# Practical Application: Hardy Weinberg Equilibrium

Instructor: Amanda Robb
In this lesson, you will practice how to use the Hardy Weinberg equation to evaluate environmental conditions and population dynamics. After reviewing what the Hardy Weinberg equation and equilibrium is, we'll try some practice problems.

## What Is the Hardy Weinberg Equilibrium?

What happens when everything is in balance in your life? Homework fits perfectly into your after school schedule and there's just enough time to call your best friend after dinner. Everything feels good! Ecological populations can also be in equilibrium, where things are in balance and no major changes like natural selection, genetic drift, or gene flow are occurring. Scientists describe this state as the Hardy Weinberg equilibrium and have an equation to explain the frequencies of different alleles during it:

p2 + 2pq + q2 = 1

Here, p is the frequency of the dominant allele, and q is the frequency of the recessive allele. This equation describes the relationships between the different genotypes in a population at equilibrium, where p2 is the frequency of homozygous dominant individuals, 2pq is the frequency of heterozygous individuals and q2 is the frequency of homozygous recessive individuals.

Next, let's look at how we can apply this formula to understand how populations change during and outside of Hardy Weinberg equilibrium.

## Practice Problem 1 - Applying the Hardy Weinberg Formula

A population of rabbits has two alleles for color. The dominant allele (B) codes for dark fur and the recessive allele (b) codes for white fur. If the allelic frequency of the dominant allele is 0.45 and the allelic frequency of the recessive allele is 0.55, what is the percentage of heterozygous individuals in the population?

### Step 1: Find p and q

The first step in any Hardy Weinberg problem is to find the values for p and q. In this problem, the values are provided and p = 0.45, while q = 0.55.

### Step 2: Choose the Correct Part of the Hardy Weinberg Equation

Next, we need to figure out what the problem is asking for and find the corresponding part of the Hardy Weinberg equation. Here, they ask for heterozygous individuals, so we're going to use 2pq.

### Step 3: Solve

We know that the percentage of heterozygotes is equal to 2pq, where p is the frequency of the dominant allele and q is the frequency of the recessive allele. So, we can plug in our values from the problem as follows:

• 2 * 0.45 * 0.55 = 0.495

Next, we can multiply this frequency by 100 in order to get the percentage that is heterozygous in the population.

• 0.495 * 100 = 49.5%

So, 49.5% of this population is heterozygous.

## Practice Problem 2 - Assessing Population Dynamics

Next, let's consider a problem where they ask you to compare real population data to predicted values from the Hardy Weinberg equilibrium.

Imagine a population of elk. The dominant allele codes for long antlers and the recessive allele codes for short antlers. The frequency of the dominant allele is 0.6 and the frequency of the recessive allele is 0.4. The actual percentage of heterozygotes in the population is 65%. Is this population in equilibrium?

### Step 1: Find p and q

Like the previous problem, p and q are both given. The dominant allele frequency, p, is equal to 0.6 and the recessive allele frequency, q, is equal to 0.4.

### Step 3: Solve

Plug the values given for the dominant allele and the recessive allele into the heterozygote part of the equation:

• 2pq = 2 * 0.6 * 0.4 = 0.48

Next, convert the frequency to a percentage by multiplying by 100.

• 0.48 * 100 = 48%

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