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Partitioning of variance – Genetic models

This chapter explores the partitioning of variance in genetic models, focusing on qualitative traits like coat color and quantitative traits like size. It covers topics such as dominance, interaction between alleles, and the infinitesimal model. The chapter also discusses breeding values, heritability, and misconceptions about heritability.

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Partitioning of variance – Genetic models

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  1. Partitioning of variance – Genetic models Chapter 5

  2. Qualitative versus Quantitative Traits Qualitative: coat color Quantitative: size

  3. Quantitative genetics of multiple loci

  4. Dominance Interaction between alleles on a single locus Multiple loci Interaction among alleles at different loci  epistasis Components of the genotype: G =  + A + D + I Components of the variance: VG = VA + VD + VI Quantitative genetics of multiple loci

  5. The “Infinitesimal Model” • Model assumptions • Many genes affect the trait • Each gene has a small effect • Consequences • Genotypic values and breeding values follow normal distribution • Relationships between traits are linear • Relationship between phenotype and breeding value is linear

  6. From now on we will work with the infinitesimal model • We will characterise traits in terms of variances and covariances. • Variance: a measurement for differences • Covariance: a measurement for resemblance • Variance-Covariance refreshment • See also rules Chapter 2 - last page

  7. Eggs /week, Phenotypic Eggs/week, Genotypic A simple example: the mean and variance

  8. Eggs /week, phenotypic Eggs/week, genotypic Next: the co-variance! = *

  9. And finally : the correlation!

  10. Lets fit a line! A . . . . Y . . . . P X b = 3,2 / 2 = 1,6 a = 4 – 1,6*4 = -2,4 Y = -2,4 + 1,6X

  11. Breeding value estimation is about regression! A . . . . True additive genetic value! . . . correlation . Estimated value! P P

  12. Regression explained True Y Estimated Y Total variance Error Variance Variance explained

  13. Relationship between “r” and “b”

  14. From regression to heritability

  15. Let’s have a break….

  16. Genetic models Genetic models: a (simplified) description of the genetic reality Partitioning of variance: where do differences between animals come from?

  17. Introduction • Why do we need genetic models? Understanding and quantifying resemblance between relatives: Chapter 5 + Chapter 6 provide us with the tools Which “part of the resemblance” is due to genetics and what is environmental. • Estimating breeding values (course GIL & Chapter 7) • Estimating genetic parameters (course MSLS).

  18. Basic genetic model Transmission model Common environmental model Repeatability model Multiple traits Which models?

  19. Pi = () + Gi + Ei P = phenotype = what we measure G = genotype E = environment differences (variation) in P  Var(P) Var(P)  due to differences in G or in E? contribution of G and E to Var(P) Cow 2 15 kg milk Cow 1 25 kg milk Basic genetic model

  20. Heritability H2 (broad sense) • Partitioning of variance • P = G + E • Var(P) =?

  21. Heritability H2 (broad sense) • Partitioning of variance • P = G + E • Var(P) = Var(G+E) = Var(G) + Var(E) + 2 Cov(G,E) • H2 = broad sense heritability = proportion of differences that is due to genetics • Ratio of variances: • H2  [0 …. 1]

  22. Heritability h2 (narrow sense) • Partitioning of variance • P = G + E = A + D + I + E • Var(P) = Var(A) + Var(D) + Var(I) + Var(E) • h2 = proportion of differences that is due to differences in breeding values (A): • h2  [0 …. 1] • h2  H2

  23. Heritability Phenotype = Genotype + Environment High heritability (h2 =1) Phenotype = Genetics WYSIWYG: What You See Is What You Get Low heritability (h2 =0) Phenotype = Environment

  24. Aim: improve the performance of the next generation as compared to the present generation performance of offspring: Breeding Value P = A + D + I + E Conclusion: h2 determines genetic improvement Not inherited by offspring: combinations of alleles Inherited by offspring Genetic Improvement: H2 or h2?

  25. Milk yield: P = 7000 kg, h2 = 0.3 2100 kg due to genetics, 4900 kg due to environment Wrong!, h2 relates to deviations from the mean If the population mean is 7500 kg then… Misconceptions about heritability (h2) 0.3*(7000-7500) = -150Kg is due to genetic effects!

  26. Misconceptions about heritability (h2) • Low heritable traits are not determined by genetic factors • Wrong!, low h2 means low genetic variance

  27. Misconceptions about heritability (h2) The PANDA’S Thumb exhibiting “polydactyly”.

  28. Milk yield: P = 7000 kg, h2 = 0.3 2100 kg due to genetics, 4900 kg due to environment Wrong!, h2 relates to deviations from the mean Low heritable traits are not determined by genetic factors Wrong!, low h2 means low genetic variance Heritability is a fixed value Wrong! h2 depends on the circumstances e.g. Temperate versus tropical climate Free-range barn versus cages restricted or ad libitum feeding Misconceptions about heritability (h2)

  29. Misconceptions about heritability (h2) Selection might change the heritability Change in environment might change the heritability • What is the heritability • indication whether a trait can be changed successfully by means of selection.

  30. Cattle Swine Poultry Horse Sheep Human Salmon Finger ridge count Height Weight Fat % Meal size Stature Egg weight Character Back- fat Fibre Diameter Flesh colour Teat number Fleece weight Teat length Daily gain Body weight Handed-ness Milk yield Weight Pulling ability Egg number Maturation age Claws Litter size Jumping Temp-erament Fertility Feather pecking Dressage Fertility Fertility Dressing %

  31. Transmission model Deals with the transmission of genes from parents to offspring. Transmission of genes = reproduction Half of the genes come from the sire, the other half from the dam.

  32. Transmission model Half of the genes come from the sire, the other half from the dam. Breeding value offspring: Aoff = ½Asire + ½Adam???? This would imply that full sisters/brothers are identical: they have the same sire and the same dam. Is this the case? Let’s look at the inheritance of a single gene.

  33. Transmission model Half of the genes come from the sire. Half of the genes come from the dam. Which “half” is transmitted by sire or dam is unknown = Mendelian sampling

  34. Simple example: • Three genes • Additive effect (no dominance) • Each allele has an effect of 1 • We simply add the effects to obtain the breeding value: • As= 1+1+1-1-1-1 = 0 1/1 1/-1 -1/-1

  35. As= 0 AD= 2 1/1 1/-1 -1/-1 1/-1 1/1 1/-1 1/1 1/1 -1/1 1/-1 -1/1 -1/-1 A=½AS+½AD+MS ½(0) + ½(2) + (+3) = 4 ½(0) + ½(2) + (-3) = -2

  36. As= 0 AD= 2 1/1 1/-1 -1/-1 1/-1 1/1 1/-1 1/1 1/1 -1/1 1/-1 -1/1 -1/-1 A=½AS+½AD+MS ½(0) + ½(2) + (+3) = 4 ½(0) + ½(2) + (-3) = -2

  37. Mendelian sampling represents: Transmission model Variance • MS = Independent of everything else - uncertainty!! • Infinitesimal model: Variance of breeding values does not change from one generation to the next

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