In a population of 2500, how many babies would you expect to have cystic fibrosis, a homozygous recessive condition, if the frequency of the dominant allele is 0.9 and the population is at Hardy–Weinberg equilibrium? a. 0.9×2500=2250 b. 2×0.9×0.1×2500=450 c. 0.9×0.1×2500=225 d. 0.1x0.1x2500=25

Verified step by step guidance

1. Step 1: Understand the problem. We are asked to find the number of babies expected to have cystic fibrosis, a homozygous recessive condition, in a population of 2500. The frequency of the dominant allele is given as 0.9 and the population is at Hardy-Weinberg equilibrium.
2. Step 2: Recall the Hardy-Weinberg principle. This principle states that the frequency of alleles in a population will remain constant from generation to generation in the absence of other evolutionary influences. The equation for Hardy-Weinberg equilibrium is p^2 + 2pq + q^2 = 1, where p is the frequency of the dominant allele, q is the frequency of the recessive allele, p^2 is the frequency of homozygous dominant individuals, 2pq is the frequency of heterozygous individuals, and q^2 is the frequency of homozygous recessive individuals.
3. Step 3: Calculate the frequency of the recessive allele (q). Since p + q = 1, and we know that p = 0.9, we can solve for q: q = 1 - p = 1 - 0.9 = 0.1.
4. Step 4: Calculate the expected number of babies with cystic fibrosis. Since cystic fibrosis is a homozygous recessive condition, we are interested in q^2, which represents the frequency of homozygous recessive individuals. So, q^2 = (0.1)^2 = 0.01. To find the expected number of babies with cystic fibrosis, we multiply this frequency by the total population: 0.01 * 2500 = 25.
5. Step 5: The correct answer is d. 0.1x0.1x2500=25. This means we would expect 25 babies in this population to have cystic fibrosis.

Key Concepts

Hardy-Weinberg Equilibrium

The Hardy-Weinberg equilibrium is a principle that describes the genetic variation in a population that is not evolving. It states that allele and genotype frequencies will remain constant from generation to generation in the absence of evolutionary influences. This model assumes no mutation, migration, selection, or genetic drift, allowing for the prediction of genotype frequencies based on allele frequencies.

Allele Frequency

Allele frequency refers to how often a particular allele appears in a population compared to other alleles for the same gene. In this context, the frequency of the dominant allele (0.9) and the recessive allele (0.1) can be used to calculate the expected number of individuals with a specific genotype, such as those with cystic fibrosis, which is caused by the homozygous recessive genotype.

Genotype Calculation

To determine the expected number of individuals with a homozygous recessive condition like cystic fibrosis, we use the formula p^2 for the recessive genotype, where p is the frequency of the recessive allele. In this case, with a recessive allele frequency of 0.1, the expected proportion of homozygous recessive individuals in the population can be calculated as (0.1)^2, which is then multiplied by the total population size to find the expected number of affected individuals.