STA6178_2005(5) - QTL Mapping Quantitative Trait Loci...

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QTL Mapping Quantitative Trait Loci (QTL): A chromosomal segments that contribute to variation in a quantitative phenotype
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Maize Teosinte tb-1 / tb-1 mutant maize
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Mapping Quantitative Trait Loci (QTL) in the F2 hybrids between maize and teosinte
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Nature 432 , 630 - 635 (02 December 2004) The role of barren stalk1 in the architecture of maize ANDREA GALLAVOTTI(1,2), QIONG ZHAO(3), JUNKO KYOZUKA(4), ROBERT B. MEELEY(5), MATTHEW K. RITTER1,*, JOHN F. DOEBLEY( 3), M. ENRICO PÈ(2) & ROBERT J. SCHMIDT(1) 1 Section of Cell and Developmental Biology, University of California, San Diego, La Jolla, California 92093-0116, USA 2 Dipartimento di Scienze Biomolecolari e Biotecnologie, Università degli Studi di Milano, 20133 Milan, Italy 3 Laboratory of Genetics, University of Wisconsin, Madison, Wisconsin 53706, USA 4 Graduate School of Agriculture and Life Science, The University of Tokyo, Tokyo 113-8657, Japan 5 Crop Genetics Research, Pioneer-A DuPont Company, Johnston, Iowa 50131, USA * Present address: Biological Sciences Department, California Polytechnic State University, San Luis Obispo, California 93407, USA
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Effects of ba1 mutations on maize development Mutant Wild type No tassel Tassel
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A putative QTL affecting height in BC Sam- Height QTL ple (cm, y) genotype 1 184 Qq (1) 2 185 Qq (1) 3 180 Qq (1) 4 182 Qq (1) 5 167 qq (0) 6 169 qq (0) 7 165 qq (0) 8 166 qq (0) If the QTL genotypes are known for each sample, as indicated at the left, then a simple ANOVA can be used to test statistical significance.
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Suppose a backcross design Parent QQ (P1) x qq (P2) F1 Qq x qq (P2) BC Qq qq Genetic effect a* 0 Genotypic value μ +a* μ
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QTL regression model The phenotypic value for individual i affected by a QTL can be expressed as, y i = μ + a* x* i + e i where is the overall mean, x* i is the indicator variable for QTL genotypes, defined as x* i = 1 for Qq 0 for qq , a* is the “real” effect of the QTL and e i is the residual error, e i ~ N(0, σ 2 ). x* i is missing
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Data format for a backcross Sam- Height Marker genotype QTL ple (cm, y) M 1 M 2 Aa aa 1 184 Mm (1) Nn (1) ½ ½ 2 185 Mm (1) Nn (1) ½ ½ 3 180 Mm (1) Nn (1) ½ ½ 4 182 Mm (1) nn (0) ½ ½ 5 167 mm (0) nn (1) ½ ½ 6 169 mm (0) nn (0) ½ ½ 7 165 mm (0) nn (0) ½ ½ 8 166 mm (0) Nn (0) ½ ½ Observed data Missing data Complete data = +
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Two statistical models I - Marker regression model y i = μ + ax i + e i where • x i is the indicator variable for marker genotypes defined as x i = 1 for Mm 0 for mm , a is the “effect” of the marker (but the marker has no effect. There is the a because of the existence of a putative QTL linked with the marker) e i ~ N(0, σ 2 )
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Heights classified by markers (say marker 1) Marker Sample Sample Sample group size mean variance Mm n 1 = 4 m 1 =182.75 s 2 1 = mm n 0 = 4 m 0 =166.75 s 2 0 =
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The hypothesis for the association between the marker and QTL H 0 : m 1 = m 0 H 1 : m 1 m 0 Calculate the test statistic: t = (m 1 –m 0 )/ [s 2 (1/n 1 +1/n 0 )], where s 2
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STA6178_2005(5) - QTL Mapping Quantitative Trait Loci...

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