Question

problem 1
in a population of 500 frogs, 20 show a recessive trait for skin color. assuming the trait is determined by a single gene with dominant and recessive alleles, calculate:

• the frequency of the recessive allele (q)

0.2
the frequency of the dominant allele (p)
0.8
the percentage of heterozygous frogs in the population

Explanation:

Step1: Calculate recessive genotype freq.

First, find the frequency of the recessive genotype ($q^2$).
$q^2 = \frac{20}{500} = 0.04$

Step2: Find recessive allele freq. ($q$)

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

Step3: Find dominant allele freq. ($p$)

Use the Hardy-Weinberg equation $p + q = 1$.
$p = 1 - q = 1 - 0.2 = 0.8$

Step4: Calculate heterozygous frequency

Use the Hardy-Weinberg term for heterozygotes: $2pq$.
$2pq = 2 \times 0.8 \times 0.2 = 0.32$
Convert to percentage: $0.32 \times 100 = 32\%$

Answer:

• The frequency of the recessive allele (q): $0.2$
• The frequency of the dominant allele (p): $0.8$
• The percentage of heterozygous frogs in the population: $32\%$