Hardy-Weinberg Principle: A Complete Guide

Lesson Overview

• What Is the Hardy-Weinberg Principle?
• The Hardy-Weinberg Equation
• Example 1: Hair Length in Mice
• Example 2: Flower Color in Snapdragons
• Example 3: Earlobes in Humans
• Breakdown
• Solving Hardy-Weinberg Problems: Step-by-Step
• Common Mistakes to Avoid
• Quick Practice: Concept Check
• Key Takeaway

Imagine a population where traits remain unchanged through generations - no matter how many offspring are born, the genetic makeup stays the same. While this is unlikely in real life, it forms the foundation of the Hardy-Weinberg Principle, a core idea in population genetics.

If the actual genetic makeup of a population does not match the Hardy-Weinberg predictions, something - like natural selection or mutation - is changing the population. For students, mastering this principle is essential in understanding how traits pass through generations and how populations evolve.

What Is the Hardy-Weinberg Principle?

The Hardy-Weinberg Principle states that allele and genotype frequencies in a large, randomly mating population remain constant across generations - unless affected by evolutionary forces. In this "equilibrium state," evolution is not occurring.

Assumptions of Hardy-Weinberg Equilibrium

For a population to stay in Hardy-Weinberg equilibrium, the following five conditions must be met:

Memory trick: "Large Random M and M No's" - Large population, Random mating, No mutation, No migration, No selection.

The Hardy-Weinberg Equation

There are two key equations in the Hardy-Weinberg model:

1. Allele frequency equation:
   p plus q equals 1
   • p represents the frequency of the dominant allele
   • q represents the frequency of the recessive allele

1. Genotype frequency equation:
   p squared plus 2pq plus q squared equals 1
   • p squared is the frequency of the homozygous dominant genotype
   • 2pq is the frequency of heterozygotes
   • q squared is the frequency of the homozygous recessive genotype

These equations allow us to calculate how common different genotypes and alleles are in a population - assuming equilibrium conditions are met.

Example 1: Hair Length in Mice

Given:

• Long hair is recessive (allele h), short hair is dominant (allele H).
• In a population of 100 mice, 9 mice have long hair.

Step 1: Start with q squared
Because long hair is recessive, only mice with genotype hh show the trait. So q squared equals 9 divided by 100, which is 0.09.

Step 2: Find q and p
Take the square root of 0.09 to get q. So, q equals 0.3.
Then, p equals 1 minus 0.3, which is 0.7.

Step 3: Find genotype frequencies

• p squared (HH) equals 0.49
• 2pq (Hh) equals 2 times 0.7 times 0.3, which is 0.42
• q squared (hh) equals 0.09

Step 4: Apply these to the population
Out of 100 mice:

• 49 mice have genotype HH (short hair)
• 42 mice have genotype Hh (short hair)
• 9 mice have genotype hh (long hair)

Answering questions:

• How many mice have short hair? Add HH and Hh: 49 plus 42 equals 91.
• What is the frequency of the h allele? q equals 0.3 or 30 percent.

Hair Length Breakdown

Example 2: Flower Color in Snapdragons

In snapdragons, flower color shows incomplete dominance. That means:

• RR = red
• Rr = pink
• rr = white

Given:

• 81 percent of flowers are red (RR)

Step 1: Identify p squared
Red flowers are RR. So, p squared equals 0.81.
p equals the square root of 0.81, which is 0.9.
Then q equals 1 minus 0.9, or 0.1.

Step 2: Calculate genotype frequencies

• p squared (RR) = 0.81
• 2pq (Rr) = 2 times 0.9 times 0.1 = 0.18
• q squared (rr) = 0.01

Answers to possible quiz questions:

• Red flowers: 81 percent
• Pink flowers (heterozygotes): 18 percent
• White flowers: 1 percent
• Frequency of white allele (r): 0.1 or 10 percent

Example 3: Earlobes in Humans

Free earlobes (allele E) are dominant; attached earlobes (allele e) are recessive.

Given:

• 64 percent of people have free earlobes.

So, 36 percent must have attached earlobes (recessive trait).
That means q squared equals 0.36
q equals square root of 0.36 = 0.6
Then p equals 1 minus 0.6 = 0.4

Genotype frequencies:

• p squared (EE) = 0.16
• 2pq (Ee) = 2 times 0.4 times 0.6 = 0.48
• q squared (ee) = 0.36

Summary:

• Recessive allele frequency (e) = 60 percent
• Dominant allele frequency (E) = 40 percent
• Percentage with attached earlobes = 36 percent
• Percentage with free earlobes = 64 percent
• Carriers (Ee) = 48 percent

Take This Quiz:

Breakdown

Solving Hardy-Weinberg Problems: Step-by-Step

1. Start with known genotype or phenotype data.
   If you know the percentage of a recessive trait in the population, that gives you q squared.
   
2. Find allele frequencies.
   Take the square root of q squared to get q. Then use p equals 1 minus q.
   
3. Calculate genotype frequencies.
   • p squared = frequency of homozygous dominant
   • 2pq = frequency of heterozygotes
   • q squared = frequency of homozygous recessive
     
4. Check your math.
   All genotype frequencies should add to 1 (or 100 percent).
   
5. Apply to population size.
   Multiply each frequency by the total number of individuals to get counts.

Common Mistakes to Avoid

Quick Practice: Concept Check

1. If 4 percent of the population has a recessive trait, what is the carrier frequency?
   • q squared = 0.04
   • q = 0.2, p = 0.8
   • 2pq = 2 times 0.8 times 0.2 = 0.32 → 32 percent of population are carriers
     
2. Cystic fibrosis affects 1 in 2,500 people. What percent are carriers?
   • q squared = 1 divided by 2500 = 0.0004
   • q = 0.02, p = 0.98
   • 2pq = 2 times 0.98 times 0.02 = 0.0392 → 3.92 percent are carriers
     
3. True or False: Heterozygotes are always less frequent than homozygotes.
   • False. When p and q are both 0.5, heterozygotes are most frequent (50 percent)

Key Takeaway

The Hardy-Weinberg Principle allows scientists to track genetic stability in a population. If a population meets the five conditions, the gene pool stays the same over time.

Key formulas to remember:

• p plus q = 1
• p squared plus 2pq plus q squared = 1

Key assumptions to know:

• No mutation
• No migration
• Large population
• Random mating
• No selection

Use Hardy-Weinberg to:

• Calculate allele and genotype frequencies
• Determine carrier frequencies
• Detect whether a population is evolving

By practicing examples and avoiding common pitfalls, students can confidently apply this principle to real-world problems in genetics and population biology.

Take This Quiz: