Question

ConsiderapopulationinwhichthefrequencyofalleleAisp \(=0.7\) and thefrequencyofalleleais \(q=0.3\), andwheretheallelesarecodominant. What will be the allele frequencies after one generation if the following occurs? (a) \(w_{A A}=1, w_{A a}=0.9, w_{a a}=0.8\) (b) \(w_{A A}=1, w_{A a}=0.95, w_{a a}=0.9\) (c) \(w_{A A}=1, w_{A a}=0.99, w_{a a}=0.98\) (d) \(w_{A A}=0.8, w_{A a}=1, w_{a a}=0.8\)

Short answer

Question: Calculate the new allele frequencies after one generation for each given case. Answer: (a) p ≈ 0.692, q ≈ 0.308 (b) p ≈ 0.695, q ≈ 0.305 (c) p ≈ 0.698, q ≈ 0.302 (d) p ≈ 0.702, q ≈ 0.298

Step-by-step solution

Calculate the initial genotype frequencies

Using the given initial allele frequencies (\(p = 0.7\), \(q = 0.3\)), we can calculate the initial genotype frequencies: \(AA: p^2 = (0.7)^2 = 0.49\) \(Aa: 2pq = 2(0.7)(0.3) = 0.42\) \(aa: q^2 = (0.3)^2 = 0.09\)

Calculate the resultant genotype frequencies after selection

Now apply the selection coefficients given in each part of the problem to calculate the resultant genotype frequencies after selection: (a) \(AA: 1 \times 0.49 = 0.49\) \(Aa: 0.9 \times 0.42 = 0.378\) \(aa: 0.8 \times 0.09 = 0.072\) (b) \(AA: 1 \times 0.49 = 0.49\) \(Aa: 0.95 \times 0.42 = 0.399\) \(aa: 0.9 \times 0.09 = 0.081\) (c) \(AA: 1 \times 0.49 = 0.49\) \(Aa: 0.99 \times 0.42 = 0.4158\) \(aa: 0.98 \times 0.09 = 0.0882\) (d) \(AA: 0.8 \times 0.49 = 0.392\) \(Aa: 1 \times 0.42 = 0.42\) \(aa: 0.8 \times 0.09 = 0.072\)

Calculate the new allele frequencies after selection

To determine the new allele frequencies, normalize the genotype frequencies and then apply the Hardy-Weinberg equilibrium formulas: (a) Total frequency after selection: \(0.49 + 0.378 + 0.072 = 0.94\) New allele frequencies: \(p = \frac{0.49 + 0.5 \times 0.378}{0.94} \approx 0.692\), \(q = \frac{0.072 + 0.5 \times 0.378}{0.94} \approx 0.308\) (b) Total frequency after selection: \(0.49 + 0.399 + 0.081 = 0.97\) New allele frequencies: \(p = \frac{0.49 + 0.5 \times 0.399}{0.97} \approx 0.695\), \(q = \frac{0.081 + 0.5 \times 0.399}{0.97} \approx 0.305\) (c) Total frequency after selection: \(0.49 + 0.4158 + 0.0882 = 0.994\) New allele frequencies: \(p = \frac{0.49 + 0.5 \times 0.4158}{0.994} \approx 0.698\), \(q = \frac{0.0882 + 0.5 \times 0.4158}{0.994} \approx 0.302\) (d) Total frequency after selection: \(0.392 + 0.42 + 0.072 = 0.884\) New allele frequencies: \(p = \frac{0.392 + 0.5 \times 0.42}{0.884} \approx 0.702\), \(q = \frac{0.072 + 0.5 \times 0.42}{0.884} \approx 0.298\) Hence, we have found the new allele frequencies after one generation for each given case.

Key concepts

Codominant Alleles

In genetics, when alleles are codominant, both alleles in a heterozygous individual contribute to the phenotype. This means that each parent passes on an allele that equally affects the offspring's traits. Unlike complete dominance, where one allele masks the effect of another, codominance allows both alleles to be fully and independently expressed.
For example, if you imagine a flower color determined by two codominant alleles, a flower with the genotype Aa may show both color traits represented by A and a.
This concept is crucial in the exercise, as it assumes codominant alleles for computations of allele and genotype frequencies across generations. Codominance leads to observable differences in offspring and plays a key role in understanding how traits are passed on when no allele overpowers another.

Genotype Frequencies

Genotype frequencies are essential in predicting the genetic makeup of a population. They reflect how common specific genetic combinations (AA, Aa, aa) are within a population. To calculate these frequencies, we typically utilize the Hardy-Weinberg principle. With the initial allele frequencies provided (p = 0.7, q = 0.3), the genotypes are computed as follows:

• AA: \( p^2 = (0.7)^2 = 0.49 \)
• Aa: \( 2pq = 2(0.7)(0.3) = 0.42 \)
• aa: \( q^2 = (0.3)^2 = 0.09 \)

The genotype frequencies help us understand how alleles are paired within the population and predict the traits seen in the next generation. They change based on selection pressure and other evolutionary forces, a concept further explored in our selection coefficients section.

Selection Coefficients

Selection coefficients measure the relative fitness of different genotypes within a population. Each coefficient indicates how likely a genotype is to survive and reproduce compared to others. In the given exercise, they influence the resulting genotype frequencies after one generation.
For example, in scenario (a), the selection coefficients are \( w_{A A}=1 \), \( w_{A a}=0.9 \), and \( w_{a a}=0.8 \). These coefficients imply that individuals with genotype AA are more likely to pass on their genes than those with genotype aa. The effect of these coefficients will modify the genotype frequencies:

• AA stays at 0.49 (unchanged because its coefficient is 1)
• Aa reduces to 0.378 because \( 0.9 imes 0.42 = 0.378 \)
• aa drops to 0.072 because \( 0.8 imes 0.09 = 0.072 \)

Selection coefficients play a pivotal role in evolutionary biology by determining how populations adapt over time.

Hardy-Weinberg Equilibrium

The Hardy-Weinberg equilibrium is a fundamental principle in population genetics. It proposes that allele and genotype frequencies within a large, randomly-mating population remain constant unless disturbed by evolutionary forces. This equilibrium provides a mathematical baseline to detect the impact of forces like selection, mutation, migration, and genetic drift.
To check if a population is in Hardy-Weinberg equilibrium, you need to compare observed and expected genotype frequencies calculated from allele frequencies. For example, if a population's observed genotype frequencies match those predicted by \( p^2 + 2pq + q^2 = 1 \), it suggests that the population is not undergoing forces that alter its genetic structure.
Even though the exercise above assumes codominance and selection, the Hardy-Weinberg model helps establish initial conditions before the application of selection coefficients. This principle is useful as a starting point for understanding how populations evolve over time when subject to various pressures.