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Office hours 3-4pm Wednesdays 304A Stanley Hall

Office hours 3-4pm Wednesdays 304A Stanley Hall. Simulation/theory. Expect 0.09 of a locus to reach LOD=3 by chance. Not 1-locus dominant, or 1-locus incomplete dominance, or…. (F2’s). Doesn’t look like this…. C3H parent. SWR parent. Quantitative trait linkage test.

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Office hours 3-4pm Wednesdays 304A Stanley Hall

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  1. Office hours3-4pm Wednesdays304A Stanley Hall

  2. Simulation/theory Expect 0.09 of a locus to reach LOD=3 by chance.

  3. Not 1-locus dominant, or 1-locus incomplete dominance, or… (F2’s) Doesn’t look like this… C3H parent SWR parent

  4. Quantitative trait linkage test Not counting recombinants. Statistical test for goodness of fit. (F2’s)

  5. >1 locus controlling trait (One mouse family) Just reporting significance of goodness of fit.

  6. What if… Magnitude of spread within group has not changed. Locus effect is weaker. C3H parent F2’s, C/C at marker F2’s, C/S at marker F2’s, S/S at marker SWR parent

  7. Correct interpretation: Difference between S and C at this locus has a causal role in blood pressure variation, but effect is modest. C3H parent F2’s, C/C at marker F2’s, C/S at marker F2’s, S/S at marker SWR parent

  8. Correct interpretation: “Effect of having an S allele” Difference between S and C at this locus has a causal role in blood pressure variation, but effect is modest. C3H parent F2’s, C/C at marker F2’s, C/S at marker F2’s, S/S at marker SWR parent

  9. Correct interpretation: “Effect of having an S allele” Most loci underlying human disease look like this. C3H parent F2’s, C/C at marker F2’s, C/S at marker F2’s, S/S at marker SWR parent

  10. Complex traits (one family, mouse model)

  11. Complex traits Just reporting significance of goodness of fit. (one family, mouse model)

  12. Complex traits Genetic differences at both loci affect the trait (one family, mouse model)

  13. Complex traits Each locus responsible for half? (one family, mouse model)

  14. Complex traits Each locus responsible for half? Depends on the model. (one family, mouse model)

  15. Complex traits (one family, mouse model)

  16. Complex traits (one family, mouse model) Each locus responsible for a third?

  17. Complex traits If 5 loci, each responsible for a fifth? 10 loci? … The more loci, the smaller the effects and the harder to detect.

  18. Complex traits One common result of a linkage study is no significant linkage anywhere. Genetic complexity is the rule; simple 1- or 2-locus models are the exception

  19. We haven’t talked about humans lately… With model organisms, can always study a single cross/family with lots of progeny, so better statistical power to detect weak loci. And less chance of locus heterogeneity.

  20. Distributions   = mean x N

  21. Distributions  

  22. Heritability in exptal organisms Genetically identical Genetically different

  23. Heritability in exptal organisms Genetically identical Genetically different Which population has the bigger variance? Red Green

  24. Heritability in exptal organisms Genetically identical Genetically different Why is the green curve taller? There are more mice in the green population More mice in the green population have high blood pressure Fewer differences between mice in the green population Less environmental error/noise in the green population

  25. Heritability in exptal organisms Genetically identical (each curve adds to 100%) Genetically different Why is the green curve taller? There are more mice in the green population More mice in the green population have high blood pressure Fewer differences between mice in the green population Less environmental error/noise in the green population

  26. Heritability in exptal organisms (blood pressure) (blood cholesterol) Trait 1 Trait 2 Green = genetically identical, red = genetically different

  27. Heritability in exptal organisms Trait 1 Trait 2 Green = genetically identical, red = genetically different Which trait is more likely to be controlled by polymorphisms between the mice in the red population? Trait 1 Trait 2

  28. Heritability in exptal organisms e t Genetic variance = total var - “environmental var” g = t -e

  29. Heritability in exptal organisms e t Genetic variance = total var - “environmental var” “How much of the trait difference between genetically different individuals is due to polymorphisms?” g = t -e

  30. Heritability in exptal organisms e t Genetic variance = total var - “environmental var” Heritability H2 = g = t -e g/t

