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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 = 20,010,99 = 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) = 20,198 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) = 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 +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