregation of the recessive, continued

The joint probability of rr in offspring fromfull sib breeding depends on:

The segregation of rr among the offspringP(rr) = 20,01981/16 = 0,0025

This corresponds to an increase in f(rr) of 25 times compared to the original population

Segregation of the recessive, continued

F = 0,25 25 % increase in the frequency of homozygotes - both recessive and dominant - And a loss of heterozygotes

Genotype AA Aa aa Frequency p2 2pq q2

+pqF -2pqF +pqF

The tabular method- two basic formulas

• Inbreeding (F) for an animal is equal to half of the relationship between its parents

• Additive relationship (aXY) between two animals is equal to half of the relationship between the one animal, X, and the other animal, Y’s, parents, A and B

The tabular method : Example

The tabular method : Example continued

The tabular method : Example continued

The tabular method : Example continued