Question

problem 3
in a population of 2,500 beetles, 100 are homozygous recessive for a wing shape
trait. determine:

• the frequency of the recessive allele (q)

• the frequency of the dominant allele (p)

• the expected number of heterozygous beetles

Explanation:

Step1: Calculate recessive genotype frequency

First, find the frequency of the homozygous recessive genotype ($q^2$) by dividing the number of homozygous recessive beetles by the total population.
$q^2 = \frac{100}{2500} = 0.04$

Step2: Find recessive allele frequency (q)

Take the square root of $q^2$ to get the frequency of the recessive allele.
$q = \sqrt{0.04} = 0.2$

Step3: Find dominant allele frequency (p)

Use the Hardy-Weinberg equilibrium equation $p + q = 1$ to solve for p.
$p = 1 - q = 1 - 0.2 = 0.8$

Step4: Calculate heterozygote frequency

Use the Hardy-Weinberg term for heterozygotes ($2pq$) to find their frequency, then multiply by the total population to get the number of heterozygous beetles.
$2pq = 2 \times 0.8 \times 0.2 = 0.32$
Number of heterozygous beetles = $0.32 \times 2500 = 800$

Answer:

• The frequency of the recessive allele (q): $0.2$
• The frequency of the dominant allele (p): $0.8$
• The expected number of heterozygous beetles: $800$