Answer to Question #184580 in Evolution for Kaylee Flowers

Question

In Drosophilia, the allele for normal length wings is dominant over the allele for vestigial wings. In a population of 1,000 individuals, 360 show the recessive phenotype. How many individuals would you expect to be homozygous dominant?

Answer 1

Use the Harvey-Weinberg Equations:

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

where $p^2$ = homozygous dominant

2pq = heterozygous dominant,

and $q^2$ = homozygous recessive

360 out of 1000 show recessive phenotype: q^2. This equates to 36%,

or 0.36. So, q must be equal to 0.6 as it is the square root of 0.36.

Using p + q = 1, and the fact that q is 0.6, solve for p.

p = 1 – q

So, p is equal to 0.4.

Homozygous dominant is rewritten as $p^2: (0.4)^2 = 0.16$ or 16%.

Since 16% of the 1,000 individuals are homozygous dominant, multiply

$0.16 \times 1000$ to get number: 160 individuals are homozygous dominant.