1000 fruit flies in HWE red eye dominant sepia eye recessi

1000 fruit flies in HWE red eye = dominant sepia eye = recessive 640 red. How many are \"true breeding\" red? Find g^2! 1000 - 640 = # r r = g^2 find g find p p^2 = true breeding red freq times 1000 = # true breeding red

Solution

We use the Hardy-Weinberg equation which will give us the frequencies of the different genotypes that are available here ->(PP, Pp, and pp) along with the frequencies of the alleles here.

We have in tootal 1000 fruit flies, andas it is given 640 of them have red eyes. This gives us the conclusion that 360 have sepia eyes(1000-640).

According to The Hardy-Weinberg equation we have:

p + q = 1, where p is defined as the frequency of one given allele (it is the dominant allele) and on the other hand q is the frequency of the other allele (which is usually recessive allele). Now when we square both sides of the equation, we will get the following:

p + q = 1
(p + q)^2 = 1^2
p^2 + 2pq + q^2 = 1,

In these equations we have p^2 which is the frequency of the homozygous dominant genotype,Moreover the 2pq is the frequency of the heterozygous genotype and   finally we have the q^2 which is the frequency of the recessive genotype.

Now if 360 flies out of 1000 have sepia eyes

=>Then the frequency of the given recessive phenotype will be 360/1000 = 0.36

Moreover the recessive phenotype   usually results only from the homozygous recessive genotype situation,

=>The frequency of the recessive genotype is equal to the frequency of the recessive phenotype,

so that q^2 = 0.36,

so we get the q = 0.6

since p + q = 1,

then p = 1 - q = 1 - 0.6 = 0.4

Now we have the frequency of the homozygous dominant genotype is p^2 = (0.4)^2 = 0.16

On the otherhans the frequency of the heterozygous genotype is 2pq = 2 * 0.4 * 0.6 = 0.48



p^2 + 2pq + q^2 = 1
0.16 + 0.48 + 0.36 = 1

Now the frequency of individuals whi ch are usually homozygous for red eye color is given by p^2 and is 0.16

As a result the number of individuals in the population of 1000 which will be   homozygous for red eye color is given by 0.16 * 1000 = 160