calculate allele frequencies in 5th generation

Daniel Parker

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28-02-2025

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Understanding how allele frequencies change across generations is fundamental to population genetics. This article will guide you through calculating allele frequencies in a population's fifth generation, assuming the Hardy-Weinberg equilibrium principles apply. We'll explore the underlying assumptions and provide a step-by-step example.

Understanding Hardy-Weinberg Equilibrium

The Hardy-Weinberg principle states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences. These influences include:

• Mutation: Changes in the DNA sequence.
• Gene flow: Movement of alleles between populations.
• Genetic drift: Random fluctuations in allele frequencies, especially pronounced in small populations.
• Non-random mating: Individuals choosing mates based on specific genotypes.
• Natural selection: Differential survival and reproduction of individuals with certain genotypes.

If these factors are negligible, the principle allows us to predict allele and genotype frequencies using simple equations.

The Hardy-Weinberg Equations

The core equations are:

• p + q = 1 where 'p' represents the frequency of one allele (e.g., allele A) and 'q' represents the frequency of the other allele (e.g., allele a) in a two-allele system.
• p² + 2pq + q² = 1 where p² represents the frequency of homozygous dominant genotype (AA), 2pq represents the frequency of heterozygous genotype (Aa), and q² represents the frequency of homozygous recessive genotype (aa).

Calculating Allele Frequencies: A Step-by-Step Example

Let's imagine a population where we're tracking a single gene with two alleles, A and a. We know the genotype frequencies in the initial (first) generation:

• AA: 0.64
• Aa: 0.32
• aa: 0.04

Step 1: Calculate Allele Frequencies in the First Generation

Using the genotype frequencies, we can calculate the allele frequencies:

• q² = 0.04 (frequency of aa) Therefore, q = √0.04 = 0.2 (frequency of allele a)
• p = 1 - q = 1 - 0.2 = 0.8 (frequency of allele A)

Step 2: Assuming Hardy-Weinberg Equilibrium

The crucial assumption here is that the population remains in Hardy-Weinberg equilibrium across generations. This means allele and genotype frequencies will remain the same in the subsequent generations (2nd, 3rd, 4th, and 5th). Therefore, the allele frequencies in the 5th generation will be the same as in the 1st generation:

• p (5th generation) = 0.8
• q (5th generation) = 0.2

Step 3: Calculate Genotype Frequencies in the 5th Generation (Optional)

If you also need the genotype frequencies in the 5th generation, you can use the Hardy-Weinberg equation:

• AA (5th generation) = p² = (0.8)² = 0.64
• Aa (5th generation) = 2pq = 2 * 0.8 * 0.2 = 0.32
• aa (5th generation) = q² = (0.2)² = 0.04

Important Considerations

Remember, the Hardy-Weinberg principle is a model. Real-world populations rarely meet all the assumptions perfectly. However, it serves as a useful baseline for understanding how allele frequencies might change in the absence of evolutionary forces. Deviations from the expected frequencies can indicate that one or more of the evolutionary influences are at play.

Further analyses, including chi-square tests, can help determine if a population significantly deviates from Hardy-Weinberg equilibrium. These statistical tests compare observed genotype frequencies with those expected under Hardy-Weinberg equilibrium.

This example demonstrates a straightforward calculation. For more complex scenarios with multiple alleles or different starting conditions, computational tools or more advanced population genetic models are often needed. But the fundamental principles remain the same.