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  1. QTL mapping in animals

  2. QTL mapping in animals • It works

  3. QTL mapping in animals • It works • It’s cheap

  4. QTL mapping in animals • It works • It’s cheap • It’s relevant to human studies

  5. Genomic resource Nature December 5 2002

  6. No more crosses?

  7. In silico mapping

  8. Method

  9. Method

  10. F0 Parental Generation F1 Generation F2 Generation Interbreeding for approximately 20 generations to produce recombinant inbreds Recombinant Inbreds

  11. RI strain phenotypes

  12. RI strain genotypes

  13. QTL for airway responsiveness

  14. Power n -2 = (ta + tb)2/(s2QTL/s2RES) ta and tb are values on the t distribution corresponding to the desired a value s2QTL is the phenotypic variance explained by a QTL s2RES the unexplained variance.

  15. Experimentally verified QTL for airway responsiveness Zhang, Y. et al.A genome-wide screen for asthma-associated quantitative trait loci in a mouse model of allergic asthma. Hum. Mol. Genet. 8, 601-605 (1999).

  16. Inbred Strain Cross

  17. Quantitative Trait Locus Detection

  18. Marker QTL M r Q m q

  19. Marker QTL M r Q m q MM QQ Qq qq Mm QQ Qq qq mm QQ Qq qq

  20. Marker QTL MM QQ Mm QQ Mm QQ P (QQ | MM) = (1-r)2 P (Qq | MM) = 2r(1-r) P (qq | MM) = r2 (1-r)2 + 2r(1-r) + r2

  21. QTL Genotypic values Alleles at the QTL: q and Q Additive value: a Degree of dominance: d mQQ = m + 2a mQq = m + a(1+d) mqq = m

  22. Mean values for marker genotypes

  23. Mean values for marker genotypes

  24. Two things follow • Contrasts of single marker means can be used to detect QTL

  25. Example QTLeffects.xls

  26. Example REAL_DATA/Real data.xls

  27. Two things follow • Contrasts of single marker means can be used to detect QTL • Estimates of position and effect are confounded

  28. Additive and dominance estimates

  29. Flanking markers M1 M2 m1 m2

  30. Flanking markers M1 M2 m1 m2 M1M1 M2M2 M1M1 M2m2 M1M1 m2m2 M1m1 M2M2 M1m1 M2m2 M1m1 m2m2 m1m1 M2M2 m1m1 M2m2 m1m1 m2m2

  31. M1 Q M2 m1 q m2 Interval mapping r12 r1 r2

  32. M1 Q M2 m1 q m2 Interval mapping r12 r1 r2 r2 =( r12 – r1)/(1-2r1) No interference r2 = r12- r1 Complete interference

  33. M1 Q M2 m1 q m2 Interval mapping r12 r1 r2 M1M1 M2M2 p(M1QM2 | M1QM2) = ((1-r1) (1-r2)/2)2

  34. M1 Q M2 m1 q m2 Interval mapping r12 r1 r2 p(QQ|M1M1M2M2) = ((1-r1) 2(1-r2)2)/(1-r12)2 p(Qq|M1M1M2M2) = (2r1r2(1-r1) (1-r2) )/(1-r12)2 p(qq|M1M1M2M2) = (r12r22)/(1-r12)2

  35. Significance thresholds

  36. Permutation tests to establish thresholds Empirical threshold values for quantitative trait mapping GA Churchill and RW Doerge Genetics, 138, 963-971 1994 An empirical method is described, based on the concept of a permutation test, for estimating threshold values that are tailored to the experimental data at hand.

  37. Permutation tests Trait values are randomly reassigned to genotypes 10,000 re-samplings for 1% value

  38. Permutation tests • Robust to departures from normality • Robust to missing or erroneous data • Easy to implement

  39. Significance Thresholds Lander, E. Kruglyak, L. Genetic dissection of complex traits: guidelines for interpreting and reporting linkage resultsNature Genetics. 11, 241-7, 1995

  40. Maximum likelihood methods

  41. Maximum likelihood methods

  42. Maximum likelihood methods

  43. M1 Q M2 M1 q M2 Interval mapping r12 r1 r2

  44. M1 Q M2 M1 q M2 Interval mapping r12 r1 r2

  45. Maximum likelihoodTest statistic

  46. Example SIMULATED_DATA WinQTL