use the Hardy–Weinberg principle to calculate allele and genotype frequencies in populations and state the conditions when this principle can be applied (the two equations for the Hardy–Weinberg principle will be provided, as shown in the Mathematica

Natural and Artificial Selection

Selection is the process by which certain genotypes become more common in a population because they confer a reproductive advantage. It can be divided into two main types:

• Natural selection – the environment “selects” individuals with traits that improve survival and reproduction.
• Artificial selection – humans deliberately breed individuals with desirable traits.

Key Concepts

1. Variation exists within populations (genetic and phenotypic).
2. Some variations affect fitness (the ability to survive and reproduce).
3. Individuals with higher fitness leave more offspring, changing allele frequencies over generations.

Hardy–Weinberg Principle

The Hardy–Weinberg principle provides a mathematical model for a population that is not evolving. It allows us to calculate expected allele and genotype frequencies and to test whether a real population is evolving.

For a gene with two alleles, A and a, let:

• \$p\$ = frequency of allele A
• \$q\$ = frequency of allele a
• \$p + q = 1\$

The expected genotype frequencies are:

\$\$

\begin{aligned}

\text{Frequency of } AA &= p^{2} \\

\text{Frequency of } Aa &= 2pq \\

\text{Frequency of } aa &= q^{2}

\end{aligned}

\$\$

These equations are often written together as the Hardy–Weinberg equation:

\$\$

p^{2} + 2pq + q^{2} = 1

\$\$

Calculating Allele and Genotype Frequencies

Example problem:

1. In a population of 200 beetles, 72 are homozygous dominant (AA), 96 are heterozygous (Aa), and 32 are homozygous recessive (aa).
2. Calculate \$p\$, \$q\$, and the expected genotype frequencies.

Solution:

Calculate allele frequencies:

\$\$

p = \frac{2(AA) + (Aa)}{2N}

= \frac{2(72) + 96}{2(200)}

= \frac{240}{400}

= 0.60

\$\$

\$\$

q = 1 - p = 0.40

\$\$

Expected genotype frequencies under Hardy–Weinberg equilibrium:

\$\$

\begin{aligned}

AA &: p^{2} = (0.60)^{2} = 0.36 \\

Aa &: 2pq = 2(0.60)(0.40) = 0.48 \\

aa &: q^{2} = (0.40)^{2} = 0.16

\end{aligned}

\$\$

Since the observed frequencies match the expected frequencies, the population is currently in Hardy–Weinberg equilibrium.

Conditions for Hardy–Weinberg Equilibrium

The principle applies only when the following five conditions are met (no evolutionary forces acting):

• Large population size – minimizes random genetic drift.
• No mutation – allele identities remain unchanged.
• No migration (gene flow) – no new alleles are introduced or lost.
• Random mating – individuals pair without regard to genotype.
• No natural or artificial selection – all genotypes have equal reproductive success.

If any of these conditions are violated, allele frequencies are expected to change over time, indicating that evolution is occurring.

Linking Selection to Hardy–Weinberg

When selection is present, the genotype frequencies deviate from the \$p^{2} : 2pq : q^{2}\$ ratios. By comparing observed frequencies with expected Hardy–Weinberg frequencies, we can infer the type and strength of selection.

For example, if the heterozygote (Aa) has higher fitness than either homozygote (over‑dominance), the observed frequency of Aa will be greater than \$2pq\$, indicating balancing selection.

Summary

• Natural and artificial selection change allele frequencies by favouring certain genotypes.
• The Hardy–Weinberg principle provides a null model for a non‑evolving population.
• Calculating \$p\$, \$q\$, and genotype frequencies allows us to test whether a population is evolving.
• All five Hardy–Weinberg conditions must be satisfied for the equations to be applicable.