Why you should know about experimental crosses

1. Why you should know about experimental crosses

2. Why you should know about experimental crosses • To save you from embarrassment

3. Why you should know about experimental crosses • To save you from embarrassment • To help you understand and analyse human genetic data

4. Why you should know about experimental crosses • To save you from embarrassment • To help you understand and analyse human genetic data • It’s interesting

5. Experimental crosses

6. Experimental crosses • Inbred strain crosses • Recombinant inbreds • Alternatives

7. Inbred Strain Cross

8. Backcross

9. F2 cross Generation F0 F1 F2

10. Data conventions AA = A BB = B AB = H Missing data = -

11. Data conventions Genotype file

12. Data conventions Genotype file Phenotype file

13. Data conventions Genotype file Phenotype file Map file

14. Map file • Use the latest mouse build and convert physical to genetic distance: 1 Mb = 1.6 cM • Use our genetic map: http://gscan.well.ox.ac.uk/

15. Analysis • If you can’t see the effect it probably isn’t there

16. 1400 1200 1000 800 Phenotype 600 400 200 0 0.5 AA AB BB

17. Backcross genotypes Red = Hom Blue = Het

18. Statistical analysis

19. Linear models • Also known as • ANOVA • ANCOVA • regression • multiple regression • linear regression

24. QTL snp

25. +1 0 -1 QTL snp

26. +1 0 -1 QTL snp

27. +1 0 -1 QTL snp

28. +1 0 -1 QTL snp

29. QQ qq qQ

30. +1 0 0 1 -1 0 QTL snp

31. +1 0 0 1 -1 0 QTL snp

32. 100 90 10 0 90 80 QQ qq qQ

33. 100 90 10 0 90 10 10 90 80 QQ qq qQ

34. Hypothesis testing H0: H1:

35. Hypothesis testing H0: y ~1 H1: y ~ 1 + x

36. Hypothesis testing H0: y ~ 1 H1: y ~ 1 + x H1 vs H0 : Does x explain a significant amount of the variation?

37. Hypothesis testing H0: y ~ 1 H1: y ~ 1 + x H1 vs H0 : Does x explain a significant amount of the variation? LOD score likelihood ratio

38. Hypothesis testing H0: y ~ 1 H1: y ~ 1 + x H1 vs H0 : Does x explain a significant amount of the variation? LOD score likelihood ratio Chi Square test p-value logP

39. Hypothesis testing H0: y ~ 1 H1: y ~ 1 + x H1 vs H0 : Does x explain a significant amount of the variation? LOD score likelihood ratio Chi Square test p-value logP linear models only SS explained / SS unexplained F-test (or t-test)

40. Hypothesis testing H0: y ~ 1 + x H1: y ~ 1 + x + x2 H1 vs H0 : Does x2 explain a significant extra amount of the variation?

41. PRACTICAL: hypothesis test for identifying QTLs To start: 1. Copy the folder faculty\valdar\AnimalModelsPractical to your own directory. 2. Start R 3. File -> Change Dir… and change directory to your AnimalModelsPractical directory 4. Open Firefox, then File -> Open File, and open “f2cross_and_thresholds.R” in the AnimalModelsPractical directory H0: phenotype ~ 1 H1: phenotype ~ a H2: phenotype ~ a + d Test: H1 vs H0 H2 vs H1 H2 vs H0

42. PRACTICAL: Chromosome scan of F2 cross

43. Two problems in QTL analysis • Missing genotype problem • Model selection problem

44. Missing genotype problem

45. Solutions to the missing genotype problem • Maximum likelihood interval mapping • Haley-Knott regression • Multiple imputation

46. Interval mapping

47. Interval mapping qq genotype 10 qQ genotype 20

48. Interval mapping qq genotype 10 qQ genotype 20

49. Interval mapping qq genotype 10 qQ genotype 20 Which is the true situation? qq qQ

50. Interval mapping qq genotype 10 qQ genotype 20 Which is the true situation? Fit both situations and then weight them qq 0.5 “mixture” model 0.5 qQ ML interval mapping