  31. Heritability in exptal organisms Trait 1 Trait 2 Green = genetically identical, red = genetically different Which trait has a higher heritability? Trait 1 Trait 2

  32. Fig. 21.13

  33. ??? What is (the square of) this quantity? Environmental variance Total variance Genetic variance Population variance

  34. Why h2? “Are DNA differences controlling my trait?” Otherwise, why bother with genetic mapping?

  35. Heritability in humans: MZ twins http://www.sciam.com/media/inline/15DD5B0E-AB41-23B8-2B1E53E8573428C5_1.jpg http://www.twinsinsurance.net/images/twins.jpg http://www.twinsrealm.com/othrpics/twins16.jpg http://www.twinsrealm.com/othrpics/sarahandsandra.jpg Mean over all = z

  36. Heritability in humans: MZ twins http://www.sciam.com/media/inline/15DD5B0E-AB41-23B8-2B1E53E8573428C5_1.jpg http://www.twinsinsurance.net/images/twins.jpg http://www.twinsrealm.com/othrpics/twins16.jpg http://www.twinsrealm.com/othrpics/sarahandsandra.jpg Mean each pair = zi

  37. Heritability in humans: MZ twins http://www.sciam.com/media/inline/15DD5B0E-AB41-23B8-2B1E53E8573428C5_1.jpg http://www.twinsinsurance.net/images/twins.jpg http://www.twinsrealm.com/othrpics/twins16.jpg http://www.twinsrealm.com/othrpics/sarahandsandra.jpg Mean each pair = zi Each individual = zij

  38. Heritability in humans: MZ twins http://www.sciam.com/media/inline/15DD5B0E-AB41-23B8-2B1E53E8573428C5_1.jpg http://www.twinsinsurance.net/images/twins.jpg http://www.twinsrealm.com/othrpics/twins16.jpg http://www.twinsrealm.com/othrpics/sarahandsandra.jpg Mean each pair = zi Each individual = zij (zij - z)2   Total mean sq = T

  39. Heritability in humans: MZ twins http://www.sciam.com/media/inline/15DD5B0E-AB41-23B8-2B1E53E8573428C5_1.jpg http://www.twinsinsurance.net/images/twins.jpg http://www.twinsrealm.com/othrpics/twins16.jpg http://www.twinsrealm.com/othrpics/sarahandsandra.jpg Mean each pair = zi Each individual = zij (zij - z)2   Total mean sq = T (zij - zi)2   Within pairs mean sq = N

  40. Heritability in humans: MZ twins http://www.sciam.com/media/inline/15DD5B0E-AB41-23B8-2B1E53E8573428C5_1.jpg http://www.twinsinsurance.net/images/twins.jpg http://www.twinsrealm.com/othrpics/twins16.jpg http://www.twinsrealm.com/othrpics/sarahandsandra.jpg Mean each pair = zi Each individual = zij (zij - z)2   Total mean sq = T (zij - zi)2 “Environment” alone   Within pairs mean sq = N

  41. Heritability in humans: MZ twins http://www.sciam.com/media/inline/15DD5B0E-AB41-23B8-2B1E53E8573428C5_1.jpg http://www.twinsinsurance.net/images/twins.jpg http://www.twinsrealm.com/othrpics/twins16.jpg http://www.twinsrealm.com/othrpics/sarahandsandra.jpg Mean each pair = zi Each individual = zij (zij - z)2   Total mean sq = T (zij - zi)2   Within pairs mean sq = N (zi - z)2  Between pairs mean sq = N-1

  42. Heritability in humans: MZ twins http://www.sciam.com/media/inline/15DD5B0E-AB41-23B8-2B1E53E8573428C5_1.jpg http://www.twinsinsurance.net/images/twins.jpg http://www.twinsrealm.com/othrpics/twins16.jpg http://www.twinsrealm.com/othrpics/sarahandsandra.jpg Mean each pair = zi Each individual = zij (zij - z)2   Total mean sq = T (zij - zi)2   Within pairs mean sq = N (zi - z)2  Between pairs mean sq = “Environment” and genetics N-1

