Class 3

• 1. Construction of genetic maps

• 2. Single marker QTL analysis

• 3. QTL cartographer

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 r1, …, rm denote the recombination fractions for consecutive intervals.

• Let n1, …, nm denote the observed number of recombinations in consecutive intervals

Genetic maps 2

• The corresponding likelihood function

• Maximum likelihood estimates of r1, …, rm

m

i

nni

nim

ii rrrrL1

1 )1(),,(

n

nr ii ˆ

Building linkage groups

• Testing for H0: ri=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

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)

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.

• 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.

Example 1

B C D E

A 0.09 0.56 0.50 0.55

B 0.50 0.51 0.50

C 0.17 0.30

D 0.16

Example 2

B C D

A 0.09 0.19 0.17

B 0.26 0.22

C 0.32

Xia- genotype of i-th individual at locus a

Xia = 1/2 - individual is heterozygous at locus a

Xia = -1/2 - individual is homozygous at locus a Data for QTL mapping

Y1,...,Yn - vector of trait values for n backcross individuals

X=[Xij], 1 ≤ i ≤ n, 1 ≤ j ≤ m - genotypes of m markers

Single marker QTL analysis

Single marker analysis

• Student test.

• Regression approach

• F2 population (possibility of detecting dominance) – ANOVA or regression.

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

• 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

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’’