Final answer:
The expected frequency of individuals with the homozygous recessive genotype in a population of butterflies is 0.04 when the frequency of the recessive allele is 0.2 and the population is in Hardy-Weinberg equilibrium.
Step-by-step explanation:
In a population of butterflies, the frequency of the recessive allele for a particular trait is 0.2.
In Hardy-Weinberg equilibrium, the frequency of individuals with the homozygous recessive genotype can be calculated using the Hardy-Weinberg equation: p² + 2pq + q² = 1.
In this equation, p² represents the frequency of the homozygous dominant genotype, 2pq represents the frequency of the heterozygous genotype, and q² represents the frequency of the homozygous recessive genotype.
Since q represents the frequency of the recessive allele, which is 0.2, we can substitute this value into the equation to find the frequency of the homozygous recessive genotype:
q² = (0.2)²
= 0.04
So, the expected frequency of individuals with the homozygous recessive genotype is 0.04.