STA6178_2005(1) - Human Chromosomes Male Xy X y Female XX X...

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Unformatted text preview: Human Chromosomes Male Xy X y Female XX X XX Xy Daughter Son Gene, Allele, Genotype, Phenotype Chromosomes from Father Mother Gene A , with two alleles A and a Genotype Phenotype AA 185 100 AA 182 104 Aa 175 103 Aa 171 102 aa 155 101 aa 152 103 Height IQ Regression model for estimating the genotypic effect Phenotype = Genotype + Error y i = x i j + e i x i is the indicator for QTL genotype j is the mean for genotype j e i ~ N (0, 2 ) The genotypes for the trait are not observable and should be predicted from linked neutral molecular markers (M) Uniqueness for our genetic problem M 1 M 2 M 3 M m QTL . . . Our task is to construct a statistical model that connects the QTL genotypes and marker genotypes through observed phenotypes The genes that lead to the phenotypic variation are called Quantitative Trait Loci (QTL) Subject Marker (M) Genotype frequency M 1 M 2 M m Phenotype (y) QQ ( 2 ) Qq ( 1 ) qq ( ) 1 AA (2) BB (2) y 1 2 AA (2) BB (2) ... y 2 3 Aa (1) Bb (1) ... y 3 4 Aa (1) Bb (1) ... y 4 5 Aa (1) Bb (1) ... y 5 6 Aa (1) bb (0) ... y 6 7 aa (0) Bb (1) ... y 7 8 aa (0) bb (0) y 8 Data Structure n = n 22 + n 21 + n 20 + n 12 + n 00 + n 02 + n 01 + n 00 Parents AA aa F 1 Aa F 2 AA A a aa Finite mixture model for estimating genotypic effects y i ~ p ( y i | , ) = f 2 ( y i ) + f 1 ( y i ) + f ( y i ) QTL genotype ( j ) QQ Qq qq Code 2 1 f j ( y i ) is a normal distribution density with mean j and variance 2 = ( 2 , 1 , ), = ( 2 ) where [ ] [ ] [ ] [ ] [ ] = = = = = + + = + + + + + + = + + = n i i i i i i i n i i i i n i i i i n i i i i n i i i i y f y f y f y f y f y f y f y f y f y f y f y f y f y f y f 1 | | | 1 00 | 00 | 00 | 1 21 | 21 | 21 | 1 22 | 22 | 22 | 1 4 1 2 1 4 1 ) ( ) ( ) ( ) ( ) ( ) ( ... ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 00 21 22 1 1 2 22 1 1 2 2 1 1 2 2 1 1 2 2 1 2 j | i is the conditional (prior) probability of QTL genotype j (= 2, 1, 0) given marker genotypes for subject i (= 1, , n )....
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This note was uploaded on 12/01/2011 for the course STA 6178 taught by Professor Staff during the Fall '11 term at University of Florida.

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STA6178_2005(1) - Human Chromosomes Male Xy X y Female XX X...

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