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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
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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
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Definition, Inbreeding
• Inbreeding occurs after mating of related individuals
• The degree of inbreeding Fx is the probability of identical homozygosity due to common ancestors
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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
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Example: Double first cousin breeding
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Simple forms of relationship
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Simple forms of relationship, continued
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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
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Segregation of identical homozygotes by full sib breeding
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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
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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
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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
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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
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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
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The tabular method : Example
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The tabular method : Example continued
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The tabular method : Example continued
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The tabular method : Example continued