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

Selection & Evolution (Cambridge AS & A‑Level Biology – Topic 17)

1. Introduction

Selection is the primary evolutionary force that changes the genetic composition of populations over time. It works together with mutation, gene flow, genetic drift and non‑random mating to drive evolution and, ultimately, speciation.

2. Natural Selection

2.1 Definition (three‑step process)

1. Variation: Individuals in a population differ in heritable traits (e.g., colour, size, enzyme efficiency).
2. Differential reproductive success (fitness): Some phenotypes are better suited to the environment and leave more offspring.
3. Inheritance: The advantageous traits are passed to the next generation.

2.2 Classic example – Peppered moth (Biston betularia)

• Two colour morphs: light (typical) and dark (melanic).
• During the Industrial Revolution soot‑covered trees favoured the dark morph; after clean‑air legislation the light morph increased again.
• The change in frequency of the “dark” allele (D) over generations illustrates natural selection in action.

2.3 Linking the steps to “fitness” terminology

In the syllabus “fitness” is defined as the average number of offspring produced by an individual of a given genotype. The second step above therefore directly refers to differential fitness.

3. Artificial Selection

Human‑directed breeding that deliberately changes allele frequencies.

Examples

• Dwarf wheat (Rht genes): Early 20th century breeders selected the dwarfing allele R because it increased yield. Repeated crossing of Rr or RR plants raised the frequency of R from ≈0.1 to >0.9 within a few generations.
• Selective breeding of dogs (e.g., Labrador Retriever): Breeders choose individuals with a preferred coat colour, temperament or size. Over many generations the allele(s) responsible for these traits become much more common.
• Broiler chickens: Selection for rapid growth and large breast muscle has increased alleles that promote muscle development, while reducing alleles associated with slower growth.

4. Other Evolutionary Mechanisms that Disturb Hardy–Weinberg Equilibrium

5. Hardy–Weinberg Principle

5.1 Why it matters

The principle provides a null model for a population that is not evolving. By comparing observed genotype frequencies with the expected Hardy–Weinberg (HW) frequencies, we can infer whether one or more evolutionary forces are acting.

5.2 Core equations (two‑allele locus)

For a diploid, sexually reproducing organism with alleles A and a:

\$p + q = 1\$

\$\$\begin{aligned}

\text{AA: } & p^{2}\\[2pt]

\text{Aa: } & 2pq\\[2pt]

\text{aa: } & q^{2}

\end{aligned}\$\$

5.3 Conditions for Hardy–Weinberg equilibrium

1. Very large (effectively infinite) population – eliminates genetic drift.
2. No migration (gene flow) into or out of the population.
3. No mutation introducing new alleles.
4. Random mating – individuals pair without regard to genotype.
5. No natural or artificial selection – all genotypes have equal reproductive success.
6. Organisms are diploid and sexually reproducing (the wording used in the official syllabus).

Violation of any of these conditions means the population is evolving.

6. Calculating Allele & Genotype Frequencies

Example 1 – Using phenotype data (pea flower colour)

Population: 200 pea plants. Purple (dominant P) vs. white (recessive p).

• Purple (PP or Pp): 170 plants
• White (pp): 30 plants

Step‑by‑step calculation

1. Calculate q from the recessive phenotype:
   

   \$q^{2}= \frac{30}{200}=0.15\quad\Rightarrow\quad q=\sqrt{0.15}\approx0.387\$

2. Find p: \$p = 1 - q = 1 - 0.387 \approx 0.613\$
3. Predict genotype frequencies:
   

   • PP: \$p^{2}=0.613^{2}\approx0.376\$
   • Pp: \$2pq=2(0.613)(0.387)\approx0.474\$
   • pp: \$q^{2}=0.150\$

4. Convert to expected numbers (multiply by 200):
   

   • PP ≈ 0.376 × 200 ≈ 75
   • Pp ≈ 0.474 × 200 ≈ 95
   • pp = 30 (matches observed)

Example 2 – Testing a second generation for evolution (chi‑square test)

Chi‑square calculation (df = 1):

\$\chi^{2}= \sum\frac{(O-E)^{2}}{E}= \frac{(80-75.2)^{2}}{75.2}+ \frac{(90-94.8)^{2}}{94.8}+ \frac{(30-30.0)^{2}}{30.0}=0.31\$

Critical value at the 5 % significance level (df = 1) is 3.84. Because 0.31 < 3.84, we fail to reject the null hypothesis – the population is still in HW equilibrium (no detectable evolution).

