Hardy-Weinberg Equilibrium: Understanding Evolutionary Stability

AP Biology Unit 7.5

The Hardy-Weinberg equilibrium is a theoretical model in population genetics that describes how allele frequencies in a population remain stable over time—assuming certain ideal conditions are met. This equilibrium gives us a baseline to assess if evolution is occurring in a population. If allele frequencies are stable, then evolution isn’t happening; if they’re changing, then natural forces are at play.

But what exactly does this model mean, and how can it help us understand evolutionary dynamics? Let’s dive in!

What is Hardy-Weinberg Equilibrium?

The Hardy-Weinberg equilibrium describes a population where allele frequencies remain constant over generations. Essentially, it suggests that, in the absence of external forces, the genetic makeup of a population does not change. This provides a baseline or “null hypothesis” for measuring genetic variation and evolutionary forces.

For Hardy-Weinberg equilibrium to apply, the following five conditions must be met:

1. No Mutations – No new alleles are added to the gene pool.

2. No Natural Selection – All individuals have equal chances of survival, meaning no traits are favored.

3. No Gene Flow – No migration or movement of individuals between populations.

4. Infinite Population Size – The population is large enough that random genetic drift has no effect.

5. Random Mating – Individuals pair by chance, not by selecting specific traits.

Obviously, these conditions are virtually impossible to meet in a natural setting. However, this model gives scientists a theoretical “control” to understand when and how evolution is occurring.

Calculating Allele Frequencies: The Hardy-Weinberg Equations

Hardy-Weinberg equilibrium is represented by two key equations that allow us to calculate the allele and genotype frequencies in a population:

1. Allele Frequency Equation:

p + q = 1
Where:

• p = Frequency of the dominant allele.

• q = Frequency of the recessive allele.

2. Genotype Frequency Equation:

p² + 2pq + q² = 1
Where:

• p² = Frequency of homozygous dominant individuals.

• 2pq = Frequency of heterozygous individuals.

• q² = Frequency of homozygous recessive individuals.

This helps us determine the genetic structure of a population—how common each genotype is.

Example Calculation

Imagine we have a population of 100 birds, with 16 of them displaying a recessive trait (grey feathers). Let’s break down the steps to calculate the allele and genotype frequencies:

1. Step 1: Calculate Recessive Genotype Frequency (q²)

   • Since 16 of the birds have grey feathers, the recessive genotype frequency (²) is 16/100 = 0.16.

2. Step 2: Calculate Recessive Allele Frequency (q)

   • Take the square root of q²: √0.16 = 0.4.

3. Step 3: Calculate Dominant Allele Frequency (p)

   • Since p + q = 1:
     p = 1 – 0.4 = 0.6.

4. Step 4: Calculate Genotype Frequencies

   • Homozygous Dominant (p²): 0.6² = 0.36 (36% of the population).

   • Heterozygous (2pq): 2 * 0.6 * 0.4 = 0.48 (48% of the population).

   • Homozygous Recessive (q²): 0.16 (16% of the population).

Real-World Applications

The Hardy-Weinberg model helps biologists understand if populations are evolving and estimate the effect of different evolutionary pressures like mutation, migration, and natural selection.

For instance, if the observed genotype frequencies differ from the expected values calculated using Hardy-Weinberg, it indicates that one or more of the five conditions is not being met—suggesting that evolutionary forces are at play.

Example Problem: Applying Hardy-Weinberg

A rare genetic disorder is caused by a recessive allele (“a”). In a population, the frequency of this recessive allele (“q”) is 0.02. Calculate the following:

• Frequency of the dominant allele (“A”):
  p = 1 – q = 1 – 0.02 = 0.98.

• Frequency of homozygous recessive individuals (“aa”):
  q² = 0.02² = 0.0004 (0.04%).

• Frequency of heterozygous individuals (“Aa”):
  2pq = 2 * 0.98 * 0.02 = 0.0392 (3.92%).

By solving this, we’re assuming that no mutation, migration, genetic drift, or non-random mating is affecting the population. It’s a great way to test whether evolutionary forces are occurring.

Conclusion: A Theoretical Snapshot of Evolution

While the Hardy-Weinberg equilibrium is an idealized model, it provides valuable insights into the genetic stability or change of populations over time. By comparing observed genetic data to the expected equilibrium, biologists can identify which evolutionary forces are at play, offering insights into adaptation and survival dynamics.

Ready to Master Hardy-Weinberg? Practice a few problems to solidify your understanding, and soon you’ll see how this model serves as a foundational concept in understanding evolutionary biology. 🌱