  43. Heritability in humans: MZ twins http://www.sciam.com/media/inline/15DD5B0E-AB41-23B8-2B1E53E8573428C5_1.jpg http://www.twinsinsurance.net/images/twins.jpg http://www.twinsrealm.com/othrpics/twins16.jpg http://www.twinsrealm.com/othrpics/sarahandsandra.jpg Mean each pair = zi Each individual = zij (zij - z)2   Total mean sq = T (zij - zi)2   Within pairs mean sq = N (zi - z)2  = b2 = g2 + e2 Between pairs mean sq = N-1

  44. Heritability in humans: MZ twins http://www.sciam.com/media/inline/15DD5B0E-AB41-23B8-2B1E53E8573428C5_1.jpg http://www.twinsinsurance.net/images/twins.jpg http://www.twinsrealm.com/othrpics/twins16.jpg http://www.twinsrealm.com/othrpics/sarahandsandra.jpg Mean each pair = zi Each individual = zij (zij - z)2   Total mean sq = T (zij - zi)2   Within pairs mean sq = = w2 N (zi - z)2  = b2 Between pairs mean sq = N-1

  45. Heritability in humans: MZ twins http://www.sciam.com/media/inline/15DD5B0E-AB41-23B8-2B1E53E8573428C5_1.jpg http://www.twinsinsurance.net/images/twins.jpg http://www.twinsrealm.com/othrpics/twins16.jpg http://www.twinsrealm.com/othrpics/sarahandsandra.jpg Mean each pair = zi Each individual = zij (zij - z)2   Total mean sq = = t2 T (zij - zi)2   Within pairs mean sq = = w2 (zi - z)2  = b2 Between pairs mean sq = N-1

  46. Analysis of variance (ANOVA) http://www.sciam.com/media/inline/15DD5B0E-AB41-23B8-2B1E53E8573428C5_1.jpg http://www.twinsinsurance.net/images/twins.jpg http://www.twinsrealm.com/othrpics/twins16.jpg http://www.twinsrealm.com/othrpics/sarahandsandra.jpg Mean each pair = zi Each individual = zij (zij - z)2   Total mean sq = = t2 =b2 + w2 T (zij - zi)2   Within pairs mean sq = = w2 (zi - z)2  = b2 Between pairs mean sq = N-1

  47. Heritability in humans: MZ twins http://www.sciam.com/media/inline/15DD5B0E-AB41-23B8-2B1E53E8573428C5_1.jpg http://www.twinsinsurance.net/images/twins.jpg http://www.twinsrealm.com/othrpics/twins16.jpg http://www.twinsrealm.com/othrpics/sarahandsandra.jpg Mean each pair = zi Each individual = zij b2 w2 (zij - z)2   h2 = Total mean sq = = t2 t2 T (zij - zi)2   Within pairs mean sq = = w2 N (zi - z)2  = b2 Between pairs mean sq = N-1

  48. Heritability in humans: MZ twins http://www.sciam.com/media/inline/15DD5B0E-AB41-23B8-2B1E53E8573428C5_1.jpg http://www.twinsinsurance.net/images/twins.jpg http://www.twinsrealm.com/othrpics/twins16.jpg http://www.twinsrealm.com/othrpics/sarahandsandra.jpg The fraction of the total variance that is attributable to differences between pairs (i.e. is genetic). b2 w2 h2 = t2

  49. Another approach: MZ and DZ http://www.sciam.com/media/inline/15DD5B0E-AB41-23B8-2B1E53E8573428C5_1.jpg http://www.twinsinsurance.net/images/twins.jpg http://www.twinsrealm.com/othrpics/twins16.jpg http://www.twinsrealm.com/othrpics/sarahandsandra.jpg (zij - zi)2   Within pairs mean sq = = w2 N

  50. Another approach: MZ and DZ http://www.sciam.com/media/inline/15DD5B0E-AB41-23B8-2B1E53E8573428C5_1.jpg http://www.twinsinsurance.net/images/twins.jpg http://www.twinsrealm.com/othrpics/twins16.jpg http://www.twinsrealm.com/othrpics/sarahandsandra.jpg (zij - zi)2   Within pairs mean sq = = w2 N w2(DZ) w2 (MZ)] h2 =

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