STA6178_2005(7) - Composite Method for QTL Mapping Zeng...

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Composite Method for QTL Mapping Zeng (1993, 1994) Limitations of single marker analysis Limitations of interval mapping The test statistic on one interval can be affected by QTL located at other intervals (not precise); Only two markers are used at a time (not efficient) Strategies to overcome these limitations Equally use all markers at a time (time consuming, model selection, test statistic) One interval is analyzed using other markers to control genetic background
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Foundation of composite interval mapping Interval mapping – Only use two flanking markers at a time to test the existence of a QTL (throughout the entire chromosome) Composite interval mapping – Conditional on other markers, two flanking markers are used to test the existence of a QTL in a test interval Note: An understanding of the foundation of composite interval mapping needs a lot of basic statistics. Please refer to A. Stuart and J. K. Ord’s book, Kendall’s Advanced Theory of Statistics , 5 th Ed, Vol. 2. Oxford University Press, New York.
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Assume a backcross and one marker Aa × aa Aa aa Mean Frequency ½ ½ 1 “Value” 1 0 ½ “Deviation” ½ Variance σ 2 = (½) 2 ×½ + (-½) 2 ×½ = ¼ Two markers, A and B : AaBb × aabb AaBb Aabb aaBb aabb Frequency ½(1-r) ½r ½r ½(1-r) “Value” ( A ) 1 1 0 0 “Value” ( B ) 1 0 1 0 Covariance σ AB = (1-2r)/4 Correlation = 1 - 2r
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Conditional variance: σ 2 | = σ 2 - σ 2  / σ 2 = ¼ - [(1-2r)/4] 2 /(¼) = r(1-r) For general markers, j and k, we have Covariance σ jk = (1 - 2r jk )/4 Correlation = 1 - 2r jk Conditional variance: σ 2 k|j = σ 2 k - σ 2 kj / σ 2 j = ¼ - [(1-2r jk )/4] 2 /(¼) = r jk (1-r jk )
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Three markers, j, k and l Covariance between markers j and k conditional on marker l: σ jk|l = σ jk - σ jl σ kl / σ 2 l = [(1-2r jk )-(1-2r jl )(1-2r kl )]/4
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STA6178_2005(7) - Composite Method for QTL Mapping Zeng...

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