Population Genetics & the Hardy-Weinberg Principle Revision Notes for AQA A-Level Biology

Population Genetics & the Hardy-Weinberg Principle

Understanding populations and gene pools

When studying genetics, we often need to look beyond individual crosses and examine entire populations. This allows us to understand how genetic traits are distributed and maintained across groups of organisms.

A species is defined as a group of similar organisms that can reproduce together to produce fertile offspring. Within a species, a population refers to a group of organisms of the same species living in a particular area at a particular time, where they have the potential to interbreed.

The gene pool represents the complete range of alleles present in a population. When we want to measure how common a particular allele is within a population, we calculate the allele frequency - this tells us how often that allele occurs and is usually expressed as a percentage of the total population or as a decimal number.

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Population-level genetic studies are essential for understanding how traits are maintained and evolve over time. Unlike individual crosses that show inheritance patterns between specific parents and offspring, population genetics reveals the broader patterns of genetic variation across entire groups of organisms.

The Hardy-Weinberg principle

The Hardy-Weinberg principle is a mathematical model that makes predictions about allele frequencies in populations. It states that the frequencies of alleles in a population will remain constant from one generation to the next, provided certain conditions are met.

However, this principle only applies under very specific conditions:

Large population size
No immigration or emigration
No mutations occurring
No natural selection taking place
Random mating between all possible genotypes

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When these conditions are not met, allele frequencies will change between generations, indicating that evolutionary forces are acting on the population. In reality, these ideal conditions are rarely found in natural populations, which is why evolution occurs.

Hardy-Weinberg equations

The Hardy-Weinberg principle uses two key equations to calculate frequencies within populations.

Allele frequency equation

For a gene with two alleles, the relationship between their frequencies is:

$p + q = 1$

Where:

$p$ = frequency of one allele (usually the dominant one)
$q$ = frequency of the other allele (usually the recessive one)

The total frequency of all possible alleles for a characteristic must equal 1.0, so if you know the frequency of one allele, you can calculate the frequency of the other by rearranging: $q = 1 - p$ .

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Worked Example: Calculating Allele Frequencies

If red flowers (R) are dominant and white flowers (r) are recessive, and the frequency of R is 0.4, then:

Step 1: Use the equation $p + q = 1$

$p$ (frequency of R) = 0.4
$q$ (frequency of r) = $1 - 0.4 = 0.6$

Therefore, the frequency of r must be 0.6.

Genotype frequency equation

To predict the frequencies of different genotypes in a population, we use:

$p^2 + 2pq + q^2 = 1$

Where:

$p^2$ = frequency of the homozygous dominant genotype
$2pq$ = frequency of the heterozygous genotype
$q^2$ = frequency of the homozygous recessive genotype

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Worked Example: Calculating Genotype Frequencies

Using our flower colour example, if there are two alleles (R and r) with frequencies of 0.4 and 0.6 respectively:

Step 1: Calculate homozygous dominant frequency

RR (homozygous dominant): $p^2 = 0.4^2 = 0.16$

Step 2: Calculate heterozygous frequency

Rr (heterozygous): $2pq = 2 × 0.4 × 0.6 = 0.48$

Step 3: Calculate homozygous recessive frequency

rr (homozygous recessive): $q^2 = 0.6^2 = 0.36$

Check: $0.16 + 0.48 + 0.36 = 1.00$ ✓

Applications of Hardy-Weinberg calculations

The Hardy-Weinberg equations have practical applications in understanding real-world genetic scenarios and detecting evolutionary changes in populations.

Predicting carrier frequencies

The Hardy-Weinberg equations are particularly useful for calculating the frequency of carriers for recessive genetic conditions.

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Worked Example: Cystic Fibrosis Carrier Frequency

Cystic fibrosis occurs in approximately 1 in every 2500 births in the UK.

Step 1: Calculate q (recessive allele frequency)

Frequency of cystic fibrosis (ff genotype) = $\frac{1}{2500} = 0.0004$
Since $q^2 = 0.0004$ , then $q = \sqrt{0.0004} = 0.02$

Step 2: Calculate p (dominant allele frequency)

Using $p + q = 1$ : $p = 1 - 0.02 = 0.98$

Step 3: Calculate carrier frequency

Frequency of carriers (Ff) = $2pq = 2 × 0.98 × 0.02 = 0.039$

Result: Approximately 3.9% of the UK population are carriers of cystic fibrosis.

Detecting evolutionary forces

The Hardy-Weinberg principle can also help identify when evolutionary factors are affecting allele frequencies. If measured allele frequencies change significantly between generations, this suggests that one or more of the Hardy-Weinberg conditions are not being met.

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When allele frequencies change over time, it indicates that evolutionary forces such as natural selection, genetic drift, gene flow, or mutations are influencing the population. This makes Hardy-Weinberg calculations valuable tools for detecting evolution in action.

For example, if cystic fibrosis frequency changed from 1 in 2500 to 1 in 3500 over 50 years, we could calculate that the recessive allele frequency had changed from 0.02 to 0.017. Since Hardy-Weinberg conditions predict no change, this difference indicates that external factors such as immigration, emigration, mutations, or natural selection must be influencing allele frequencies in the population.

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Key Points to Remember:

The Hardy-Weinberg principle predicts that allele frequencies remain constant under specific conditions: large population, no migration, no mutations, no natural selection, and random mating
Use $p + q = 1$ to calculate allele frequencies when one frequency is known
Use $p^2 + 2pq + q^2 = 1$ to predict genotype frequencies from allele frequencies
Hardy-Weinberg calculations are particularly useful for determining carrier frequencies of recessive genetic conditions
Changes in allele frequencies between generations indicate that evolutionary forces are acting on the population

Population Genetics & the Hardy-Weinberg Principle (AQA A-Level Biology): Revision Notes