Question

Consider a population in which the frequency of allele \(A\) is \(p=0.7\) and the frequency of allele \(a\) is \(q=0.3,\) and where the alleles are codominant. 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 updated allele frequencies for scenarios (a), (b), (c), and (d) after one generation, given the initial frequencies and fitness values of genotypes AA, Aa, and aa. a) Fitness values: \(w_{AA} = 1, w_{Aa} = 0.9, w_{aa} = 0.8\) b) Fitness values: \(w_{AA}=1, w_{Aa}=0.95, w_{aa}=0.9\) c) Fitness values: \(w_{AA}=1, w_{Aa}=0.99, w_{aa}=0.98\) d) Fitness values: \(w_{AA}=0.8, w_{Aa}=1, w_{aa}=0.8\) Initial allele frequencies: \(p = 0.7, q = 0.3\)

Step-by-step solution

(Calculate mean fitness of the population W)

We need to calculate the mean fitness of the population, W, using the given fitness values and initial frequencies. Using the formula, W = \(p^2w_{AA} + 2pqw_{Aa} + q^2w_{aa}\), and the values provided, we have \(W = (0.7^2 * 1) + (2 * 0.7 * 0.3 * 0.9) + (0.3^2 * 0.8)\).

(Find the new allele frequencies)

We use the calculated W along with the given initial frequencies p and q and genotype fitness values to calculate the new frequencies of alleles A and a using the formulas above. New frequency of A = (\(0.7^2 * 1 + 0.5 * 0.7 * 0.3 * 0.9\)) / \(W\), New frequency of a = (\(0.3^2 * 0.8 + 0.5 * 0.7 * 0.3 * 0.9\)) / \(W\). Do the same calculations for scenarios (b), (c), and (d) by plugging in the respective fitness values for each genotype. #b) Calculation of new frequencies with given fitness values# Calculate \(W\), new frequency of A, and new frequency of a as in (a) for the given fitness values \(w_{AA}=1, w_{Aa}=0.95, w_{aa}=0.9\) #c) Calculation of new frequencies with given fitness values# Calculate \(W\), new frequency of A, and new frequency of a as in (a) for the given fitness values \(w_{AA}=1, w_{Aa}=0.99, w_{aa}=0.98\) #d) Calculation of new frequencies with given fitness values# Calculate \(W\), new frequency of A, and new frequency of a as in (a) for the given fitness values \(w_{AA}=0.8, w_{Aa}=1, w_{aa}=0.8\) After calculating the new frequency values for each scenario, we will have the updated allele frequencies after one generation for all four cases.

Key concepts

Population Genetics

Population genetics is a branch of biology that studies the distribution of genetic variations within populations and how these variations change over time. Factors that affect genetic variation include mutations, genetic drift, gene flow, and natural selection. Allele frequency, a key concept in this field, measures how common an allele is in a population. By calculating and tracking allele frequencies, scientists can predict and understand evolutionary changes in populations.

When solving exercises related to population genetics, such as changes in allele frequencies, it is critical to account for all possible genetic combinations and their proportions in a population. This means taking into consideration the genotype frequencies and how they contribute to the next generation's gene pool. The allele frequencies will not change if the population is in Hardy-Weinberg equilibrium, meaning that the population is not evolving. However, if certain forces like selection are at play, we can expect allele frequencies to shift as a response to these selective pressures.

Codominance

Codominance occurs when two different alleles at a locus are both fully expressed in a heterozygote, resulting in a phenotype that shows aspects of both alleles. Unlike in complete dominance, where the dominant allele masks the recessive allele, in codominance both alleles contribute to the phenotype. This becomes particularly important when calculating new allele frequencies because the genotypes will express new combinations of traits, making calculations more complex than in cases of complete dominance.

Let's say we are looking at flower color where red is codominant with white, resulting in flowers with both red and white patches. For such cases, genetic diagrams can be highly useful for visualizing and predicting the outcomes of crosses between different genotypes. Keep in mind that in codominant relationships, the heterozygous condition is just as crucial in calculating allele frequencies as the homozygous conditions.

Genotype Fitness

Genotype fitness, often symbolized by 'w', reflects the reproductive success of a genotype relative to other genotypes. It is a measure of survival and reproduction and is one of the factors that can cause allele frequencies to change over time. In population genetics calculations, the fitness of a genotype determines how much it contributes to the next generation's gene pool.

When analyzing problems like the one where different scenarios with varying fitness values are provided, it’s important to understand that genotypes with higher fitness will contribute more offspring to the next generation. This leads to a change in allele frequencies. In exercises, be alert for situations where the fitness of the heterozygote is between those of the homozygotes, as this can indicate a situation of stabilizing selection, or when the heterozygote fitness is higher, which could indicate overdominance or heterozygote advantage.

Hardy-Weinberg Principle

The Hardy-Weinberg principle is a fundamental concept in population genetics that provides a mathematical baseline for understanding genetic variation in a population under the assumption of no evolution occurring. According to this principle, allele and genotype frequencies in a large, randomly mating population remain constant across generations unless specific factors such as mutation, migration, genetic drift, nonrandom mating, or selection are present. The principle is based on a set of equations that predict the expected genotype frequencies from allele frequencies.

The usefulness of the Hardy-Weinberg principle lies in its role as a null hypothesis for detecting evolutionary forces. If observed genotype frequencies deviate from Hardy-Weinberg expectations, we can infer that evolutionary pressures might be at work. To solve exercises relating to the Hardy-Weinberg equilibrium, it is essential to familiarize oneself with its equation: p² + 2pq + q² = 1, where p and q represent the frequencies of two alleles, and p², 2pq, and q² represent the genotype frequencies for the homozygous dominant, heterozygous, and homozygous recessive genotypes, respectively. This framework allows us to predict what a non-evolving population's genetic structure should look like, serving as a benchmark for studies of evolutionary change.