A large population of land turtles on an isolated island has two alleles that determine shell thickness. The allele for thicker shells is dominant over the allele for thinner shells, which occurs at a frequency of 20%. Assuming Hardy-Weinberg equilibrium, what should be the frequency of homozygous thicker-shell turtles in the population?

Explanation

To find the frequency of homozygous thicker-shell turtles in the population, we use the Hardy-Weinberg principle. This principle provides a mathematical model to calculate the genetic variation in a population under certain conditions. The alleles are represented as follows: Let p denote the frequency of the dominant allele (thicker shell). Let q denote the frequency of the recessive allele (thinner shell). We are told that the frequency of the thinner shell allele (recessive, represented as q²) is 20%. Thus, we can express this as: q² = 0.20 To find q, we take the square root of both sides: q = √0.20 ≈ 0.447 Next, we know that the sum of the frequency of dominant and recessive alleles must equal 1: p + q = 1 So we can calculate p: p = 1 - q Substituting the value we found for q: p = 1 - 0.447 ≈ 0.553 Finally, to find the frequency of homozygous dominant (thicker shell) turtles, we find p²: p² = (0.553)² ≈ 0.305 Now, to find the percentage, we multiply by 100: 0.305 × 100 ≈ 30.5% Thus, the frequency of homozygous thicker-shell turtles in the population is approximately 30.5%, meaning it does not correspond to any of the provided options (A. 4%, B. 16%, C. 50%, D. 64%). However, if the question intended for a clear value based on 20% being passed as 0.2 in Hardy-Weinberg terms, we know that typically the number for homozygous dominant patterns can be related back to the standard calculations from the squared terms in the Hardy-Weinberg equations.