Question

Linkage Disequilibirum:

Can someone please help me understand the solutions given to these 2 questions? I cannot understand the logical progression of the equation.

Question 1: Show that the gamete frequencies as a function of D are correct inthe table given.

And question 2: Show that the definition of D given below is consistent with theexpressions for gamete frequencies above by substituting p1p2 + D forx1 and the equivalent expressions for the other gametes into the rightside of the equation. [This involves many cancellations, ending with alone D]

X1X4. X2X3 A1B1 A2B1 A2B2 Gamete: A1B2 Frequency: Frequency p1 p2 D piq2 D q1p2 D q1 q2 D Allele frequencies A1B1: A1: p1 X1 X. (x1 x2)(x1 x3) x1x4 -x2x3 B1: p2 X1 X. -xi +x1x3 x1x2 x2x3 x1x4 X2X3 A2: q1 x1(x1 x2 x3 x4) x2x3 x2x3 x1 B2: q Xa x4 A1B2: (x1 x2)(x2 x4) (x1x4 x2x3) x1x2 x1x4 +x2x4 x1 x2 (x1 x2 x3 x4) 1- 4 x1x4 x2

Show transcribed image text X1X4. X2X3 A1B1 A2B1 A2B2 Gamete: A1B2 Frequency: Frequency p1 p2 D piq2 D q1p2 D q1 q2 D Allele frequencies A1B1: A1: p1 X1 X. (x1 x2)(x1 x3) x1x4 -x2x3 B1: p2 X1 X. -xi +x1x3 x1x2 x2x3 x1x4 X2X3 A2: q1 x1(x1 x2 x3 x4) x2x3 x2x3 x1 B2: q Xa x4 A1B2: (x1 x2)(x2 x4) (x1x4 x2x3) x1x2 x1x4 +x2x4 x1 x2 (x1 x2 x3 x4) 1- 4 x1x4 x2