Question

3) A friend of yours conducting field research in Indiana also claims that they have blue and pink daisies growing in their fields as well. Multiple harvests of daisies from Indiana fields were performed and genetic analysis determined that there are 6 times as many heterozygous blue daisies in the population as there are homozygous dominant blue daisies. a. What is the allelic frequency of blue and pink daisies in the Indiana field population?

Answer 1

Sol.

Here, blue daisies are dominant over pink daisies.

Let, allele P represents the dominant blue daisies and p represents the recessive pink daisies.

Genotype of the homozygous dominant blue daisies, heterozygous blue daisies and homozygous recessive pink daisies are PP, Pp and pp respectively.

As per the given data, there are 6 times as many heterozygous blue daisies in the population as there are homozygous dominant blue daisies.

Let frequency of homozygous dominant blue daisies be x and frequency of homozygous recessive pink daisies be y

So, the frequency of heterozygous blue daisies will be equal to 6x.

Now, using Hardy-Weinberg equilibrium equation, we can easily determine the frequency of homozygous recessive pink daisies as follows:

p^2 +2pq+ q^2 = 1

Here,p represents the frequency of homozygous dominant blue daisies,pq represents the frequency of heterozygous blue daisies and q represents the frequency of recessive pink daisies.

Putting p=x, pq=6x and q=y, in the above equation, we get x^2 + 2*6x + y^2 = 1

y^2 = -x^2 - 12x + 1

Solving this equation, by the formula for quadratic equation, we get

x = [-(-12)±√{(-12)^2 - 4*(-1)*1}]/2(-1)

=(12±2√37)/(-2)

x(1)=(12+2√37)/(-2)

= -12.08

x(2)=(12-2√37)/(-2)

=0.08

Since, frequency can never be negative,so x(1) can't be accepted.

Hence, the frequency of homozygous dominant blue daisies will be x= 0.08

Now, putting the value of x=0.08 in the equation for y, we get

y^2 = -x^2 - 12x + 1

= -(0.08)^2 - 12*0.08 + 1

= -0.0064 - 0.96 +1

= 0.0336

y= 0.18

Hence the frequency of homozygous recessive pink daisies will be equal to y = 0.18

Also, the frequency of heterozygous blue daisies will be equal to 6x= 0.48

So, the allelic frequencies of homozygous dominant blue, heterozygous blue and homozygous recessive pink daisies in the Indiana field population are 0.08 , 0.48 and 0.18 respectively.