We know that Hardy-Weinberg conditions include the following equations:
[tex] p^{2}+2pq+ q^{2}=1 [/tex]
where [tex] p+q=1 [/tex]
And where p = dominant, and q = recessive; this means that [tex] p^{2} [/tex] is equal to the homozygous dominant, [tex] 2pq [/tex] is the heterozygous, and [tex] q^{2} [/tex] is the homozygous recessive .
So we have 100 total cats, with 4 having the recessive white coat color. That means we have a ratio of [tex] \frac{4}{100} [/tex] or 0.04. Let that equal our [tex] q^{2} [/tex] value.
So when we solve for q, we get:
[tex] q^{2}=0.04 [/tex]
[tex] q=\sqrt{0.04} =0.2 [/tex]
Now that we have our q value, we can use the other equation to find p:
[tex] p+q=1 [/tex]
[tex] p+0.2=1 [/tex]
[tex] p=0.8 [/tex]
So then we can solve for our heterozygous population:
[tex] 2pq=2(0.8)(0.2)=0.32 [/tex]
This is the ratio of the population. So we then multiply this number by 100 to get the number of cats that are heterozygous:
[tex] 0.32*100=32cats [/tex]
So now we know that there are 32 heterozygous cats in the population.
