Question

A population of flour beetles has 1,000 individuals. Normally the beetles are red; however, this population is polymorphic for a mutant autosomal body color, black, designated by bb. Red is dominant to black, so BB and Bb genotypes are red. Assume the population is at Hardy-Weinberg equilibrium, with equal frequencies of the two alleles. What would be the expected frequencies of the homozygous dominant, heterozygous, and homozygous recessive genotypes (in that order) after 100 generations, assuming that no selection or other evolutionary processes were operating?

Answer 1

At Hardy-Weinberg equilibrium with equal allele frequencies, the expected genotype frequencies of homozygous dominant, heterozygous, and homozygous recessive in the flour beetle population remain 0.25, 0.50, and 0.25 respectively, even after 100 generations.

Step-by-step explanation:

If we have a population of flour beetles at Hardy-Weinberg equilibrium with equal frequencies of the two alleles (B for red and b for black), we can calculate the expected genotype frequencies even after 100 generations, assuming no evolutionary processes affect these frequencies.

Given that allele frequencies are equal, we designate p (the frequency of the dominant allele B) and q (the frequency of the recessive allele b) both as 0.5 since p + q = 1. Utilizing the Hardy-Weinberg principle which states that the genotype frequencies in a population can be represented as p² + 2pq + q² = 1, we can calculate:

• The frequency of homozygous dominant (BB) as p² = (0.5)² = 0.25
• The frequency of heterozygous (Bb) as 2pq = 2(0.5)(0.5) = 0.50
• The frequency of homozygous recessive (bb) as q² = (0.5)² = 0.25

Therefore, without any selection or other evolutionary processes interfering, the expected frequencies of the homozygous dominant, heterozygous, and homozygous recessive genotypes will remain at 0.25, 0.50, and 0.25, respectively, even after 100 generations.