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 bmutation rate for achondroplasia and express the rate as the num- ber of mutant genes per given number of gametes.

Short answer

Answer: The estimated mutation rate for achondroplasia is 1 in 50,000 genes.

Step-by-step solution

Determine the genotypes of the parents

To determine the mutation rate, we must first analyze the genotypes of the parents. We know that achondroplasia is a dominant trait, so an affected individual would have the genotype Aa (where A represents the dominant achondroplasia gene and a represents the recessive gene). Since, two infants have normal parents, their genotypes would be aa.

Calculate the probability of having an affected child

Now that we know the genotypes of the parents, we can calculate the probability of having an affected child. Let's denote P(Aa|aa) as the probability of a child having achondroplasia given that both parents are normal. Since there were two affected infants with normal parents, this probability would be calculated as: P(Aa|aa) = (Number of affected infants with normal parents) / (Total number of infants in the survey) = 2 / 50,000

Estimate the mutation rate

The mutation rate can be estimated by using the probability of having an affected child with normal parents (P(Aa|aa)). To get the number of mutant genes per gamete in each parent, we can divide this probability by 2 (since a child inherits one gamete from each parent): Mutation rate = P(Aa|aa) / 2 = (2 / 50,000) / 2 = 1 / 50,000 So the mutation rate for achondroplasia is 1 in 50,000 genes.

Key concepts

Understanding Genetics

Genetics is the science that explains how traits are passed from parents to their offspring through genes. Genes are units of heredity made up of DNA and are responsible for various biological characteristics. Each individual receives a set of genes from both the mother and father, making up the genetic constitution known as the genotype.

Humans have two copies of each gene, one inherited from each parent. These genes can be dominant or recessive; a dominant gene will express its trait even if there is only one copy present, while a recessive gene requires two copies to manifest the trait. In the context of achondroplasia, a form of dwarfism, the gene responsible for this condition is dominant.

Dominant Traits and Their Expression

Dominant traits are expressed when at least one dominant allele (gene variant) is present in the genotype. In the case of achondroplasia, the presence of a dominant allele (A) will result in the dwarfism phenotype, regardless of the second allele. Consequently, individuals with the genotypes AA or Aa will display the characteristic features of achondroplasia.

However,

Understanding Genotypes in Achondroplasia

If an individual has achondroplasia, they could have either AA or Aa genotypes, but traditionally, those with AA are not viable, meaning individuals with the condition typically have the Aa genotype. Conversely, the genotype aa represents normal height, as both alleles are recessive.

Calculating Mutation Rate

Mutation rate calculation involves determining the frequency at which a gene changes from one form to another. In achondroplasia, the mutation rate calculates how often the normal allele (a) changes into the mutant, dominant allele (A) that causes the condition.

To calculate the mutation rate, as seen in the example, you start by considering all occurrences where the condition has arisen due to a mutation – which means looking at children with achondroplasia born to parents who do not have the condition (both with the genotype aa). By dividing the number of new mutations (in this case, 2 affected infants) by the total number of births surveyed (50,000) and then halving the result since each child receives one gene from each parent, we determine the mutation per gene per gamete.

In essence:

Simple Mutation Rate Formula

Mutation Rate = (Number of new mutations) / (Total number of gametes studied) The clarity of this formula allows students to grasp the concept easily and apply it in various genetic scenarios.