explain how selection, the founder effect and genetic drift, including the bottleneck effect, may affect allele frequencies in populations

Cambridge IGCSE/A‑Level Biology – Selection, Founder Effect & Genetic Drift

Learning Objective

Explain how natural selection, artificial selection, the founder effect and genetic drift (including the bottleneck effect) may affect allele frequencies in populations.

Context Box – Where This Unit Fits in the Syllabus

This topic (Topic 17 – Selection & Evolution) is a gateway to the A‑Level extensions (Topics 12‑19) and builds on several earlier units.

What you’ll need later (A‑Level extensions): concepts of homeostasis, control, classification, and genetic technology all rely on an understanding of how allele frequencies can change.

1. Core Genetic Concepts

• Allele frequency (p, q): proportion of a particular allele among all alleles at a locus. For a bi‑allelic gene, p + q = 1.
• Hardy–Weinberg equilibrium (HW): In a large, randomly mating population with no evolutionary forces (no mutation, migration, selection, drift), genotype frequencies remain constant:

  • AA = p², Aa = 2pq, aa = q²
  • These frequencies are the reference point for detecting evolutionary change.

• Effective population size (Nₑ): the number of breeding individuals that contribute genes to the next generation. Nₑ often differs from the census size (N) because of:

  • Unequal sex ratios (e.g., 1 male : 10 females)
  • Variation in reproductive success (some individuals have many offspring, others none)
  • Fluctuating population size over time

2. Natural Selection

Deterministic, non‑random force that changes allele frequencies because some genotypes have higher fitness.

2.1. The V‑D‑I Process

1. Variation: Genetic differences exist (e.g., allele A vs a).
2. Differential survival/reproduction: Fitness (w) differs among genotypes. Example: w_AA > w_Aa > w_aa.
3. Inheritance: Offspring receive the advantageous alleles.

2.2. Quantitative Description

The change in allele frequency caused by selection is:

\[

\Delta p = \frac{p q \, (wA - wa)}{\bar w}

\]

• w_A and w_a are the average fitnesses of alleles A and a (weighted by genotype frequencies).
• \(\bar w\) is the mean fitness of the whole population:

  \[

  \bar w = p^{2}w{AA}+2pq\,w{Aa}+q^{2}w_{aa}

  \]

2.3. Worked Numerical Example (AO2)

Suppose a population has:

• Initial allele frequency: p = 0.4 (so q = 0.6)
• Fitness values: w_AA = 1.1, w_Aa = 1.0, w_aa = 0.9

Step‑by‑step:

1. Calculate genotype frequencies (HW):

   • AA = p² = 0.16
   • Aa = 2pq = 0.48
   • aa = q² = 0.36

2. Mean fitness:

   \[

   \bar w = (0.16)(1.1)+(0.48)(1.0)+(0.36)(0.9)=0.176+0.48+0.324=0.98

   \]

3. Average fitness of each allele:

   \[

   wA = \frac{(p^{2})w{AA}+pq\,w_{Aa}}{p}= \frac{0.16(1.1)+0.24(1.0)}{0.4}= \frac{0.176+0.24}{0.4}=1.09

   \]

   \[

   wa = \frac{(q^{2})w{aa}+pq\,w_{Aa}}{q}= \frac{0.36(0.9)+0.24(1.0)}{0.6}= \frac{0.324+0.24}{0.6}=0.94

   \]

4. Change in allele frequency:

   \[

   \Delta p = \frac{(0.4)(0.6)(1.09-0.94)}{0.98}= \frac{0.24(0.15)}{0.98}=0.0367

   \]

5. New allele frequency after one generation:

   \[

   p' = p + \Delta p = 0.4 + 0.0367 \approx 0.44

   \]

This shows a modest increase in the favoured allele A due to directional selection.

2.4. Types of Selection (with examples)

3. Artificial Selection

Human‑directed selection that mimics natural selection but with intentional choice of breeding individuals.

• Often imposes strong, directional pressure.
• Can rapidly increase the frequency of a target allele, sometimes to fixation (p = 1).
• May reduce overall genetic diversity if only a few individuals contribute to the next generation (e.g., pedigree dogs).
• Example: Selection for high milk yield in dairy cattle.

4. Genetic Drift

Random (stochastic) change in allele frequencies caused by sampling error in finite populations.

