Breeding Value versus Genetic Value

Transcription

1 Breeding Value versus Genetic Value Gene351 (not( Gene251) Lecture 6

2 Key terms Breeding value Genetic value Average effect of alleles Reading: Prescribed None Suggested Falconer & McKay, 1996

3 Revision

4 Basis of inheritance Diploid parents Meiosis X Haploid gamettes (sperm and egg) Fertilization Diploid offspring

5 Basis of inheritance: single locus model Parents A1A2 x A1A2 Gametes A1 A2 A1 A2 F1 A1A1 A1A2 A2A1 A2A2

6 Under Hardy-Weinberg equilibrium genotype frequencies can be estimated from allele frequencies Assuming H-W H W equilibrium if p = frequency of A1 allele if q = frequency of A2 allele Genotype frequencies are p 2 A1A1 2pq q 2 A1A2 A2A2 A1 A2 A1 A1A1 (pxp=p 2 ) A2A1 (qxp) A2 A1A2 (pxq) A2A2 (qxq=q 2 )

7 Assumptions of Hardy-Weinberg equilibrium Equal survival of genotypes (no one genotype has selective advantage over another) Equal fertility of genotypes these imply no selection Large samples of animals Random mating of animals Gene frequency same in each sex

8 H-W W calculation example Assume the population alleles frequency of A1 and A2 are 0.9 and 0.1 respectively, what are the genotype frequencies? A1A1 p2 0.9 x 0.9 = pq 2 x 0.9 x 0.1 = 0.18 A1A2 A2A2 q2 0.1 x 0.1 =

9 H-W W calculation example continued If the genotypic values of A1A1, A1A2 and A2A2 are 10, 0 and -10 respectively, what is the population mean? Population mean = sum of (values x frequency) A1A x 10 = 8.1 A1A x 0 = 0 A1A x -10 =

10 Breeding value versus genetic value under a single locus model

11 Breeding value An individuals breeding value can also be described as the sum of the average effect of the individuals alleles For example, if an A1 allele is worth +5 and an A2 allele is worth -2, then an A1A2 heterozygote has a breeding value of 3.

12 The following three examples use a single locus model to demonstrate Calculation of breeding value as the sum of the average effect of alleles The difference between genetic value and breeding value

13 No dominance, p=q=0.5 Genotype A 2 A 2 A 1 A 2 A 1 A 1 Value Frequency Pop n mean 300 Genetic value Breeding value Average effect of A1 = 10 Average effect of A2= -10 With no dominance the genetic and breeding values are equal. With equal allele frequency the average effects of A1 and A2 are of equal magnitude

14 Working from previous slide Population mean = sum of frequency x values 280 x x x 0.25 = 300 Genetic value = deviation from population mean e.g. A2A2 = = -20 Breeding value = sum of average effect of alleles Average effect of A1 A1 allele will meet A1 at frequency p and A2 at frequency q A1A1 x p + A1A2 x q = 20 x x 0.5 = 10 Average effect of A2 A2 allele will meet A1 at frequency p and A2 at frequency q A2A1 x p + A2A2 x q = 0 x x 0.5 = -10

15 Some dominance, p=q=0.5 Genotype A 2 A 2 A 1 A 2 A 1 A 1 Value Frequency Pop n mean 305 Genetic value Breeding value Average effect of A1 = 10 Average effect of A2= -10 With some dominance the genetic and breeding values differ. Dominance deviation is excluded from the breeding value.

16 Working from previous slide Population mean = sum of frequency x values 280 x x x 0.25 = 305 Genetic value = deviation from population mean e.g. A2A2 = = -25 Breeding value = sum of average effect of alleles Average effect of A1 A1 allele will meet A1 at frequency p and A2 at frequency q A1A1 x p + A1A2 x q = 15 x x 0.5 = 10 Average effect of A2 A2 allele will meet A1 at frequency p and A2 at frequency q A2A1 x p + A2A2 x q = 5 x x 0.5 = -10

17 No dominance, p=0.1, q=0.9 Genotype A 2 A 2 A 1 A 2 A 1 A 1 Value Frequency Pop n mean 284 Genetic value Breeding value Average effect of A1 = 18 Average effect of A2= -2 With unequal allele frequencies the average effects of A1 and A2 are of different magnitude. The average effect of an allele is greater if the allele is rare.

18 Working from previous slide Population mean = sum of frequency x values 280 x x x 0.01 = 284 Genetic value = deviation from population mean e.g. A2A2 = = -4 Breeding value = sum of average effect of alleles Average effect of A1 A1 allele will meet A1 at frequency p and A2 at frequency q A1A1 x p + A1A2 x q = 36 x x 0.9 = 18 Average effect of A2 A2 allele will meet A1 at frequency p and A2 at frequency q A2A1 x p + A2A2 x q = 16 x x 0.9 = -2

19 Summary Breeding values are expressed as a deviation of the population mean (with the population mean dependent on genotypic values and frequencies) With no dominance G=A, with dominance G A G Animals with a rare allele will have a larger (either positive or negative) breeding value

20 Breeding values are additive As breeding values are the sum of average effects, the heterozygote is always half-way between the two homozygotes (irrespective of dominance) Example 1: A1A1 = 10, A2A2 = -10 and A1A2 = 0 Example 3: A1A1 = 36, A2A2 = -44 and A1A2 = 16 Breeding values are said to be additive

21 Breeding values can be used to predict progeny performance Using example 1 from before: p=q=0.5 average effect of A1=10, of A2= -10 A1A1=20, A1A2=0, A2A2= -20 Expected genetic value of offspring from an A1A1 sire is ˆ ˆ 0 20 = A + = = G o Check: sire passes on A1, dams have equal frequency of A1 & A2, progeny are equally A1A1 and A1A2, and 20x0.5 +0x0.5=10

22 Breeding values can be used to predict progeny performance Using example 3 from before: p=0.1, q=0.9 average effect of A1=18, of A2= -2 A1A1=36, A1A2=16, A2A2= -4 Expected genetic value of offspring from an A1A2 sire is ˆ ˆ 0 16 = A + = = G o Check: sire passes on A1 and A2 in equal frequency, dams have frequency of A1 =0.1 & A2=0.9, and progeny are 0.5x0.1 A1A x0.9 A1A x0.1 A2A x0.9A2A2 = 0.05x x x x-4 = 8

23 A point to remember Breeding values are halved when used to predict progeny performance, as breeding value represent the sum of the average effect of two alleles, only one of which is passed on.

24 Summary Genetic value is value of genes to SELF includes dominance deviation, which cannot be passed on to progeny (as each parent transmits one allele) Breeding value is value of genes to PROGENY sum of the average effect of the two alleles carried the average effect of an allele depends on the frequency of the allele in the population

25 You don t need to memorise these formula, just be comfortable with the concept Genetic variance Genetic variance at a locus can be determined from allele frequencies and average effects of alleles V A = 2 pq( α1 α 2) 2 V = ( 2 pqd D 2 )

26 A final note You can conceptualize that these concepts relating to genetic and breeding value could be extended from a single locus model to a multiple locus model