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Linkage disequilibrium D equals

$D=x_{11}−p1⋅q1$

where:

Haplotype Frequency

$A_{1}B_{1} = x_{11}$

$A_{1}B_{2} = x_{12}$

$A_{2}B_{1} = x_{21}$

$A_{2}B_{2} = x_{22}$

and

Allele Frequency

$A_{1}=p_{1}= x_{11}+x_{12}$

$A_{2} = p_{2}=x_{21}+x_{22}$

$B_{1} = q_{1}=x_{11}+x_{21}$

$B_{2} = q_{2}=x_{12}+x_{22}$

Shouldn't:

1) $D = x_{11}-p_{1}q_{1}$ or $x_{11} = p_{1}q_{1}+D $

2) $**D= x_{12}-p_{1}q_{2}$ or $x_{12} = p_{1}q_{2}+D**$

3) $**D= x_{21}-p_{2}q_{1}$ or $x_{21} = p_{2}q_{1}+D**$

4) $D= x_{22}-p_{2}q_{2}$ or $x_{22} = p_{2}q_{2}+D$

Why do all the papers show:

1) $x_{11}=p_{1}q_{1}+D$

2) $**x_{12}=p_{1}q_{2}-D**$

3) $**x_{21}=p_{2}q_{1}-D**$

4) $x_{22}=p_{2}q_{2}+D$

ex: http://en.wikipedia.org/wiki/Linkage_disequilibrium

Question:

why for the relationship between the haplotype frequencies and allele frequencies and D is there a difference in sign. In other words by the formula shouldn't it always be +D rather than -D?

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  • $\begingroup$ Your question would be more appreciable if you'd use MathJax. For example "x12=p1q2-D" becomes "$X_{12}=p_1q_1-D$" by writing "X_{12}=p_1q_1-D" between dollar signs. More info about MathJax here $\endgroup$ – Remi.b Sep 17 '14 at 1:45

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