7. Selection Coefficients & Relative Fitness

7.1 Definitions

• Relative fitness (w): Reproductive success of a genotype relative to the most successful genotype (set to 1).
• Selection coefficient (s): The reduction in fitness of a genotype compared with the optimum; \$s = 1 - w\$.

7.2 Numerical example

Genotypes AA, Aa and aa have fitness values:

\$w{AA}=1.00,\qquad w{Aa}=0.90,\qquad w_{aa}=0.80\$

Initial allele frequencies: \$p=0.6\$, \$q=0.4\$.

Genotype frequencies before selection:

\$\$\begin{aligned}

AA &: p^{2}=0.36\\

Aa &: 2pq=0.48\\

aa &: q^{2}=0.16

\end{aligned}\$\$

After selection (multiply by \$w\$):

\$\$\begin{aligned}

AA' &: 0.36\times1.00 = 0.36\\

Aa' &: 0.48\times0.90 = 0.432\\

aa' &: 0.16\times0.80 = 0.128

\end{aligned}\$\$

Normalise (total = 0.92):

\$\$\begin{aligned}

AA'' &= \frac{0.36}{0.92}=0.391\\

Aa'' &= \frac{0.432}{0.92}=0.470\\

aa'' &= \frac{0.128}{0.92}=0.139

\end{aligned}\$\$

New allele frequencies:

\$p' = AA'' + \tfrac{1}{2}Aa'' = 0.391 + 0.235 = 0.626\$

\$q' = 1 - p' = 0.374\$

Thus, selection against the recessive genotype (aa) increases the frequency of allele A from 0.60 to 0.63 in a single generation.

Use in population‑genetics models: The values of w and s are inserted into recurrence equations (e.g., \$p' = \frac{p^{2}w{AA}+pq w{Aa}}{\bar w}\$) to predict allele‑frequency change over many generations.

8. From Selection to Speciation

8.1 Adaptive radiation (sympatric pathway)

Darwin’s finches on the Galápagos Islands colonised different ecological niches. Divergent selection on beak size and shape produced distinct feeding strategies, eventually leading to reproductive isolation and the formation of separate species.

8.2 Allopatric speciation (geographic isolation)

When a population is split by a physical barrier (e.g., a mountain range or a newly formed river), each sub‑population evolves independently. Genetic drift, mutation and local selection can cause the two groups to accumulate incompatibilities, so that if they later come into contact they can no longer interbreed.

8.3 Suggested diagram

Flowchart: Variation → Differential fitness → Inheritance → Change in allele frequencies → (a) Adaptive radiation → Reproductive isolation → Speciation; (b) Geographic isolation → Independent evolution → Reproductive isolation → Speciation.

9. Links to Other Syllabus Topics

• Topic 6 – Inheritance: HW provides the quantitative basis for Mendelian ratios and for calculating carrier frequencies.
• Topic 12 – Genetic technology: Molecular markers (e.g., PCR‑based SNP detection) are used to measure allele frequencies in natural populations.
• Topic 13 – Biodiversity: Understanding how selection shapes genetic diversity helps explain patterns of species richness.
• Topic 15 – Ecology: Habitat change alters selective pressures, feeding back into the evolutionary process.

10. Summary – Key Points to Remember

• Natural selection = variation → differential fitness → inheritance.
• Artificial selection is human‑directed and can act across kingdoms (plants & animals).
• Hardy–Weinberg equilibrium requires five conditions plus that the organisms are diploid and sexually reproducing.
• Allele frequencies (p, q) are calculated from genotype or phenotype data; genotype frequencies are \$p^{2}\$, \$2pq\$, \$q^{2}\$.
• Chi‑square test: compare observed and expected numbers; reject HW if \$\chi^{2} > 3.84\$ (df = 1, 5 % significance).
• Relative fitness (w) and selection coefficient (s) quantify how strongly a genotype is favoured or disfavoured and are used in predictive population‑genetics models.
• Continued selection can lead to reproductive isolation via adaptive radiation (sympatric) or geographic separation (allopatric), ultimately producing new species.