Genetic Variation and Hardy-Weinberg Equilibrium

I. Genetic Variation

Genetic variation refers to the differences in DNA sequences among individuals within a population. It is essential for evolution because it provides the raw material on which natural selection can act.

A. Sources of Genetic Variation

1. Mutations (random changes in DNA):

   • Can occur in somatic cells (not passed to offspring) or germ-line cells (heritable).

   • Types of mutations:

     • Neutral mutations: Have no significant effect.

     • Deleterious mutations: Harmful and reduce survival/reproduction.

     • Beneficial mutations: Provide an advantage and may increase in frequency over generations.

   • Example:

     • A mutation in the CCR5 gene provides resistance to HIV by preventing the virus from entering cells.

2. Recombination (during meiosis):

   • Crossing over in meiosis shuffles alleles, creating new allele combinations.

   • Leads to increased genetic diversity.

3. Gene Pool:

   • The total collection of alleles in a population.

   • Populations (not individuals) evolve through changes in the gene pool.

II. Measuring Genetic Variation

To quantify genetic variation, we examine allele and genotype frequencies.

A. Allele Frequency

The proportion of a specific allele within a population.

Allele frequency=Number of copies of an allele in the populationTotal number of alleles in the population\text{Allele frequency} = \frac{\text{Number of copies of an allele in the population}}{\text{Total number of alleles in the population}}Allele frequency=Total number of alleles in the populationNumber of copies of an allele in the population​

Example:

• Suppose a population has 100 individuals (diploid, so 200 total alleles).

• If there are 50 dominant A alleles, the allele frequency of A is: f(A)=50/200=0.25%

B. Genotype Frequency

The proportion of individuals in the population with a specific genotype.

Genotype frequency=Number of individuals with a genotypeTotal individuals in the population\text{Genotype frequency} = \frac{\text{Number of individuals with a genotype}}{\text{Total individuals in the population}}Genotype frequency=Total individuals in the populationNumber of individuals with a genotype​

Example:

• If 5 individuals are heterozygous (Aa) in a population of 100, 5/100= 0.05

III. Hardy-Weinberg Equilibrium (HWE)

A. Definition

The Hardy-Weinberg Equilibrium (HWE) describes a population where allele and genotype frequencies remain constant over generations in the absence of evolutionary forces.

HWE serves as a null model to determine whether evolution is occurring.

B. Conditions for Hardy-Weinberg Equilibrium

For a population to be in Hardy-Weinberg Equilibrium, five conditions must be met:

1. No natural selection – All individuals must have equal reproductive success.

2. No gene flow (migration) – No movement of alleles into or out of the population.

3. No mutations – The gene pool remains unchanged.

4. Large population size – Reduces genetic drift (random allele frequency changes).

5. Random mating – No preference for mates based on genotype.

If any of these conditions are violated, evolution is occurring.

C. Hardy-Weinberg Equations

1. Allele Frequency Equation:

   p+q=1p + q = 1p+q=1

   • p² = frequency of the dominant allele (A)

   • q² = frequency of the recessive allele (a)

2. Genotype Frequency Equation:

   p²+2pq+q²=1

   Where:

   • p²= frequency of homozygous dominant (AA)

   • 2pq = frequency of heterozygous (Aa)

   • q²= frequency of homozygous recessive (aa)

D. Applying Hardy-Weinberg Equilibrium

Step-by-Step Example: Eye Color in a Population

Problem:

• In a population of 30 students, 6 have blue eyes (bb, recessive trait).

• Calculate the allele and genotype frequencies.

Step 1: Find q² (homozygous recessive frequency)

q²=6/30=.20

Step 2: Find q (recessive allele frequency)

Squareroot .20 =.45

Step 3: Find p (dominant allele frequency)

1-.45 + .55, p= .55

Step 4: Find Genotype Frequencies

• Homozygous dominant (AA): p²= (0.55)² = 0.3025

• Heterozygous (Aa): 2pq = 2(0.55)(0.45) = 0.495

• Homozygous recessive (bb): q²=(0.25²)=.200

Thus, 30.25% of the population has brown eyes (AA), 49.5% are carriers (Aa), and 20% have blue eyes (bb).

E. Using Hardy-Weinberg to Detect Evolution

If allele or genotype frequencies change over time, it means one of the Hardy-Weinberg conditions has been violated and evolution is occurring.

Example:
If migration introduces new alleles, or natural selection favors a specific genotype, the population will not be in Hardy-Weinberg equilibrium.

IV. Key Takeaways

• Genetic variation arises from mutations and recombination.

• Populations evolve, not individuals.

• Hardy-Weinberg Equilibrium describes a non-evolving population.

• If allele/genotype frequencies change, evolution is happening.

• HWE provides a mathematical framework to test if evolution is occurring.