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.

Verified step by step guidance

1. Identify the key information: Achondroplasia is a dominant trait, 50,000 births were surveyed, 5 infants had achondroplasia, 3 had affected parents, and 2 had normal parents.
2. Understand that affected infants with normal parents represent new mutations, since achondroplasia is dominant and the parents are unaffected (homozygous normal).
3. Calculate the total number of gametes that contributed to the 50,000 births. Since each individual has two parents, the total number of gametes is twice the number of births: \$2 \times 50,000$.
4. Determine the number of new mutations, which is equal to the number of affected infants with normal parents (2 in this case).
5. Calculate the mutation rate by dividing the number of new mutations by the total number of gametes: mutation rate = \(\frac{\text{number of new mutations}}{\text{total number of gametes}} = \frac{2}{2 \times 50,000}\).

Key Concepts

Dominant Inheritance

Dominant inheritance means that only one copy of a mutant allele is needed for the trait to be expressed. In achondroplasia, individuals with one mutant gene show the dwarfism phenotype, so affected parents can pass the trait directly to offspring. Understanding dominance helps interpret how traits appear in families.

Mutation Rate Calculation

Mutation rate is the frequency at which new mutations arise in a gene per generation. It can be estimated by comparing the number of affected individuals with no affected parents (new mutations) to the total number of gametes in the population. This rate is often expressed as mutations per number of gametes.

Gametes and Population Genetics

Gametes are reproductive cells (sperm and eggs) that carry genes to the next generation. In population genetics, the total number of gametes is twice the number of individuals because each individual produces two gametes. This concept is essential for calculating mutation rates in a population.