4.1. Key Features

• Most pronounced in small populations (low Nₑ).
• Probability that a neutral allele becomes fixed equals its current frequency (p).
• Expected change per generation is zero, but the variance is:

  \[

  \text{Var}(\Delta p)=\frac{p q}{2Nₑ}

  \]

4.2. Modelling Drift

When a population of size N reproduces, the number of copies of allele A in the next generation follows a binomial distribution:

\[

p' \;\sim\; \frac{1}{2N}\,\text{Binomial}(2N,\,p)

\]

4.3. Graph‑Building Tip (AO2)

To visualise drift, plot allele frequency (p) on the y‑axis against generation number on the x‑axis. Using a spreadsheet, apply the binomial sampling step repeatedly (e.g., 100 generations) and connect the points. Each run will give a different trajectory, illustrating the unpredictability of drift.

5. Founder Effect

A special case of drift that occurs when a new population is established by a small number of individuals taken from a larger source population.

• Allele frequencies in the new population can differ markedly from the source because only the founders’ genes are represented.
• Rare alleles in the original population may become common (or fixed) in the founder population, and vice‑versa.
• Usually leads to reduced genetic variation and can increase the incidence of recessive genetic disorders.
• Example: High prevalence of Ellis‑van Crest disease in the Amish community.

Factors that Intensify the Founder Effect

• Very small founding size (e.g., ≤ 10 individuals).
• Geographic or cultural isolation that prevents gene flow from the source.

6. Bottleneck Effect

A sharp, temporary reduction in population size caused by an environmental or anthropogenic event.

• Survivors constitute a random sample of the original gene pool, so allele frequencies may shift dramatically.
• Rare alleles are especially vulnerable to loss.
• After the population expands, the new gene pool reflects the post‑bottleneck frequencies.
• Example: Cheetah populations after the Pleistocene megafaunal extinction show extremely low heterozygosity.

Typical Sequence

1. Large population (genetically diverse).
2. Sudden reduction to a small size (bottleneck).
3. Random sampling of alleles among survivors → altered frequencies.
4. Population rebounds; lost alleles are rarely recovered.

7. Other Evolutionary Forces (Brief Mention – Syllabus Expectation)

• Mutation: introduces new alleles; the only source of genetic novelty.
• Migration (gene flow): movement of individuals (or gametes) between populations; tends to homogenise allele frequencies.
• Both mutation and migration can act simultaneously with selection or drift, but they are not the focus of this note.

8. Linkage & Genetic Hitch‑hiking (A‑Level Extension)

When a favourable allele is linked to a nearby neutral allele, the neutral allele can increase in frequency simply because it “rides” with the selected allele. This is called genetic hitch‑hiking and is an important concept when interpreting patterns of genetic variation around selected loci.

9. Comparison of Selection vs. Drift (including Founder & Bottleneck)

10. Quick‑Check Box – HW Assumptions Violated by Each Evolutionary Force

11. How Evolutionary Forces Alter Allele Frequencies – Step‑by‑Step Procedure

1. Start with a population in HW equilibrium: p² + 2pq + q² = 1.
2. Apply the evolutionary force:

   • Selection: calculate <(\(\bar w\))> and use the selection equation to obtain the new allele frequency p'.
   • Drift: sample 2Nₑ alleles at random; the resulting p' follows a binomial distribution B(2Nₑ, p).
   • Founder/Bottleneck: treat the reduced population as a new Nₑ and apply drift during the founding or recovery phase.

3. Iterate over successive generations to observe trajectories toward:

   • Fixation (p = 1 or p = 0)
   • Stable polymorphism (balance of selection and drift)
   • Loss of genetic variation (especially after bottlenecks)

12. Quick Reference – Key Equations & Definitions

• Allele‑frequency change by selection: \(\displaystyle \Delta p = \frac{p q (wA - wa)}{\bar w}\)
• Mean fitness: \(\displaystyle \bar w = p^{2} w{AA} + 2pq\, w{Aa} + q^{2} w_{aa}\)
• Variance of drift: \(\displaystyle \text{Var}(\Delta p) = \frac{p q}{2Nₑ}\)
• Probability of fixation (neutral allele): \(\displaystyle P_{\text{fix}} = p\)
• Effective population size (Nₑ): size of an idealised population that would lose heterozygosity at the same rate as the actual population.
• Mutation: introduces new alleles at rate μ per generation.
• Migration (gene flow): changes allele frequencies by proportion m of migrants each generation.

13. Summary

Allele frequencies are dynamic. Deterministic forces such as natural and artificial selection drive adaptive change by preferentially increasing the frequency of beneficial alleles. Stochastic forces—genetic drift, the founder effect, and bottleneck events—randomly alter frequencies, especially in small or newly established populations, often reducing overall genetic variation. Recognising how these mechanisms operate, and being able to quantify their effects, is essential for interpreting evolutionary patterns, managing breeding programmes, and evaluating conservation strategies.