p p p Locus B Totals AB A B B b p p p p ( 1 - PowerPoint PPT Presentation

Linkage Equilibrium Expected for Distant Loci Haplotype Frequencies � p p p Locus B Totals AB A B B b � � � p p p p ( 1 p ) Locus A A p p p Ab A b A B AB Ab A a p p p � � � p p p ( 1 p ) p aB ab a aB a B A B � � � � p p p ( 1 p )( 1 p ) Totals p p 1 . 0 B b ab a b A B Linkage Disequilibrium Expected for Nearby Loci Disequilibrium Coefficient D AB � � D p p p � p p p AB AB A B AB A B � � p p p D � � � AB A B AB p p p p ( 1 p ) � � Ab A b A B p p p D Ab A b AB � � � p p p ( 1 p ) p � � p p p D aB a B A B aB a B AB � � � � � � p p p ( 1 p )( 1 p ) p p p D ab a b AB ab a b A B

D AB is hard to interpret What is the range of D AB ? � What are the maximum and minimum possible values of D AB when � Sign is arbitrary … • p A = 0.3 and p B = 0.3 • A common convention is to set A, B to be the • p A = 0.2 and p B = 0.1 common allele and a, b to be the rare allele � Can you derive a general formula for this � Range depends on allele frequencies range? • Hard to compare between markers D’ – A scaled version of D More on D’ � Pluses: � D � AB D 0 � • D’ = 1 or D’ = -1 means no evidence for � AB min( p p , p p ) � D ' � A B a b AB D recombination between the markers � � AB D 0 AB � • If allele frequencies are similar, high D’ means min( p p , p p ) � A b a B the markers are good surrogates for each other � Ranges between –1 and +1 � Minuses: • More likely to take extreme values when allele • D’ estimates inflated in small samples frequencies are small • � 1 implies at least one of the observed haplotypes • D’ estimates inflated when one allele is rare was not observed

� ² (also called r 2 ) More on r 2 � r 2 = 1 implies the markers provide exactly the 2 D � � ² AB same information � � p ( 1 p ) p ( 1 p ) A A B B � ² � The measure preferred by population � geneticists 2 n � Ranges between 0 and 1 � Measures loss in efficiency when marker A is • 1 when the two markers provide identical information replaced with marker B in an association study • 0 when they are in perfect equilibrium • With some simplifying assumptions (e.g. see Pritchard � Expected value is 1/2 n and Przeworski, 2001)