Question

Achondroplasia is a dominant trait that causes a characteristic form of dwarfism. In a survey of 50,000 births, five infants with achondroplasia were identified. Three of the affected infants had affected parents, while two had normal parents. Calculate the mutation rate for achondroplasia and express the rate as the number of mutant genes per given number of gametes.

Short answer

Answer: The mutation rate for achondroplasia is 1 mutant gene per 12,500 gametes.

Step-by-step solution

Determine the proportion born to normal parents

Given that there are two infants with achondroplasia born to normal parents, the proportion of infants with achondroplasia born to normal parents is: Proportion = (Number of affected infants born to normal parents) / (Total number of affected infants) Proportion = 2 / 5

Calculate the mutation rate per birth

To calculate the mutation rate per birth, divide the number of affected infants born to normal parents by the total number of births: Mutation rate per birth = (Number of affected infants born to normal parents) / (Total number of births) Mutation rate per birth = 2 / 50,000

Convert the mutation rate per birth to the mutation rate per gamete

Since there are two gametes (sperm and egg) for each birth and the mutation can occur in either, multiply the mutation rate per birth by 2 to get the mutation rate per gamete: Mutation rate per gamete = 2 * (Mutation rate per birth) Mutation rate per gametype= 2 * (2 / 50,000)

Simplify the expression

Now, simplify the expression to find the mutation rate per gamete: Mutation rate per gamete = 4 / 50,000 Mutation rate per gamete = 1 / 12,500 The mutation rate for achondroplasia is 1 mutant gene per 12,500 gametes.