Question

Consider a population of garden pea plants in which the genes \(\mathrm{F}\) for full pods and \(\mathrm{f}\) for constricted pods are segregating. When a sample of 1,500 plants were classified, the following phenotypes were recorded: 1,365 full-podded plants and 135 constricted-podded plants. Assuming that the sample classified was representative of the population, and that the population was in a state of genetic equilibrium, what are the frequencies of the two alleles? How many of the full-podded plants are heterozygous?

Short answer

In conclusion, the frequencies of alleles F and f are 0.7 and 0.3, respectively. Among the full-podded plants, approximately 573 are heterozygous.

Step-by-step solution

Determine Proportions of Phenotypes

First, let's determine the proportions of the full-podded plants and constricted-podded plants in the given population. - Full-podded plants: 1365 plants - Constricted-podded plants: 135 plants - Total plants: 1500 plants The proportions of each phenotype are: Full-podded proportion (P): \[\frac{1365}{1500} = 0.91\] Constricted-podded proportion (Q): \[\frac{135}{1500} = 0.09\]

Determine Allele Frequencies

Next, we will use the Hardy-Weinberg equilibrium to determine the frequencies of the alleles F and f. The equilibrium equation is \(P^2 + 2PQ + Q^2 = 1\), where: - P is the proportion of full-podded plants (which could have genotypes FF or Ff) - Q is the proportion of constricted-podded plants (with genotype ff) - P^2 is the proportion of plants with genotype FF - 2PQ is the proportion of plants with genotype Ff - Q^2 is the proportion of plants with genotype ff Since we know the proportion of constricted-podded plants (Q² = 0.09), we can calculate the allele frequencies. To find the frequency of allele f: \[Q = \sqrt{Q^2} = \sqrt{0.09} = 0.3\] To find the frequency of allele F: \[P = 1 - Q = 1 - 0.3 = 0.7\] Therefore, the allele frequencies are: - Frequency of allele F: 0.7 - Frequency of allele f: 0.3

Determine the Number of Heterozygous Full-podded Plants

Now, let's calculate the number of heterozygous full-podded plants (Ff). First, we need to find the proportion of plants with genotype Ff (2PQ): \[2PQ = 2 \times 0.7 \times 0.3 = 0.42\] Next, we will multiply this proportion by the total number of full-podded plants (1365) to find the number of heterozygous plants among them: \[1365 \times 0.42 \approx 573\] Approximately 573 full-podded plants are heterozygous (Ff). In conclusion, the frequencies of alleles F and f are 0.7 and 0.3, respectively. Among the full-podded plants, approximately 573 are heterozygous.

Key concepts

Genetic Equilibrium

Genetic equilibrium is a critical concept in population genetics, indicating that a population's allele frequencies remain constant over time in the absence of evolutionary influences. According to the Hardy-Weinberg principle, several conditions must be met for a population to be in genetic equilibrium: large population size, random mating, no mutations, no gene flow, and no natural selection. When these criteria are met, it implies that the genetic variation in the population is stable, making predictions about future generations a significant possibility.

If a population is in Hardy-Weinberg equilibrium, predicting the genetic makeup of the offspring becomes straightforward. However, it is important to recognize that real-world populations often deviate from these idealized conditions due to various evolutionary pressures. Nevertheless, the concept serves as a baseline from which scientists can measure genetic changes over time. It is a fundamental principle used for understanding how populations evolve and how genetic diversity is maintained or altered.

Allele Frequencies

Allele frequencies represent the relative abundance of different versions (alleles) of a gene in a population. These frequencies are a cornerstone of population genetics since they provide insights into the genetic diversity of a population. The frequency of an allele is calculated by dividing the number of copies of that allele by the total number of copies of all alleles for that gene in the population.

Understanding these frequencies is crucial for predicting how traits will be passed to future generations. The Hardy-Weinberg equation, which centralizes on allele frequencies, is an essential tool for geneticists to estimate the prevalence of certain traits (phenotypes). For instance, in the textbook exercise, it was calculated that the frequencies for alleles F and f were 0.7 and 0.3. These values help us understand the genetic variability within the population and predict the odds of particular alleles being passed down.

Heterozygous

A heterozygous individual carries two different alleles of a gene, one inherited from each parent. This genetic makeup can influence an individual's phenotype - the set of observable characteristics. In the context of the Hardy-Weinberg equilibrium, the proportion of heterozygous individuals within a population is an important measure because it directly affects the genetic diversity of the population.

In the exercise, to determine the number of heterozygous full-podded plants, the proportion was calculated using the Hardy-Weinberg principle. The calculated number of heterozygous individuals (573 out of 1365 full-podded plants) highlights the significance of understanding how genotypes can be distributed in a population. Keeping tabs on the proportion of heterozygous individuals is also essential for predicting the robustness of a population in adapting to environmental changes.

Phenotype Proportions

Phenotype proportions in a population reflect the observable traits of organisms, such as full or constricted pods in pea plants. These proportions can tell us how a particular genetic trait is expressed in the population and, when combined with our understanding of genetics, allow us to deduce the underlying allele frequencies. In Hardy-Weinberg terms, the phenotypes are often linked with the genotype frequencies (P² for homozygous dominant, 2PQ for heterozygous, and Q² for homozygous recessive).

The phenotype proportions are directly observable and, as such, offer a more tangible connection to genetics for students. For instance, when you see that the vast majority of pea plants have full pods, as was calculated at 91% in the exercise, you get a real-world grasp of how common that trait is. Consequently, understanding phenotype proportions is instrumental in bridging the gap between genetic theory and the living, breathing world around us.