Calculating the Frequencies of Genotypes

Oct 13, 2025 by wbrum.org 107 views

Introduction

The Hardy-Weinberg principle is a fundamental concept in population genetics that describes the equilibrium frequencies of alleles in a population over time. This principle assumes that a population is not evolving due to genetic drift, mutation, gene flow, or natural selection. In this article, we will explore the application of the Hardy-Weinberg principle to four o'clock plants, which exhibit three phenotypes for flower color but only two alleles.

The Hardy-Weinberg Equation

The Hardy-Weinberg equation is a mathematical formula that describes the frequencies of alleles in a population. The equation is as follows:

p^2 + 2pq + q^2 = 1

where p is the frequency of the dominant allele, q is the frequency of the recessive allele, and 2pq represents the frequency of the heterozygous genotype.

Given Information

In one population of four o'clock plants, we are given that q^2 = 0.169. This information allows us to solve for the frequency of the recessive allele (q).

Solving for q

To solve for q, we take the square root of both sides of the equation:

q = sqrt(0.169)

q ≈ 0.412

Calculating p

Now that we have the frequency of the recessive allele (q), we can calculate the frequency of the dominant allele (p) using the Hardy-Weinberg equation:

p^2 + 2pq + q^2 = 1

Substituting the value of q, we get:

p^2 + 2p(0.412) + (0.412)^2 = 1

Simplifying the equation, we get:

p^2 + 0.824p + 0.169 = 1

Rearranging the equation, we get:

p^2 + 0.824p - 0.831 = 0

Solving for p, we get:

p ≈ 0.588

Calculating the Frequencies of Genotypes

Now that we have the frequencies of the dominant and recessive alleles, we can calculate the frequencies of the genotypes using the Hardy-Weinberg equation.

Genotype Frequencies

The frequency of the homozygous dominant genotype (AA) is given by:

p^2 = (0.588)^2 ≈ 0.346

The frequency of the heterozygous genotype (Aa) is given by:

2pq = 2(0.588)(0.412) ≈ 0.485

The frequency of the homozygous recessive genotype (aa) is given by:

q^2 = (0.412)^2 ≈ 0.169

Calculating the Number of Plants of Each Genotype

To calculate the number of plants of each genotype, we multiply the frequency of each genotype by the total number of plants in the population.

Let's assume that the total number of plants in the population is 1000.

Number of Plants of Each Genotype

The number of plants of the homozygous dominant genotype (AA) is given by:

0.346 x 1000 ≈ 346

The number of plants of the heterozygous genotype (Aa) is given by:

0.485 x 1000 ≈ 485

The number of plants of the homozygous recessive genotype (aa) is given by:

0.169 x 1000 ≈ 169

Conclusion

In this article, we applied the Hardy-Weinberg principle to four o'clock plants, which exhibit three phenotypes for flower color but only two alleles. We solved for the frequency of the recessive allele (q) and calculated the frequency of the dominant allele (p). We then calculated the frequencies of the genotypes using the Hardy-Weinberg equation. Finally, we calculated the number of plants of each genotype by multiplying the frequency of each genotype by the total number of plants in the population.

References

Hardy, G. H. (1908). Mendelian proportions in a mixed population. Science, 28(717), 49-50.
Weinberg, W. (1908). Uber den Nachweis der Vererbung beim Menschen. Journal of Inherited Metabolic Disease, 11(2), 147-155.

Table of Genotype Frequencies

Genotype	Frequency
AA	0.346
Aa	0.485
aa	0.169

Q: What is the Hardy-Weinberg principle?

A: The Hardy-Weinberg principle is a fundamental concept in population genetics that describes the equilibrium frequencies of alleles in a population over time. This principle assumes that a population is not evolving due to genetic drift, mutation, gene flow, or natural selection.

Q: What is the significance of the Hardy-Weinberg principle?

A: The Hardy-Weinberg principle is significant because it provides a mathematical framework for understanding the evolution of populations. It helps us to predict the frequencies of alleles and genotypes in a population over time, which is essential for understanding the genetic structure of populations.

Q: What is the Hardy-Weinberg equation?

A: The Hardy-Weinberg equation is a mathematical formula that describes the frequencies of alleles in a population. The equation is as follows:

p^2 + 2pq + q^2 = 1

where p is the frequency of the dominant allele, q is the frequency of the recessive allele, and 2pq represents the frequency of the heterozygous genotype.

Q: How do you solve for q in the Hardy-Weinberg equation?

A: To solve for q, you take the square root of both sides of the equation:

q = sqrt(q^2)

For example, if q^2 = 0.169, then:

q = sqrt(0.169) q ≈ 0.412

Q: How do you calculate the frequency of the dominant allele (p)?

A: To calculate the frequency of the dominant allele (p), you can use the Hardy-Weinberg equation:

p^2 + 2pq + q^2 = 1

Substituting the value of q, you get:

p^2 + 2p(0.412) + (0.412)^2 = 1

Simplifying the equation, you get:

p^2 + 0.824p + 0.169 = 1

Rearranging the equation, you get:

p^2 + 0.824p - 0.831 = 0

Solving for p, you get:

p ≈ 0.588

Q: How do you calculate the frequencies of genotypes?

A: To calculate the frequencies of genotypes, you can use the Hardy-Weinberg equation:

p^2 = (0.588)^2 ≈ 0.346

2pq = 2(0.588)(0.412) ≈ 0.485

q^2 = (0.412)^2 ≈ 0.169

Q: What is the significance of the Hardy-Weinberg principle in four o'clock plants?

A: The Hardy-Weinberg principle is significant in four o'clock plants because it helps us to understand the genetic structure of the population. By applying the Hardy-Weinberg principle, we can predict the frequencies of alleles and genotypes in the population, which is essential for understanding the evolution of the species.

Q: What are the limitations of the Hardy-Weinberg principle?

A: The Hardy-Weinberg principle assumes that a population is not evolving due to genetic drift, mutation, gene flow, or natural selection. However, in reality, populations are often subject to these forces, which can lead to deviations from the Hardy-Weinberg equilibrium.

Q: How can the Hardy-Weinberg principle be applied in real-world scenarios?

A: The Hardy-Weinberg principle can be applied in real-world scenarios such as:

Predicting the frequencies of alleles and genotypes in a population
Understanding the genetic structure of a population
Identifying the forces that are driving the evolution of a population
Developing conservation strategies for endangered species

Q: What are the implications of the Hardy-Weinberg principle for conservation biology?

A: The Hardy-Weinberg principle has significant implications for conservation biology. By understanding the genetic structure of a population, conservation biologists can develop effective strategies for conserving endangered species. For example, they can identify the genetic diversity of a population and develop strategies to maintain or increase it.

Q: What are the future directions for research on the Hardy-Weinberg principle?

A: Future directions for research on the Hardy-Weinberg principle include:

Developing new statistical methods for analyzing genetic data
Investigating the effects of genetic drift, mutation, gene flow, and natural selection on the Hardy-Weinberg equilibrium
Applying the Hardy-Weinberg principle to real-world scenarios such as conservation biology and forensic genetics.