Chapter 4 Relationship and inbreeding Definitions Calculation of

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) = q 2 = 0, 012 = 0, 0001 f(Rr) = 2 pq = 2 0, 01 0, 99 = 0, 0198 f(RR) = p 2 = 0, 992 = 0, 9801

Segregation of the recessive, continued P F 1 F 2 P(mothers father or mothers mother is heterozygot) = 2(2 pq) = 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 % increase in the frequency of homozygotes - both recessive and dominant And a loss of heterozygotes Genotype AA Aa aa Frequency p 2 +pq. F 2 pq -2 pq. F q 2 +pq. F

The tabular method - two basic formulas • Inbreeding (F) for an animal is equal to half of the relationship between its parents • Additive relationship (a. XY) 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