Question

In a population where only the total number of individuals with the dominant phenotype is known, how can you calculate the percentage of carriers and homozygous recessives?

Short answer

Question: In a population, the total number of individuals with a dominant phenotype is 120, and the total number of individuals in the population is 200. Calculate the percentage of carriers and homozygous recessives in this population. Answer: To calculate the percentage of carriers and homozygous recessives in the population, follow the steps outlined in the solution. Use the given values X = 120 (individuals with a dominant phenotype) and N = 200 (total individuals in the population) to determine the frequencies of the dominant and recessive alleles, and then calculate the percentage of carriers and homozygous recessives.

Step-by-step solution

Understanding the Hardy-Weinberg equilibrium formula

The equation for Hardy-Weinberg equilibrium is p^2 + 2pq + q^2 = 1. In this equation, p^2 represents the frequency of homozygous dominant individuals, 2pq represents the frequency of heterozygous individuals (carriers), and q^2 represents the frequency of homozygous recessive individuals.

Find the frequency of the dominant phenotype

Given the total number of individuals with the dominant phenotype, we can calculate the frequency of the dominant phenotype by dividing the number of individuals with the dominant phenotype by the total number of individuals in the population. Let's represent the number of individuals with the dominant phenotype as X and the total number of individuals in the population as N. Then, the frequency of the dominant phenotype is: Frequency of dominant phenotype = X/N

Calculate the frequency of the recessive allele (q)

We need to find the frequency of the recessive allele q. Since the frequency of the dominant phenotype includes both homozygous dominant (p^2) and heterozygous (2pq) individuals, we can write: 1 - Frequency of dominant phenotype = q^2 Since we calculated the frequency of the dominant phenotype in Step 2, we can substitute that value here to find q^2. To find q, we will take the square root of q^2.

Calculate the frequency of the dominant allele (p)

The frequency of the dominant allele p can be found using the relationship p + q = 1. Since we found the frequency of the recessive allele q in Step 3, we can now calculate the frequency of the dominant allele p as: p = 1 - q

Calculate the percentage of carriers (heterozygous individuals)

Now we can find the percentage of carriers, which is represented by 2pq in the Hardy-Weinberg equilibrium equation. We can use the values we calculated for p and q in Steps 3 and 4: Percentage of carriers = 2 * p * q * 100

Calculate the percentage of homozygous recessives

Finally, we can calculate the percentage of homozygous recessives using the value of q we found in step 3: Percentage of homozygous recessives = q^2 * 100 By following these steps, we can calculate the percentage of carriers and homozygous recessives in a population when only the total number of individuals with the dominant phenotype is known.

Key concepts

Genotype Frequency Calculation

The calculation of genotype frequencies in a population is an essential skill in genetics, as it allows us to predict the distribution of genetic variants amongst individuals. It's particularly useful when we want to assess the genetic structure of a population at equilibrium – that is, when allele frequencies are stable from one generation to the next. This stable state is referred to as Hardy-Weinberg equilibrium.To calculate the frequency of each genotype, we use the simple but powerful Hardy-Weinberg formula: \begin{align*}\text{p}^2 &+ 2pq + \text{q}^2 = 1\end{align*}

• \(p^2\) corresponds to the frequency of homozygous dominant individuals,
• 2pq represents heterozygous individuals,
• and \(q^2\) indicates homozygous recessive individuals.

When only the number of individuals with the dominant phenotype is known, we need to combine this information with the Hardy-Weinberg equation to unlock all the genetic frequencies. We first determine the frequency of the dominant phenotype, and through algebraic manipulation and some squaring and square-rooting, we uncover the allele frequencies of \(p\) (dominant allele) and \(q\) (recessive allele). It is these frequencies that allow us to compute the proportions of each genotype within the population.

Dominant and Recessive Alleles

Understanding the difference between dominant and recessive alleles is crucial in genetics. Dominant alleles are those that manifest their phenotype even when only one copy is present in the genotype of an individual (heterozygous condition). Conversely, recessive alleles only display their phenotype when two copies are present (homozygous condition). A common misunderstanding lies in the association of 'dominant' with being more common; however, dominance only refers to the allele's ability to mask the presence of a recessive allele in the phenotype.

• Dominant alleles are denoted by \(p\) in Hardy-Weinberg calculations,
• Recessive alleles by \(q\).

The Hardy-Weinberg formula reveals that the frequencies of these alleles in a population are interdependent: knowing the frequency of one can help deduce the other. Irrespective of the alleles' dominance, it's their frequency in a population that determines genotype frequencies, as indicated by the proportion of \(p^2\), 2pq, and \(q^2\) in the population.

Population Genetics

Population genetics is the study of how genetic composition in populations changes over time and space. It combines principles from Mendelian genetics, molecular biology, and evolutionary theory to analyze genetic differences within and between populations. Hardy-Weinberg equilibrium serves as a model for understanding these changes by providing a baseline expectation for genotype frequencies when a population is not evolving. This equilibrium thus allows researchers to detect various evolutionary forces, such as natural selection, gene flow, genetic drift, mutation, and non-random mating, by observing departures from expected distributions.

Certain conditions must be met for a population to be in Hardy-Weinberg equilibrium: extremely large population size, no migrations, no mutations, random mating, and no natural selection. In real-world scenarios, these conditions are often violated to some degree, making population genetics an exciting field for investigating how and why populations change over time, shaping the biodiversity we observe today.