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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
= 0,0001
f(Rr) = 2pq = 20,010,99 = 0,0198
f(RR) = p2 = 0,992
= 0,9801
Segregation of the recessive,
continued
P
F1
F2
P(mothers father or mothers mother is heterozygot)
= 2(2pq) = 20,198
P(x is rr mothers father or mothers mother is heterozygot)
= 1/16
Segregation of the recessive,
continued
The joint probability of rr in offspring from
full sib breeding depends on:
The segregation of rr among the offspring
P(rr) = 20,01981/16 = 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
+pqF
2pq
-2pqF
q2
+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