Fig 1 is a convenient way to study HW equilibrium Note that

Fig. 1 is a convenient way to study HW equilibrium. Note that the hypotenuse joins coordinate (0, 1) with (1, 0). For any point (P, R) inside the triangle, let H denote the distance such that (P + H, R) lies on the hypotenuse. Show the following: Show that P + R + H = 1 and therefore, any point denoted by P, R, H can denote the genotype probabilities (Pr(AA), Pr(aa), Pr(Aa)) of a diploid individual.

Solution

In the given right angled triangle, the right sides measure 1 each and Hypotenuse measures 1.414 (According to Pythagoras theorem)

And H is a distance such that the point (P+H, R) lies on the hypotenuse.

To Prove :

P+R+H = 1

To be on the hypotenuse,

For the point P+H = 1, R = 0 (at origin)

And for the point R = 1, P and H are 0 ( at origin)

Hence, P+H+R= 1 therefore any point denoted by P,R,H can denote the genotype probabilities (Pr(AA), Pr(aa), Pr(Aa)) of a diploid individual.