One of the first Mendelian traits identified in humans was a dominant condition known as brachydactyly. This gene causes an abnormal shortening of the fingers or toes (or both). At the time, some researchers thought that the dominant trait would spread until 75 percent of the population would be affected (because the phenotypic ratio of dominant to recessive is 3: 1 ). Show that the reasoning was incorrect.

We are given the following information: - Dominant trait: brachydactyly (shortening of fingers and toes) - Phenotypic ratio: 3:1 (dominant:recessive)

Phenotypic ratio is 3:1, which means that 3 out of 4 individuals show the dominant trait, and 1 out of 4 individuals show the recessive trait. Let p be the frequency of the dominant allele (B) and q be the frequency of the recessive allele (b). Since B is dominant, BB and Bb genotypes will both show brachydactyly, while bb genotype will not. According to the phenotypic ratio: - 3 out of 4 individuals (BB and Bb) show the dominant trait (brachydactyly) - 1 out of 4 individuals (bb) show the recessive trait (normal fingers and toes) The frequency of the recessive genotype (bb) is 1/4 or 0.25. According to the Hardy-Weinberg equilibrium equation, q² = 0.25, where q is the frequency of the recessive allele (b).

Since we know that q² = 0.25, we can find the frequency of the recessive allele (q) by taking the square root of 0.25: q = sqrt(0.25) q = 0.5

Knowing the frequency of the recessive allele (q), we can calculate the frequency of the dominant allele (p) using the equation p + q = 1. p = 1 - q p = 1 - 0.5 = 0.5

Now that we have the frequencies of the dominant (p) and recessive (q) alleles, we can calculate the actual percentage of the population affected by the dominant trait. The percentage of the population with either the BB or Bb genotype (showing brachydactyly) is (p² + 2pq) * 100. Percentage = (0.5² + 2 * 0.5 * 0.5) * 100 Percentage = (0.25 + 0.5) * 100 Percentage = 0.75 * 100 Percentage = 75 The actual percentage of the population affected by the dominant trait (brachydactyly) is 75 percent, which is exactly the same as the researchers thought. However, it's important to note that the Hardy-Weinberg equilibrium provides a theoretical calculation when no other factors are involved (e.g., selection, migration, or mutation). In reality, the percentage of people affected by brachydactyly could be different due to these factors not being considered in this exercise.