1. Office hours 3-4pm Wednesdays 304A 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… SWR parentC3H parent (F2’s) Doesn’t look like this…

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

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

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

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

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

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

10. Complex traits (one family, mouse model)

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

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

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   x   N  = mean

21. Distributions  

22. Genetically identical Genetically different Heritability in exptal organisms

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

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

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

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

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

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

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

30. Heritability in exptal organisms Genetic variance = total var - “environmental var” Heritability H 2 = ee tt  g  =  t  -  e  g/tg/t

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

32. Fig. 21.13

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

34. Why h 2 ? “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/ot hrpics/sarahandsandra.jpg http://www.twinsrealm.com/othrpics/twins16.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/ot hrpics/sarahandsandra.jpg http://www.twinsrealm.com/othrpics/twins16.jpg Mean each pair = z i

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/ot hrpics/sarahandsandra.jpg http://www.twinsrealm.com/othrpics/twins16.jpg Each individual = z ij Mean each pair = z i

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/ot hrpics/sarahandsandra.jpg http://www.twinsrealm.com/othrpics/twins16.jpg Each individual = z ij Mean each pair = z i Total mean sq =  (z ij - z) 2 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/ot hrpics/sarahandsandra.jpg http://www.twinsrealm.com/othrpics/twins16.jpg Each individual = z ij Mean each pair = z i Total mean sq =  (z ij - z) 2 T Within pairs mean sq =  (z ij - z i ) 2 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/ot hrpics/sarahandsandra.jpg http://www.twinsrealm.com/othrpics/twins16.jpg Each individual = z ij Mean each pair = z i “Environment” alone Total mean sq =  (z ij - z) 2 T Within pairs mean sq =  (z ij - z i ) 2 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/ot hrpics/sarahandsandra.jpg http://www.twinsrealm.com/othrpics/twins16.jpg Each individual = z ij Mean each pair = z i Between pairs mean sq =  (z i - z) 2 N-1 Total mean sq =  (z ij - z) 2 T Within pairs mean sq =  (z ij - z i ) 2 N

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/ot hrpics/sarahandsandra.jpg http://www.twinsrealm.com/othrpics/twins16.jpg Each individual = z ij Mean each pair = z i “Environment” and genetics Between pairs mean sq =  (z i - z) 2 N-1 Total mean sq =  (z ij - z) 2 T Within pairs mean sq =  (z ij - z i ) 2 N

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/ot hrpics/sarahandsandra.jpg http://www.twinsrealm.com/othrpics/twins16.jpg Each individual = z ij Mean each pair = z i Between pairs mean sq =  (z i - z) 2 N-1 =  b 2 =  g 2 +  e 2 Total mean sq =  (z ij - z) 2 T Within pairs mean sq =  (z ij - z i ) 2 N

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/ot hrpics/sarahandsandra.jpg http://www.twinsrealm.com/othrpics/twins16.jpg Each individual = z ij Mean each pair = z i N Between pairs mean sq =  (z i - z) 2 N-1 Total mean sq =  (z ij - z) 2 T Within pairs mean sq =  (z ij - z i ) 2 =  w 2 =  b 2

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/ot hrpics/sarahandsandra.jpg http://www.twinsrealm.com/othrpics/twins16.jpg Each individual = z ij Mean each pair = z i Between pairs mean sq =  (z i - z) 2 N-1 Total mean sq =  (z ij - z) 2 T Within pairs mean sq =  (z ij - z i ) 2 =  w 2 =  t 2 =  b 2

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/ot hrpics/sarahandsandra.jpg http://www.twinsrealm.com/othrpics/twins16.jpg Each individual = z ij Mean each pair = z i Between pairs mean sq =  (z i - z) 2 N-1 =  w 2 =  t 2 =  b 2 +  w 2 Total mean sq =  (z ij - z) 2 T Within pairs mean sq =  (z ij - z i ) 2 =  b 2

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/ot hrpics/sarahandsandra.jpg http://www.twinsrealm.com/othrpics/twins16.jpg Each individual = z ij Total mean sq =  (z ij - z) 2 T Mean each pair = z i Within pairs mean sq =  (z ij - z i ) 2 N Between pairs mean sq =  (z i - z) 2 N-1 =  b 2 =  w 2 =  t 2 h 2 =  b 2  w 2 t2t2

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/ot hrpics/sarahandsandra.jpg http://www.twinsrealm.com/othrpics/twins16.jpg h 2 =  b 2  w 2 t2t2 The fraction of the total variance that is attributable to differences between pairs (i.e. is genetic).

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/ot hrpics/sarahandsandra.jpg http://www.twinsrealm.com/othrpics/twins16.jpg Within pairs mean sq =  (z ij - z i ) 2 N =  w 2

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/ot hrpics/sarahandsandra.jpg http://www.twinsrealm.com/othrpics/twins16.jpg Within pairs mean sq =  (z ij - z i ) 2 N =  w 2 h 2 =  w 2 (DZ)  w 2 (MZ)]

51. 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/ot hrpics/sarahandsandra.jpg http://www.twinsrealm.com/othrpics/twins16.jpg Within pairs mean sq =  (z ij - z i ) 2 N =  w 2 h 2 =  w 2 (DZ)  w 2 (MZ)] environment only

52. 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/ot hrpics/sarahandsandra.jpg http://www.twinsrealm.com/othrpics/twins16.jpg Within pairs mean sq =  (z ij - z i ) 2 N =  w 2 h 2 =  w 2 (DZ)  w 2 (MZ)] Genetic + environment

53. 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/ot hrpics/sarahandsandra.jpg http://www.twinsrealm.com/othrpics/twins16.jpg Within pairs mean sq =  (z ij - z i ) 2 N =  w 2 h 2 =  w 2 (DZ)  w 2 (MZ)] DZ twins are half as dissimilar as two unrelated people

54. Heritability in humans: MZ and DZ

55. (A more sophisticated model-fitting method)

56. Adoptee studies Biological parent# in sample % adopted sons alcoholic Alcoholic mother 8939.4 Alcoholic father 4228.6 Non-alcoholic mother 72313.6 Non-alcoholic father 102915.5 http://www3.interscience.wiley.com/journal/120049433/abstract?CRETRY=1&SRETRY=0 Rates of alcoholism in adopted males A qualitative argument for genetic contribution