If a bacterial cell contains 5,000 genes and the average mutation frequency per gene is
2 × 10⁻⁴ per generation, what is the average number of new mutations per generation?

This problem tests your grasp of mutation frequency and how individual gene mutation probabilities
scale to the entire genome. Let’s solve it step by step and examine common misconceptions.

Step-by-Step Calculation

Mutation frequency represents the probability that a mutation occurs in a specific gene during
one generation.

• Total number of genes (N): 5,000
• Mutation frequency per gene (f): 2 × 10⁻⁴

Assuming mutations occur independently across genes, the average number of new mutations per
generation is:

Average mutations = N × f

Average mutations = 5000 × (2 × 10−4)

First calculate:

5000 × 2 = 10,000

Then apply the exponent:

10,000 × 10−4 = 1

Correct Answer

The average number of new mutations per generation is: 1

This means that, on average, each bacterial cell accumulates one new mutation somewhere in its
genome every generation.

Explanation of Options and Common Misconceptions

Multiple-choice questions often include misleading distractors. Here’s how typical options arise:

Option A: 0.1

Incorrect. This usually results from dividing instead of multiplying, or
misreading the mutation frequency exponent. It ignores the cumulative effect of thousands of genes.

Option B: 1

Correct.
5000 × 2 × 10−4 = 1

This expected value (λ = 1) implies mutations follow a Poisson distribution, with approximately:

• 37% chance of zero mutations
• 37% chance of exactly one mutation per generation

Option C: 10

Incorrect. Often caused by mishandling powers of ten or using an incorrect mutation
frequency (e.g., 10⁻³). This overestimates mutations by tenfold.

Option D: 1000

Incorrect. Results from ignoring the exponent entirely or confusing gene-based
frequency with base-pair mutation rates. This value is biologically unrealistic.

Other Common Pitfall

Some students answer 0.0002, which is merely the mutation frequency per gene and
fails to account for all 5,000 genes.

Why This Matters in Bacterial Genetics

Bacteria such as Escherichia coli (≈4,600 genes) have genome-wide mutation rates of
approximately 10⁻³ per generation, consistent with this calculation.

Each round of cell division introduces roughly one mutation, providing the raw material for:

• Evolution and natural selection
• Antibiotic resistance
• Adaptation to environmental stress

This concept is essential for understanding microbial evolution, CRISPR experiments,
and population genetics.

Pro Tip for Exams

In population genetics:

• Haploid organisms (bacteria): New mutations per generation = Neμ
• Diploid organisms: New mutations per generation = 2Neμ

This connects mutation rates to genetic diversity parameters such as
θ = 4Neμ.