Take the 2-minute tour ×
Biology Stack Exchange is a question and answer site for biology researchers, academics, and students. It's 100% free, no registration required.

According to [wiki][2], linkage disequilibrium $D$ equals

$$D = x_{11} - p_1\cdot q_1$$

where:

$$ \begin{matrix} \text{Haplotype} & \text{Frequency}\\ A_1B_1 & x_{11}\\ A_{1}B_{2} & x_{12} \\ A_{2}B_{1} & x_{21} \\ A_{2}B_{2} & x_{22} \\ \end{matrix} $$

and

$$ \begin{matrix} \text{Allele} & \text{Frequency}\\ A_{1} & p_{1}=x_{11}+x_{12} \\ A_{2} & p_{2}=x_{21}+x_{22} \\ B_{1} & q_{1}=x_{11}+x_{21} \\ B_{2} & q_{2}=x_{12}+x_{22} \\ \end{matrix} $$

According to [Hartl and Clark][3], linkage disequilibrium $D$ equals:

$$D = x_{11}x_{22}-x_{12}x_{21}$$

Question

Can you please prove that these two formulations of linkage disequilibrium are equivalent (assuming that they are equivalent)? If they're not… Do we use different definitions? What are their respective meanings?

share|improve this question
    
none of your references seem to have links? –  shigeta Apr 24 at 17:12

1 Answer 1

up vote 2 down vote accepted

Just need to solve the equation. p1 = X11 + X12; q1 = X11 + X21; 1 = X11 + X12 + X21 + X22.

D = X11 - (X11 + X12) * (X11 + X21)

D = X11 - (X11X11 + X11X21 + X11X12 + X12X21)

D = X11 - X11X11 - X11X21 - X11X12 - X12X21

D = X11 * (1 - X11) - X11X21 - X11X12 - X12X21

D = X11 * (X11 + X12 + X21 + X22 - X11) - X11X21 - X11X12 - X12X21

D = X11 * (X12 + X21 + X22) - X11X21 - X11X12 - X12X21

D = X11X12 + X11X21 + X11X22 - X11X21 - X11X12 - X12X21

D = X11X22 - X12X21

Sorry for the very long answer, but I thought it would be more clear if I wrote everything out.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.