Question

Calculate the frequencies of the \(A A, A a,\) and \(a a\) genotypes after one generation if the initial population consists of \(0.2 \mathrm{AA}, 0.6\) \(A a,\) and 0.2 aa genotypes and meets the requirements of the Hardy-Weinberg relationship. What genotype frequencies will occur after a second generation?

Short answer

Answer: The frequencies after the first and second generations will be as follows: AA - 0.25, Aa - 0.50, and aa - 0.25.

Step-by-step solution

Find the values of p and q for the initial population

We know the initial frequencies of the three genotypes: AA (0.2), Aa (0.6), and aa (0.2). We now need to find the allele frequencies for A (p) and a (q) in this population. First, let's find the frequency of the dominant allele A (p): \(p = (\text{frequency of AA}) + \frac{1}{2}(\text{frequency of Aa})\) \(p = (0.2) + \frac{1}{2}(0.6)\) \(p = 0.5\) Now, let's find the frequency of the recessive allele a (q): Since p + q = 1 and p = 0.5: \(q = 1 - p\) \(q = 1 - 0.5\) \(q = 0.5\)

Calculate genotype frequencies after one generation

Using the Hardy-Weinberg equation, we can calculate the genotype frequencies after one generation: Frequency of AA: \(p^2 = 0.5^2 = 0.25\) Frequency of Aa: \(2pq = 2 \times 0.5 \times 0.5 = 0.50\) Frequency of aa: \(q^2 = 0.5^2 = 0.25\)

Calculate genotype frequencies after a second generation

Under the Hardy-Weinberg equilibrium, the genotype frequencies remain constant over generations. Therefore, the genotype frequencies after the second generation will be the same as those after the first: Frequency of AA: 0.25 Frequency of Aa: 0.50 Frequency of aa: 0.25

Key concepts

Genotype Frequencies

When studying genetics, it's important to understand how often certain combinations of alleles, known as genotypes, appear in a population. Genotype frequencies are the rates at which genotypes occur in a specific population, and they are essential in predicting how traits will be inherited by future generations. For instance, if we consider a simple genetic trait with two alleles, A and a, there are three possible genotypes: AA, Aa, and aa.

In the exercise provided, genotype frequencies were calculated based on an initial population under the Hardy-Weinberg equilibrium. We started with AA (0.2), Aa (0.6), and aa (0.2) frequencies. Using the Hardy-Weinberg principle, which predicts that genotype frequencies will remain stable from one generation to the next in the absence of evolutionary influences, we can deduce that after both one and two generations without any outside forces acting on the population, the genotype frequencies will be AA (0.25), Aa (0.50), and aa (0.25). This constancy is an assumption of the Hardy-Weinberg equilibrium and is crucial in population genetics to estimate the distribution of genetic variation.

Allele Frequencies

Allele frequencies refer to how common an allele is in a population. For a given gene with different forms—alleles—the frequency of each allele is the proportion of all alleles for that gene that one particular allele represents.

Understanding allele frequencies allows us to predict how likely certain alleles are to be passed on to the next generation. Calculating allele frequencies usually involves summing up the instances of the target allele in both homozygotes and heterozygotes, as seen in the exercise. If A is dominant and a is recessive, and the observed frequencies are AA (0.2), Aa (0.6), and aa (0.2), then the allele frequency of A (p) could be derived by taking all As from AA and half from Aa since heterozygotes contribute to the frequency of both alleles. The calculation demonstrated that both alleles, A and a, had frequencies (p and q) of 0.5, meaning each allele was just as likely to be passed on in the absence of evolutionary factors, which is a keystone of Hardy-Weinberg equilibrium.

Population Genetics

Population Genetics is the study of genetic variation within populations and involves the examination of allele and genotype frequencies, and how they change over time through processes such as selection, mutation, gene flow, and genetic drift. The Hardy-Weinberg principle is a cornerstone in this field; it provides a model that allows us to make predictions about genetic structures of populations.

The principle posits that in the absence of external factors (like non-random mating, mutation, selection, gene flow, and genetic drift), both allele and genotype frequencies will remain constant from one generation to the next, a state known as Hardy-Weinberg equilibrium. This principle also serves as a null hypothesis for testing evolutionary influences—any deviation from the expected frequencies suggests that some form of evolutionary process is occurring in the population. In our example, we assume no such influences; hence, the frequencies remain unaltered over generations.