Question

In a large, randomly mating herd of cattle, 16 percent of the newborn calves have a certain type of dwarfism because of a homozygous recessive allele. Assume Hardy-Weinberg frequencies.

a. What is the frequency of the recessive dwarfing allele?

Answer 1

The frequency of the recessive dwarfing allele can be calculated using the Hardy-Weinberg equation, which in this case gives a frequency of 40%.

Step-by-step explanation:

The frequency of the recessive dwarfing allele can be calculated using the Hardy-Weinberg equation, which is p2 + 2pq + q2 = 1. Here, p represents the frequency of the dominant allele, q represents the frequency of the recessive allele, and p2 and q2 represent the frequencies of the homozygous dominant and homozygous recessive genotypes, respectively.

In this case, we are given that 16 percent of the newborn calves have the recessive dwarfism phenotype, which means q2 = 0.16. To find q, we can take the square root of 0.16: q = √0.16 = 0.4. Since p + q = 1, we can calculate p as well: p = 1 - q = 1 - 0.4 = 0.6.

Therefore, the frequency of the recessive dwarfing allele is 0.4 or 40%.