1. Class 3 1. Construction of genetic maps 2. Single marker QTL analysis 3. QTL cartographer

2. Genetic maps 1 Under the assumption of no interference the number of crossovers in disjoint intervals are independent. Consider one linkeage group in the backcross population. Let r 1, …, r m denote the recombination fractions for consecutive intervals. Let n 1, …, n m denote the observed number of recombinations in consecutive intervals

3. Genetic maps 2 The corresponding likelihood function Maximum likelihood estimates of r 1, …, r m

4. Building linkage groups Testing for H 0 : r i =1/2 Be aware of the multiple testing problem Usually stringent test criteria are used e.g. in (Doerge 1996) the critical p-value=2*10 -4

5. Deciding on the order of markers Maximizing the likelihood function over all possible marker orders. Minimizing the total length of the map. Computationally involved Alternative – rapid chain delineation (Doerge, 1996)

6. Rapid chain delineation 1. Choose the pair of markers with the smallest distance estimate 2. Add the next marker, closest to ones already in the chain. 3. Repeat step 2 as long as there any markers left.

7. 4. Check if changing the order of any two neigboring markers improves the objective function. 5. Check if changing the order within any triplet of neigboring markers improves the objective function.

8. Example 1 BCDE A0.090.560.500.55 B0.500.510.50 C0.170.30 D0.16

9. Example 2 BCD A0.090.190.17 B0.260.22 C0.32

10. X ia - genotype of i-th individual at locus a X ia = 1/2 - individual is heterozygous at locus a X ia = -1/2 - individual is homozygous at locus a Data for QTL mapping Y 1,...,Y n - vector of trait values for n backcross individuals X=[X ij ], 1 ≤ i ≤ n, 1 ≤ j ≤ m - genotypes of m markers Single marker QTL analysis

11. Single marker analysis Student test. Regression approach F2 population (possibility of detecting dominance) – ANOVA or regression.

12. QTL Cartographer Your data Backcross population Marker genotypes 22 markers spaced every 10 cM on two chromosomes (11 markers on each). 500 individuals Rows correspond to markers. Coding : 0 – homozygote, 1 -heterozygote

13. Trait data for 500 individuals Before entering the data to QTL Cartographer Change the coding for marker genotypes from 1.00000+e01 to 1 (the same with 0) In the file with trait values change a dot for a comma Add a trait name at the top of a file

14. QTL Cartographer To create a new data set Click New and follow the instructions While entering a map information it is better to copy it from the previously prepared text file than to use a Cartographer editor. When entering a marker data click on the icon ``arranged in marker order’’