Problem 7 - Campbell Biology Concepts & Connections

Question

In a population with two alleles, \(B\) and \(b\), the allele frequency of \(b\) is \(0.4 . B\) is dominant to \(b\). What is the frequency of individuals with the dominant phenotype if the population is in Hardy-Weinberg equilibrium? a. 0.16 b. 0.36 c. 0.48 d. 0.84

Step-by-Step Solution

Answer

0.84

Step 1 - Identify allele frequencies

Given that the allele frequency of allele b is 0.4, use p + q = 1 to find the frequency of allele B. Since q (frequency of b) is 0.4, then p (frequency of B) is calculated by p = 1 - q = 1 - 0.4 = 0.6.

Step 2 - Write down the Hardy-Weinberg equation

The Hardy-Weinberg equation is\[ p^2 + 2pq + q^2 = 1 \]. Here, p^2 represents the frequency of the homozygous dominant genotype (BB), 2pq represents the frequency of the heterozygous genotype (Bb), and q^2 represents the frequency of the homozygous recessive genotype (bb).

Step 3 - Calculate the frequency of the homozygous dominant genotype (BB)

Calculate p^2: \[ p^2 = (0.6)^2 = 0.36 \]. This is the frequency of BB.

Step 4 - Calculate the frequency of the heterozygous genotype (Bb)

Calculate 2pq: \[ 2pq = 2 \times 0.6 \times 0.4 = 0.48 \]. This is the frequency of Bb.

Step 5 - Determine the frequency of individuals with the dominant phenotype

Individuals with the dominant phenotype have either the BB or Bb genotype. Add the frequencies of BB and Bb: \[ p^2 + 2pq = 0.36 + 0.48 = 0.84 \].

Key Concepts

allele frequencies

One of the foundational concepts in understanding population genetics is allele frequencies. Alleles are different forms of a gene that occupy the same position, or locus, on a chromosome. In a given population, the allele frequency pertains to how common a particular allele is compared to others at the same locus.

For instance, in our exercise, we have two alleles: B and b. The frequency of the allele b is given as 0.4. To determine the frequency of the dominant allele B, we use the equation p + q = 1, where p represents the frequency of one allele (B) and q represents the frequency of the other allele (b). Given that q (the frequency of b) is 0.4, we can find p (the frequency of B) by subtracting q from 1 (p = 1 - q). This results in p = 0.6. Knowing these allele frequencies allows us to predict how these alleles will combine to form different genotypes in the population.

dominant and recessive alleles

In genetics, alleles can either be dominant or recessive. A dominant allele is one that masks the presence of another allele, known as the recessive allele, when they are paired together in a heterozygous genotype.

In our exercise, B is the dominant allele and b is the recessive allele. This means that individuals with the genotypes BB or Bb will exhibit the dominant trait or phenotype. Only individuals with the genotype bb will express the recessive phenotype. The dominance of allele B over b is crucial in understanding how traits are passed down and expressed in a population. Recognizing whether an allele is dominant or recessive helps in predicting the observable traits and their frequencies within a population.

genotype frequencies

The frequency of different genotypes in a population can be understood using the Hardy-Weinberg equation, which is p^2 + 2pq + q^2 = 1. This equation provides a framework to predict genotype frequencies based on allele frequencies.

In our exercise, we calculate these frequencies as follows:

• The frequency of the homozygous dominant genotype BB is p^2. Substituting p = 0.6, we get \( p^2 = 0.6^2 = 0.36 \).
• The frequency of the heterozygous genotype Bb is 2pq. Substituting p and q (0.6 and 0.4), we get \( 2pq = 2 \times 0.6 \times 0.4 = 0.48 \).
• Lastly, the frequency of the homozygous recessive genotype bb is q^2. Substituting q = 0.4, we get \( q^2 = 0.4^2 = 0.16 \).

By adding the frequencies of BB and Bb, we determine that the frequency of the dominant phenotype in the population is \( 0.36 + 0.48 = 0.84 \). Understanding genotype frequencies is essential for predicting how traits are distributed in a population.